This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. math exams: 2011

## Sunday, November 27, 2011

### Question FM 11/27/2011 11:25

To accumulate 4000 at the end of 3n years, deposits of 49 are made at the end of each of the first n years and 98 at the end of each the next 2n years. The annual effective rate of interest is i. You are given $(1+i)^{n}=2$.
Determine i.

Ans: $i=0.1225$

### Question FM 11/27/2011 10:47

Lea deposits 100 into an account at the beginning of each 3-year period for 30 years. The account credits interest at an annual effective interest rate of i.
The accumulated amount in the account at the end of 30 years is X, which is 5 times the accumulated amount in the account at the end of 15 years.
Calculate X.

Ans: 6,194.72

### Question FM 11/27/2011 10:34

An annuity pays 1 at the end of each year for 20 years. Using an annual effective interest rate of i, the accumulated value of the annuity at time 2n+1 is 12.967. It is also known that $(1+i)^{n}=2.351$.
Calculate n.

Ans: $n=\frac{\ln(2.351)}{\ln(1.53641)}$

### Question FM 11/27/2011 10:26

An annuity pays 100 at the end of each of the next 10 years and 200 at the end of each of the next 10 years following. If 1=0.08, find the present value of the annuity.

Ans : $100[a_{\bar{20}}+a_{\bar{10}}\nu^{10}]$

## Saturday, November 26, 2011

### Question FM 11/21/2011 11:12

Find the force of interest at which $\bar{s}_{\bar{20}}=4\bar{s}_{\bar{10}}$.

Ans: $\delta=\frac{ln(3)}{10}$.

A student wishes to accumulate $\$100,000$in education fund at the end of 20 years. If he deposit$\$1000+X$ in the fund at the end of each of the first 10 years and $\$1000+2X$in the fund of each of the second 10 years, find X if the fund earns$6\%$effective per year. Ans:$\frac{100,000-1000s_{\bar{20}}}{s_{\bar{20}}+s_{\bar{10}}}$## Monday, November 21, 2011 ### Question FM 11/21/2011 03:52 Determine the accumulated value at time 10 years of payments that are received continuously over each year. The payment is$\$105$ during the first year, $\$110$during the second year,$\$115$ during the third year, and so on, up to the last payment of $\$150$in year 10. The annual effective interest rate is$6\%$. Ans :$100\bar{s}_{\bar{10}}+5(\bar{Is})_{\bar{10}}$### Question FM 11/21/2011 03:19 You invest$\$300$ at time 8 years, $\$600$at time 9 years,$\$900$ at time 10 years, and so on, up to the last payment at time 20 years. What is the accumulated value of these payments at time 31 years using an annual effective rate of interest of $3\%$.

Ans: $300(Ia)_{\bar{13}}(1.03)^{24}$

### Question FM 11/21/2011 02:56

You invest X now, the bank will give you 13000 at the time 7 years, 12000 at time 8 years, 110000 at time 9 years, and so on, with the last payment being at time 14 years, using an annual effective rate of interest of $8\%$, determine X.

Ans: $X=500a_{\bar{8}}+1000(Da)_{\bar{8}}$

### Question FM 11/21/2011 02:22

Lina receives $\$200$in 1 year,$\$250$ in 2 years, $\$300$in 3 years, and so on until the final payment of$\$700$. Using an annual effective rate of interest of $4\%$. Find the present value of these payments at time 0.

Ans:$50.(Ia)_{\bar{11}}+150.a_{\bar{11}}$

## Sunday, November 20, 2011

Calculate the present value at t=0 of a continuous payment stream made at the constant rate of $\rho_{t}=\$6$per year from time 3 to time 6 years. The force of interest is given by$\delta_{t}=0.04$Ans:$150[e^{-0.24}+e^{-0.12}]$### Question FM 11/20/2011 04:53 Calculate the present value at t=0 of a continuous payment stream made at the constant rate of$\rho_{t}=\$10$ per year from time 0 to time 20 years. The force of interest is given by $\delta_{t}=0.05$

Ans: $\frac{10}{0.05}[1-e^{-1}]$

## Saturday, November 19, 2011

### Question FM 11/19/2011 08:36

John receives payments at the start of each of the next 10 years. The first payment is 1000, which is paid now.
The payments from then on increase at a rate effective rate of $15\%$ each year.
Using an annual effective rate on interest of $23.05\%$, find the present value of these payments at time 0.

Ans: $1000.\frac{1-(1.07)^{-10}}{\frac{0.07}{1.07}}$

## Monday, November 14, 2011

### Question FM 11/14/2011 10:16

A bank makes payments continuously at a rate of 100 per year. The payments are made between 3 and 13 years. Find the accumulated value of these payments at time 20 years using an annual interest rate of $7\%$.

Ans: $100\frac{(1.07)^{10}-1}{ln(1.07).(1.07)^{7}}$

### Question FM 11/14/2011 11:33

Determine the present value of payments of $\%10$ to be made at the beginning of each year, starting now. The payments continue forever. The annual effective interest rate is $6\%$.

## Sunday, November 13, 2011

### Question FM 11/13/2011 9:43

Show that the ratio of the accumulated value of $\$1$invested ta rate i for n periods, to the accumulated value of$\$1$ invested at rate j for n periods, is equal to the accumulated value of 1 invested for mn periods at rate r. Find an expression for r at as a function of i,j and m.

Ans:$(\frac{1+i}{1+j})^{\frac{1}{m}}-1$

### Question FM 11/13/2011 9:32

It is known that 800 invested for two years will earn 100 in interest.
Find the accumulated value of 1000 invested at the same rate of compound interest for three years.

Ans: 1193.24

### Question FM 11/13/2011 9:16

a) Show that $d^{(m)}=i^{(m)}\nu^{\frac{1}{m}}$
b) Verbally interpret the result in a)

### Question FM 11/13/2011 9:02

Show that $m=\frac{d^{(m)}i^{(m)}}{i^{(m)}-d^{(m)}}$

Ans: 4848.31

### Question FM 11/11/2011 2:06

An investor makes four deposits into account, at end of 2, 6, 9, and 11 years. The amount of the deposits at time t is $300(1.025)^{t}$. Find the size of the account at the end of 13 years, if the nominal of discount convertible bi-monthly is 6/41.

Ans: 3796.47

### Question FM 11/11/2011 1:56

Find how long $\$100$should be left to accumulate at$8\%$effective in order that it will amount to triple the accumulated value of$\$100$ deposited at the same time at $6\%$ effective.

Ans: 58.8 years

## Thursday, November 10, 2011

### Question FM 11/10/2011 11:50

If $r=\frac{i^{(m)}}{d^{(m)}}$ express $\nu$ in terms of $r$

Ans: $r^{-m}$

### Question FM 11/10/2011 11:30

Suppose :

$1+\frac{i^{(m)}}{m}=\frac{1+\frac{i^{(5)}}{5}}{1+\frac{i^{(6)}}{6}}$

Find m?

Ans : m=30.

## Friday, October 28, 2011

### Options - Binomial Trees

1. A stock price is currently $\$60$. It is known that at the end of three months it will be either$\$63$ or $\$58$. The risk-free rate is$10 \%$per annum with continuous compounding. What is the value of three month European call option with a strik price of$\$59$?

2. A stock price is currently $\$60$. Over each of the next two 4-months periods it is expected to go up by$7\%$or down by$6 \%$per annum with continuous compounding. What is the value of a 8-month European call option with a stick price of$\$61$.

3. A stok price is currently $\$70$.It expected that at the end of 3 months it will be either$\$65$ or $\$75$. The risk-free interest rate is$6\%$per annum with continuous compounding. What is the value of a 3-months European put option with a strike price of$\$70$.

4. A stock price is currently 30. It expected that at the end of 3-months it will be either $\$27$or$\$33$.
The risk-free interest rate is 10 per annum with continuous compounding. Suppose $S_{T}$ is the stock price at the end of 3-months. What the value of
a derivative that pays off $(S_{T})^{3}-3(S_{T})^{2}$

## Saturday, October 15, 2011

### Options

1. Suppose that a party wanted to enter into an FRA that expires in 47 days and is based on 129-day LIBOR.The dealer quotes a rate of 4.65 percent
on this FRA. Assume that at expiration, the 129-day LIBOR is 4 percent and the notional principal is $\$25,000,000$. Calculate the FRA payoff on a long position. 2. Assume Dell expects to receive 30,000,000 Euro in 120 days. A dealer provides a quote of$\$0,885$ for a currency forward contratct to expire in 120 days.
Suppose that at the end of 120 days, the rate is $\$0.92$. If the settlement is in cash. Calculate the cash flow at expiration if Dell enters into a forward contract expiring in 120 days to buy dollars at$\$0.885$
3. Calculate the payoff at expiration for a call option on the S & P 100 stock index in which the underlying price is 755.21 at expiration, the multiplier is 100, and the exercise price is

1. 600
2. 800
4. Calculate the payoff at expiration for a put option on the S & P 100 stock index in which the underlying price is 755.21 at expiration, the multiplier is 100, and the exercise price is

1. 600
2. 800
5. Calculate the payoff at expiration for a call option on the British pound in which the underlying price is 1.321 at expiration, the options are on 100,000 British pound, and the exercise price is

1. 1.29
2. 1.41
6. Calculate the payoff at expiration for a put option on the British pound in which the underlying price is 1.321 at expiration, the options are on 100,000 British pound, and the exercise price is

1. 1.29
2. 1.41
7. Calculate the payoff at expiration for a put option on the British pound in which the underlying price is 1.321 at expiration, the options are on 100,000 British pound, and the exercise price is

1. 1.29
2. 1.41
8. A call option with an exercise price of 50 will expire in 146 days. No cash payments will be made by the underlying asset over the life of the option. If the underlying asset price is at 55 and the risk-free rate of return is 5.0 percent, the lower bounds for an American call option and a European call option, respectively, are closest to :

 Lower bound for American call Lower bound for European call A. 5.00 5.00 B. 5.00 5.96 C. 5.96 5.00 D. 5.96 5.96
9. A put option with an exercise price of 60 will expire in 146 days. No cash payments will be made by the underlying asset over the life of the option. If the underlying asset price is at 55 and the risk-free rate of return is 5.0 percent, the lower bounds for an American call option and a European call option, respectively, are closest to :

 Lower bound for American call Lower bound for European call A. 3.84 3.84 B. 3.84 5.00 C. 5.00 3.84 D. 5.00 5.00
10. A call with a strike price of 60 is available on a stock currently trading for 55. The call expires in six months and the risk-free rate of return is $10 %$.
The lower bound on this call value is :
1. is zero
2. is 5 if the call is American
3. is 2.2 if the call is European
4. is 3.12 if the call is European

## Wednesday, October 5, 2011

### Interest Rate

1. A trader write a June put option with a trike price of $\$20$. The price of the option is$\$3$. Under what circumstances does the trader make a gain?

2. A bank quotes you an interest rate of $13\%$ per annum with quaterly compounding. What is the equivalent rate with (a) continuous compounding and (b) annual compounding?

3. An investor receives $\$110$in one year in return for an investment of$\$100$ now.

Calculate the percentage return per annum with:

1. Annual compounding
2. semiannual compounding
3. Monthly compounding
4. Continuous compounding

## Thursday, September 8, 2011

### PCAT Quantitative Practice Questions -10

1. The least common multiple of 8, 14, and 20 is

1. $8$
2. $70$
3. $120$
4. $280$

2. What is the slope of the line $3x+y=5$

1. $-3$
2. $1$
3. $3$
4. $5$

3. What is the value of $(\frac{25}{16})^{-\frac{1}{2}}$

1. $-\frac{4}{5}$
2. $\frac{25}{16}$
3. $\frac{4}{5}$
4. $\frac{5}{4}$

4. If $y=9x+1$, then $\frac{dy}{dx}$

1. $1$
2. $3$
3. $9$
4. $9x$

1. 
2. 
3. 
4. 

5. If $c^{\frac{3}{2}}=8$, what is the value of c?

1. $3$
2. $9$
3. $27$
4. $81$

6. What is the value of $\log_{3}81=4$

1. $2$
2. $4$
3. $8$
4. $32$

7. If $f(x)=25^{x}$, then $f(\frac{1}{2})=$

1. $1$
2. $5$
3. $5\frac{1}{2}$
4. $15$

8. If $a=\frac{7}{3}$ then $\frac{1}{a}=$

1. $3$
2. $7$
3. $\frac{3}{7}$
4. $\frac{7}{3}$

9. $y(x)=\frac{2}{x}$

1. $2$
2. $\frac{2}{x^{2}}$
3. $-\frac{2}{x^{2}}$
4. $-2x^{2}$

10. What is the second derivative of $y=7x^{2}+3x+1$

1. $3$
2. $7$
3. $14$
4. $14x+3$

## Sunday, September 4, 2011

### PCAT Quantitative Practice Questions -9

Pharmacy College Admission Test

1. If $x=9$, then $3(x-3)^{2}=$

1. $108$
2. $112$
3. $84$
4. $94$

2. $(a^{7})^{6}$

1. $a^{13}$
2. $a^{42}$
3. $a^{7}$
4. $a^{6}$

3. What is the slop of the line that passes through $(-5,7)$ and $(2,-2)$?

1. $\frac{9}{7}$
2. $\frac{3}{7}$
3. $-\frac{3}{7}$
4. $\frac{-9}{7}$

4. Factor: $x^{2}-4x-5$

1. $(x-1)(x+5)$
2. $(x+1)(x-5)$
3. $(x+4)(x+1)$
4. $(x-3)(x+4)$

5. What is the y-intercept of the line expressed in the equation $2x+3y=6$?

1. $3$
2. $2$
3. $-2$
4. $\frac{2}{3}$

6. Find the domain for the given function.
$f(x)=\log(x+5)$

1. $(-5,\infty)$
2. $[-5,\infty)$
3. $(-\infty,5)$
4. $[-\infty,5)$

7. Which line is perpendicular to the y-axis?

1. $x=6$
2. $x=y-1$
3. $y=x+1$
4. $y=1$

8. $\lim_{x \to \infty}(\frac{9x^{5}-9x^{4}+3x^{3}+6x^{2}-x}{3x^{5}-5x^{2}})$

1. $3$
2. $0$
3. $-3$
4. $\infty$

9. $x^{2}+5=149$, $x=$

1. $11,-11$
2. $12,-12$
3. $14,-14$
4. None of the above

10. $\lim_{x \to 3}(\frac{x^{2}-9}{x-3})$

1. $0$
2. $\infty$
3. $6$
4. $1$

 1 A 2 B 3 D 4 B 5 B 6 A 7 D 8 A 9 B 10 C
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## Tuesday, August 30, 2011

### PCAT Quantitative Practice Questions -8

Pharmacy College Admission Test

1. Evaluate the expression: $1000(2^{-1.5})$

1. $2828,427$
2. $2000.00$
3. $353.55$
4. $3000$

2. Evaluate the expression: $\log_{49}7$

1. $\frac{1}{4}$
2. $\frac{1}{2}$
3. $\frac{2}{5}$
4. $\frac{1}{49}$

3. Place into standard form: $(5+i)-(7-7i)$

1. $-2+8i$
2. $2+8i$
3. $12+8i$
4. $-2+6i$

4. Find the domaine of the function: $f(x)=\sqrt{-6x+12}$

1. $x \geq 3$
2. $x \leq -2$
3. $x \leq -1$
4. $x \leq 2$

5. What is the value of: $3\ln e^{6}$

1. $6$
2. $18$
3. $9$
4. $12$

6. What is the value of: $\csc (150 deg)$

1. $1$
2. $-1$
3. $-2$
4. $2$

7. Solve the equation: $x^{2}-10x+50=0$

1. $5+5i$ or $5-5i$
2. $2+5i$ or $2-5i$
3. $4+5i$ or $4-5i$
4. $1+5i$ or $1-5i$

8. What is the value of $x$: $\log_{10}x=-3$

1. $0.01$
2. $0.001$
3. $0.1$
4. $1$

9. Factor the expression: $x^{2}-3ix-2$

1. $(x+i)(x+2i)$
2. $(x+i)(x-2i)$
3. $(x-i)(x-2i)$
4. $(-x-i)(x-2i)$

10. Identify the horizontal and vertical asymptotes for: $\frac{5x^{2}}{x^{2}-9}$

1. $y=5$, $x=-3$, $x=3$
2. $y=-5$, $x=-3$
3. $y=5$, $x=3$
4. $y=5$, $x=-3$
11.  1 C 2 B 3 A 4 D 5 B 6 D 7 A 8 B 9 C 10 A

### PCAT Quantitative Practice Questions -7

Pharmacy College Admission Test

1. For how many positive integers, $n$, is true that $n^{2} \leq 3n$

1. $2$
2. $3$
3. $4$
4. $5$

2. If $a^{4}=16$, then $3^{a}$

1. $3$
2. $9$
3. $16$
4. $27$

3. $\sqrt{20}\sqrt{5}=$

1. $2\sqrt{5}$
2. $10$
3. $4\sqrt{5}$
4. $5\sqrt{10}$

4. The sum of three positive consecutive even integers is x.
What is the value of the middle of the three integers?

1. $\frac{x}{3}+2$
2. $3x$
3. $\frac{x-2}{3}$
4. $\frac{x}{3}$

5. What is the average of $5^{10}$, $5^{20}$, $5^{30}$, $5^{40}$ and $5^{50}$?

1. $5^{9}+5^{19}+5^{29}+5^{39}+5^{49}$
2. $5^{30}$
3. $5^{149}$
4. $150$

6. Which of the following is equal to $(5^{6} \times 5^{9})^{10}$?

1. $25^{150}$
2. $25^{540}$
3. $5^{540}$
4. $5^{150}$

7. What is the value of $3^{\frac{1}{3}} \times 3^{\frac{2}{3}} \times 3^{\frac{3}{3}}$?

1. $3$
2. $9$
3. $27$
4. $30$

8. How many integers satisfy the inequality $|x| < 2 \pi$.

1. $3$

2. $4$

3. $7$

4. More than $7$

9. What is the average of $5^{a} \times 5^{b}=5^{300}$

1. $50$
2. $100$
3. $150$
4. $200$

10. If $5^{a}5^{b}=\frac{5^{c}}{5^{d}}$, what is d in terms of $a$, $b$ and $c$?

1. $\frac{c}{a+b}$
2. $c+ab$
3. $c-a-b$
4. $c+a-b$
 1 B 2 B 3 B 4 D 5 A 6 D 7 B 8 D 9 C 10 C

### PCAT Quantitative Practice Questions -6

Pharmacy College Admission Test

1. Which of the following is equivalent to $5^{9}$

1. $5^{4}+5^{4}+5^{1}$
2. $5^{2} \times 5^{4} \times 5^{3}$
3. $\frac{10^{9}}{2^{10}}$
4. $(5^{4})^{5}$

2. Which of the following is equivalent to $\sqrt{289}$

1. $14$
2. $15$
3. $16$
4. $17$

3. Which of the following is a perfect square?

1. $120$
2. $121$
3. $122$
4. $123$

4. Which of the following is equivalent to $3\sqrt{10}$

1. $3\sqrt{5} \times \sqrt{5}$
2. $\sqrt{90}$
3. $3\sqrt{5} + 3\sqrt{2}$
4. $3\sqrt{5}+3\sqrt{5}$

5. Which of the following is equivalent to $10^{\frac{2}{5}}$

1. $\sqrt[5]{5}$
2. $\sqrt[5]{10}$
3. $\sqrt[5]{20}$
4. $\sqrt[5]{100}$

6. Which of the following fractions is equivalent to $\frac{3}{6} \times \frac{2}{5}$?

1. $\frac{6}{30}$
2. $\frac{5}{30}$
3. $\frac{5}{11}$
4. $\frac{15}{12}$

7. Which of the following expressions is equivalent to $\frac{7}{6} \div \frac{5}{2}$?

1. $\frac{9}{6}+\frac{9}{5}$
2. $\frac{7}{8}+\frac{5}{8}$
3. $\frac{7}{6}+\frac{2}{5}$
4. $\frac{1}{7}+\frac{2}{35}$

8. If $3^{x}=729$, what is $x^{3}$?

9. What is the value of $||4|-|-7||$

1. $-11$
2. $-3$
3. $0$
4. $3$

10. What is the value of $(\sqrt{3}+\sqrt{5})^{2}-(\sqrt{8})^{2}$

1. $2\sqrt{15}$
2. $\sqrt{15}$
3. $0$
4. $15$

 1 B 2 D 3 B 4 B 5 D 6 A 7 D 8 125 9 D 10 A

### PCAT Quantitative Practice Questions -5

Pharmacy College Admission Test

1. Solve $15x-32=18-10x$

1. $-14$
2. $10$
3. $14$
4. $2$

2. Solve $\frac{x}{8}=\frac{x-2}{4}$

1. $12$
2. $4$
3. $6$
4. $-\frac{1}{2}$

3. Which of the following are the factors of $t^{2}+8t+16$

1. $(t-8)(t-2)$
2. $(t+8)(t+2)$
3. $(t+1)(t+16)$
4. $(t+4)(t+4)$

4. Solve for a in term of b, if $6a+12b=24$

1. $24-12b$
2. $2-\frac{1}{2}b$
3. $4-2b$
4. $24-18b$

5. If $ax+2b=5c-dx$, what does x equal in terms of a, b, c, and d?

1. $a-d$
2. $(5c-2b)(a-d)$
3. $\frac{5c-d-2b}{a}$
4. $\frac{5c-2b}{a-d}$

6. If $(z-9)(z+3)=0$, what are the two possible values of z?

1. $z=-9$ abd $z=3$
2. $z=9$ abd $z=0$
3. $z=0$ abd $z=-3$
4. $z=9$ abd $z=-3$

7. If $z^{2}-6z=16$, which of the following could be a value of $z^{2}+6z$?

1. $-8$
2. $112$
3. $110$
4. $18$

8. If $3\sqrt{ a}-10=2$, what is the value of a?

1. $16$
2. $4$
3. $32$
4. $64$

9. Given $\frac{(x+6)(x^{2}-2x-3)}{x^{2}+3x-18}=10$, find the value of x.

1. $18$
2. $4$
3. $12$
4. $9$

10. Solve the equation $\frac{5x}{8}-\frac{3x}{5}=2$.

1. $40$
2. $80$
3. $160$
4. $-80$

 1 D 2 B 3 D 4 C 5 D 6 D 7 B 8 A 9 D 10 B

### PCAT Quantitative Practice Questions -4

Pharmacy College Admission Test

1. $2(5x-5)+5(2x+2)=$
1. $0$
2. $20x$
3. $20x-10$
4. $20x+10$

2. If $x=a+2$, and $y=-8-a$ then $x+y=$

1. $10$
2. $2a-6$
3. $-10$
4. $-6$

3. If $x \ne -5$, then $\frac{x^{2}+3x-10}{x+5}-(x-2)=$

4. If $(a-\frac{1}{a})^{2}=8$, then $a^{2}+\frac{1}{a^{2}}=$

1. $8$
2. $6$
3. $10$
4. $12$

5. $(x+y)^{2}=16$, and $x^{2}+y^{2}=6$ then $xy=$

1. $5$
2. $10$
3. $6$
4. $4$

6. $(x+y)=2$, and $x^{2}-y^{2}=6$ then $x-y=$

1. $12$
2. $4$
3. $6$
4. $\frac{1}{3}$

7. $\frac{15y+3}{3}-5y=$

1. $1$
2. $0$
3. $10y+1$
4. $3$

8. if $b^{2}-a^{2}=9$ then $5(a-b)(a+b)=$

1. $\frac{9}{5}$
2. $4$
3. $50$
4. $-45$

9. When $c \ne 3$, then $\frac{c^{2}-9}{c-3}=$

1. $c-3$
2. $1$
3. $c+3$
4. $3-c$

10. If $b>0$, and $b^{2}-1=10 \times 12$, then $b=$

1. $1$
2. $12$
3. $10$
4. $11$

 1 B 2 D 3 0 4 C 5 A 6 D 7 A 8 D 9 C 10 D

### PCAT Quantitative Practice Questions -3

Pharmacy College Admission Test

1. If $3x+7=5x+1$

1. $2.5$
2. $3.5$
3. $4$
4. $3$

2. What is the next term in the sequence: 6, 3, 10, 7, 14, 11, ...?

1. $15$
2. $6$
3. $17$
4. $18$

3. The area of the basis of Cylinder A is 8 times the area of the basis of Cylinder B. What is the radius of Cylinder A in terms of the radius of Cylinder B?

1. $r_{A}=\frac{r_{B}}{8}$
2. $r_{A}=8r_{B}$
3. $r_{A}=4r_{B}$
4. $r_{A}=2\sqrt{2}r_{B}$

4. If $x^{2}-2xy+y^{2}=121$, $x-y=$

1. $10$
2. $11$
3. $12$
4. $13$

5. If c is equal to the sum b and twice of a, which of the following is the average of b and c?

1. $a$
2. $b$
3. $c$
4. $a+b$

6. $f(x)=4x+8$, $f(c+3)=8$, $f(c)=$

1. $-8$
2. $0$
3. $3$
4. $8$

7. $5^{n}.125^{m}=78,125$, $n+3m=$

1. $5$
2. $6$
3. $7$
4. $8$

8. $\frac{3b^{2}}{a^{3}}=27a^{2}$

1. $9a^{3}$
2. $\frac{1}{9a^{3}}$
3. $\frac{1}{a^{3}}$
4. $\frac{1}{3a^{3}}$

9. Which of the following statements must be true about the x and y coordinates that satisfy the equation $ay-ax=0$, $a \ne 0$, $x \ne 0$ ,$y \ne 0$

1. $xy=1$
2. $x=-y$
3. $y>x$
4. $x=y$

10. What is the length of the side of a cube whose volume is 125 cubic units?

1. $4$
2. $5$
3. $6$
4. $7$
 1 D 2 D 3 D 4 B 5 D 6 D 7 C 8 D 9 D 10 B

### PCAT Quantitative Practice Questions -2

Pharmacy College Admission Test

1. If $\frac{1}{2}$ of a number is 3, what is $\frac{1}{3}$ of the number?

1. $1$
2. $2$
3. $3$
4. $6$

2. If $x=-1$, then $x^{5}+x^{4}+x^{3}+x^{2}-5=$

1. $-10$
2. $-6$
3. $-5$
4. $-3$

3. If $f(x)=2^{x}+7x$, then $f(4)=$

1. $24$
2. $36$
3. $44$
4. $54$

4. If $x-3=y$, then $(y-x)^{3}=$

1. $27$
2. $54$
3. $-54$
4. $-27$

5. If $a>b$, and $\frac{a}{b}>0$, which of the following is true?

1. $a>0$
2. $b>0$
3. $ab>0$

1. I only
2. II only
3. III only
4. I and II only

6. Which of the following is equal to $(\frac{x^{-7}y^{-5}}{x^{-3}y^{3}})^{-2}$

1. $x^{8}y^{16}$
2. $\frac{x^{8}}{y^{16}}$
3. $\frac{y^{16}}{x^{8}}$
4. $x^{4}y^{8}$

7. What is the slope of the line passing through the points (-1,7) and (3,5)?

1. $\frac{1}{2}$
2. $-2$
3. $-\frac{1}{2}$
4. $1$

8. The symbol $\otimes$ represents a binary operation defined as $a \otimes b=3^{a}+2^{b}$, what is the value of $(-2)\otimes (-3)$

1. $\frac{72}{17}$
2. $-72$
3. $72$
4. $\frac{17}{72}$

9. If $\sqrt{\frac{49}{x}}=\frac{7}{3}$

1. $6$
2. $9$
3. $25$
4. $49$

10. A bike that originally sold for $150 \$$was on sale for 120 \$$. What was the rate of discount? 1.$15 \%$2.$21 \%$3.$20 \%$4.$25 \% $ 1 B 2 C 3 C 4 D 5 C 6 A 7 C 8 D 9 B 10 C ### PCAT Quantitative Practice Questions -1 Pharmacy College Admission Test 1. If$ 0.10 < x < 0.12$, which of the following could be a value of$x$? 1.$9 \%$2.$10 \% $3.$11 \% $4.$12 \% $2. If$\frac{xyz}{t}=w$and$x$and$t$are doubled, what happens to the value of w 1. The value of$w$is halved. 2. The value of$w$is four times greater. 3. The value of$w$is doubled 4. The value of$w$remains the same. 3. What is the tenth term of the pattern below?$\frac{3}{2}$,$\frac{9}{4}$,$\frac{27}{8}$,$\frac{81}{16}$,... 1.$\frac{3}{2^{10}}$2.$\frac{30}{20}$3.$(\frac{3}{2})^{10}$4.$\frac{3^{10}}{2}$4. If$a > 0$and$b < 0$, which of the following is always negative? 1.$-ab$2.$a+b$3.$|a|-|b|$4.$\frac{a}{b}$5. Which of the following number pairs is in the ratio$3:7$? 1.$\frac{1}{3}$,$\frac{1}{7}$2.$\frac{1}{7}$,$\frac{1}{3}$3.$\frac{1}{7}$,$\frac{3}{7}$4.$7$,$\frac{1}{3}$6. If$x=-\frac{1}{4}$, then$(-x)^{-3}+(\frac{1}{x})^{2}=$1.$-64$2.$16 $3.$64$4.$80$7. For which of the following values of$x$is the relationship$x < x^{2} < x^{3}$true? 1.$-3$2.$-\frac{2}{3}$3.$0$4.$\frac{2}{3} $8.$x^{2}+2xy+y^{2}=169$,$-|-(x+y)|=$9. How many distincts factors does 900 have? 1.$2$2.$ 3$3.$ 4$4.$ 5$10. If$x=-\frac{1}{7}$, then which of the following is always positive for$n > 0$? 1.$x^{n}$2.$n^{x}$3.$nx$4.$n-x$ 1 C 2 D 3 C 4 D 5 B 6 D 7 3 8 -13 9 B 10 B ## Monday, August 15, 2011 ### CLEP Precalculus Practice Questions - Algebra review 1. Factor$3a^{2}+3ab-6b^{2}$2. Factor$x^{3}-4x^{2}+2x-8$3. Factor$25a^{2}-36b^{2}$4. Resolve into factors$x^{2}-ax+bx-ab$5. Resolve into factors$6x^{2}-9ax+4bx-6ab$6. Resolve into factors$x^{2}+11x+24$7. Resolve into factors$x^{2}-10x+24$8. Resolve into factors$x^{2}-10ax+10a^{2}$## Monday, August 1, 2011 ### CLEP College Algebra Practice Questions - 12 & Answer Key 1. Which of the following is equivalent to$5^{9}$1.$5^{4}+5^{4}+5^{1}$2.$5^{2} \times 5^{4} \times 5^{3}$3.$\frac{10^{9}}{2^{10}}$4.$(5^{4})^{5}$5.$\frac{5^{5}}{5^{4}}$2. Which of the following is equivalent to$\sqrt{289}$1.$14$2.$15$3.$16$4.$17$5.$18$3. Which of the following is a perfect square? 1.$120$2.$121$3.$122$4.$123$5.$124$4. Which of the following is equivalent to$3\sqrt{10}$1.$3\sqrt{5} \times \sqrt{5}$2.$\sqrt{90}$3.$3\sqrt{5} + 3\sqrt{2}$4.$3\sqrt{5}+3\sqrt{5}$5.$\frac{3\sqrt{2}}{\sqrt{5}}$5. Which of the following is equivalent to$10^{\frac{2}{5}}$1.$\sqrt[5]{5}$2.$\sqrt[5]{10}$3.$\sqrt[5]{20}$4.$\sqrt[5]{100}$5.$\sqrt[5]{1000}$6. Which of the following fractions is equivalent to$\frac{3}{6} \times \frac{2}{5}$? 1.$\frac{6}{30}$2.$\frac{5}{30}$3.$\frac{5}{11}$4.$\frac{15}{12}$5.$\frac{9}{30}$7. Which of the following expressions is equivalent to$\frac{7}{6} \div \frac{5}{2}$? 1.$\frac{7}{30}+\frac{2}{30}$2.$\frac{9}{6}+\frac{9}{5}$3.$\frac{7}{8}+\frac{5}{8}$4.$\frac{7}{6}+\frac{2}{5}$5.$\frac{1}{7}+\frac{2}{35}$8. If$3^{x}=729$, what is$x^{3}$? 9. What is the value of$||4|-|-7||$1.$-11$2.$-3$3.$0$4.$3$5.$11$10. What is the value of$(\sqrt{3}+\sqrt{5})^{2}-(\sqrt{8})^{2}$1.$2\sqrt{15}$2.$\sqrt{15}$3.$0$4.$15$5.$30$ 1 B 2 D 3 B 4 B 5 D 6 A 7 E 8 125 9 D 10 A ### CLEP College Algebra Practice Questions - 11 & Answer Key 1. Solve$15x-32=18-10x$1.$-14$2.$10$3.$14$4.$2$5.$50$2. Solve$\frac{x}{8}=\frac{x-2}{4}$1.$12$2.$4$3.$6$4.$-\frac{1}{2}$5.$-6$3. Which of the following are the factors of$t^{2}+8t+16$1.$(t-4)(t-4)$2.$(t-8)(t-2)$3.$(t+8)(t+2)$4.$(t+1)(t+16)$5.$(t+4)(t+4)$4. Solve for a in term of b, if$6a+12b=24$1.$24-12b$2.$2-\frac{1}{2}b$3.$4-2b$4.$24-18b$5.$2b-4$5. If$ax+2b=5c-dx$, what does x equal in terms of a, b, c, and d? 1.$5c-d-2b-a$2.$a-d$3.$(5c-2b)(a-d)$4.$\frac{5c-d-2b}{a}$5.$\frac{5c-2b}{a-d}$6. If$(z-9)(z+3)=0$, what are the two possible values of z? 1.$z=-9$abd$z=3$2.$z=9$abd$z=0$3.$z=0$abd$z=-3$4.$z=9$abd$z=-3$5.$z=-12$abd$z=12$7. If$z^{2}-6z=16$, which of the following could be a value of$z^{2}+6z$? 1.$-8$2.$112$3.$110$4.$18$5.$108$8. If$3\sqrt{ a}-10=2$, what is the value of a? 1.$16$2.$4$3.$32$4.$64$5.$12$9. Given$\frac{(x+6)(x^{2}-2x-3)}{x^{2}+3x-18}=10$, find the value of x. 1.$18$2.$4$3.$12$4.$9$5.$12$10. Solve the equation$\frac{5x}{8}-\frac{3x}{5}=2$. 1.$40$2.$80$3.$160$4.$-80$5.$20$ 1 D 2 B 3 E 4 C 5 E 6 D 7 B 8 A 9 D 10 B ### CLEP College Algebra Practice Questions - 10 & Answer Key 1.$2(5x-5)+5(2x+2)=$1.$0$2.$20x$3.$20x-10$4.$20x+10$5.$10x^{2}+20+x+20$2. If$x=a+2$, and$y=-8-a$then$x+y=$1.$6$2.$10$3.$2a-6$4.$-10$5.$-6$3. If$x \ne -5$, then$\frac{x^{2}+3x-10}{x+5}-(x-2)=$4. If$(a-\frac{1}{a})^{2}=8$, then$a^{2}+\frac{1}{a^{2}}=$1.$8$2.$6$3.$10$4.$12$5.$100$5.$(x+y)^{2}=16$, and$x^{2}+y^{2}=6$then$xy=$1.$5$2.$10$3.$6$4.$4$5.$16$6.$(x+y)=2$, and$x^{2}-y^{2}=6$then$x-y=$1.$12$2.$4$3.$6$4.$\frac{1}{3}$5.$3$7.$\frac{15y+3}{3}-5y=$1.$1$2.$0$3.$10y+1$4.$3$5.$3y+1$8. if$b^{2}-a^{2}=9$then$5(a-b)(a+b)=$1.$45$2.$\frac{9}{5}$3.$4$4.$50$5.$-45$9. When$c \ne 3$, then$\frac{c^{2}-9}{c-3}=$1.$c-3$2.$1$3.$c+3$4.$3-c$5.$o$10. If$b>0$, and$b^{2}-1=10 \times 12$, then$b=$1.$9$2.$1$3.$12$4.$10$5.$11$ 1 B 2 E 3 0 4 C 5 A 6 D 7 A 8 E 9 C 10 E ### CLEP College Algebra Practice Questions - 9 & Answer Key 1. If$3x+7=5x+1$1.$2.5$2.$3.5 $3.$4 $4.$3 $5.$ 4.5$2. What is the next term in the sequence: 6, 3, 10, 7, 14, 11, ...? 1.$19$2.$15 $3.$6 $4.$ 17$5.$ 18$3. The area of the basis of Cylinder A is 8 times the area of the basis of Cylinder B. What is the radius of Cylinder A in terms of the radius of Cylinder B? 1.$r_{A}=\frac{r_{B}}{8}$2.$r_{A}=8r_{B} $3.$r_{A}=4r_{B} $4.$r_{A}=2\sqrt{2}r_{B} $5.$r_{A}=\frac{r_{B}}{4} $4. If$x^{2}-2xy+y^{2}=121$,$x-y=$1.$10$2.$11 $3.$12 $4.$13 $5.$14 $5. If c is equal to the sum b and twice of a, which of the following is the average of b and c? 1.$a$2.$b $3.$c $4.$a+b $5.$b+c $6.$f(x)=4x+8$,$f(c+3)=8$,$f(c)=$1.$-8$2.$0 $3.$3 $4.$8 $5.$-3 $7.$5^{n}.125^{m}=78,125$,$n+3m=$1.$5$2.$ 6$3.$ 7$4.$ 8$5.$ 9$8.$\frac{3b^{2}}{a^{3}}=27a^{2}$1.$3a^{3}$2.$9a^{3} $3.$\frac{1}{9a^{3}} $4.$\frac{1}{a^{3}} $5.$\frac{1}{3a^{3}} $9. Which of the following statements must be true about the x and y coordinates that satisfy the equation$ay-ax=0$,$a \ne 0$,$x \ne 0$,$y \ne 0$1.$x>y$2.$xy=1 $3.$x=-y $4.$y>x $5.$x=y $10. What is the length of the side of a cube whose volume is 125 cubic units? 1.$4$2.$ 5$3.$ 6$4.$ 7$5.$ 4.5$ 1 D 2 E 3 D 4 B 5 D 6 D 7 C 8 E 9 E 10 B ### CLEP College Algebra Practice Questions - 8 & Answer Key 1. If$\frac{1}{2}$of a number is 3, what is$\frac{1}{3}$of the number? 1.$1$2.$2 $3.$ 3$4.$ 6$5.$ 8$2. If$x=-1$, then$x^{5}+x^{4}+x^{3}+x^{2}-5=$1.$-10$2.$-6 $3.$-5$4.$-3$5.$-1$3. If$f(x)=2^{x}+7x$, then$f(4)=$1.$24$2.$ 36$3.$44 $4.$54 $5.$64 $4. If$x-3=y$, then$(y-x)^{3}=$1.$27$2.$54 $3.$ -54$4.$ -27$5.$ 81$5. If$a>b$, and$\frac{a}{b}>0$, which of the following is true? 1.$a>0$2.$b>0$3.$ab>0$1. I only 2. II only 3. III only 4. I and II only 5. I and III only 6. Which of the following is equal to$(\frac{x^{-7}y^{-5}}{x^{-3}y^{3}})^{-2}$1.$x^{8}y^{16}$2.$\frac{x^{8}}{y^{16}} $3.$\frac{y^{16}}{x^{8}} $4.$x^{4}y^{8}$5.$x^{8}y^{8}$7. What is the slope of the line passing through the points (-1,7) and (3,5)? 1.$\frac{1}{2}$2.$-2$3.$-\frac{1}{2} $4.$1$5.$2$8. The symbol$\otimes$represents a binary operation defined as$a \otimes b=3^{a}+2^{b}$, what is the value of$(-2)\otimes (-3)$1.$-\frac{17}{72}$2.$\frac{72}{17} $3.$-72 $4.$ 72$5.$ \frac{17}{72}$9. If$\sqrt{\frac{49}{x}}=\frac{7}{3}$1.$6$2.$9$3.$25$4.$49$5.$147$10. A bike that originally sold for$150 \$$was on sale for 120 \$$. What was the rate of discount?

1. $15 \%$
2. $21 \%$
3. $20 \%$
4. $25 \%$
5. $30 \%$

 1 B 2 C 3 C 4 D 5 C 6 A 7 C 8 E 9 B 10 C

### CLEP College Algebra Practice Questions - 7 & Answer Key

1. If $0.10 < x < 0.12$, which of the following could be a value of $x$?

1. $9 \%$
2. $10 \%$
3. $11 \%$
4. $12 \%$
5. $13 \%$

2. If $\frac{xyz}{t}=w$ and $x$ and $t$ are doubled, what happens to the value of w

1. The value of $w$ is two times smaller.
2. The value of $w$ is halved.
3. The value of $w$ is four times greater.
4. The value of $w$ is doubled
5. The value of $w$ remains the same.

3. What is the tenth term of the pattern below?
$\frac{3}{2}$, $\frac{9}{4}$, $\frac{27}{8}$, $\frac{81}{16}$,...

1. $\frac{3}{2^{10}}$
2. $\frac{30}{20}$
3. $(\frac{3}{2})^{10}$
4. $\frac{3^{10}}{2}$
5. $\frac{300}{200}$

4. If $a > 0$ and $b < 0$, which of the following is always negative?

1. $-ab$
2. $a+b$
3. $|a|-|b|$
4. $\frac{a}{b}$
5. $b^{a}$

5. Which of the following number pairs is in the ratio $3:7$?

1. $\frac{1}{3}$,$\frac{1}{7}$
2. $\frac{1}{7}$,$\frac{1}{3}$
3. $\frac{1}{7}$,$\frac{3}{7}$
4. $7$,$\frac{1}{3}$
5. $1$,$\frac{1}{7}$

6. If $x=-\frac{1}{4}$, then $(-x)^{-3}+(\frac{1}{x})^{2}=$

1. $-80$
2. $-64$
3. $16$
4. $64$
5. $80$

7. For which of the following values of $x$ is the relationship $x < x^{2} < x^{3}$ true?

1. $-3$
2. $-\frac{2}{3}$
3. $0$
4. $\frac{2}{3}$
5. $3$

8. $x^{2}+2xy+y^{2}=169$, $-|-(x+y)|=$

9. How many distincts factors does 900 have?

1. $2$
2. $3$
3. $4$
4. $5$
5. more than $5$

10. If $x=-\frac{1}{7}$, then which of the following is always positive for $n > 0$?

1. $x^{n}$
2. $n^{x}$
3. $nx$
4. $n-x$
5. $\frac{x}{n}$

 1 C 2 E 3 C 4 D 5 B 6 E 7 3 8 -13 9 A 10 B

### CLEP College Algebra Practice Questions - 6 & Answer Key

1. For how many positive integers, $n$, is true that $n^{2} \leq 3n$

1. $2$
2. $3$
3. $4$
4. $5$
5. more than 5

2. If $a^{4}=16$, then $3^{a}$

1. $3$
2. $9$
3. $16$
4. $27$
5. $81$

3. $\sqrt{20}\sqrt{5}=$

1. $2\sqrt{5}$
2. $10$
3. $4\sqrt{5}$
4. $5\sqrt{10}$
5. $10\sqrt{5}$

4. The sum of three positive consecutive even integers is x.
What is the value of the middle of the three integers?

1. $\frac{x}{3}-1$
2. $\frac{x}{3}+2$
3. $3x$
4. $\frac{x-2}{3}$
5. $\frac{x}{3}$

5. What is the average of $5^{10}$, $5^{20}$, $5^{30}$, $5^{40}$ and $5^{50}$?

1. $5^{9}+5^{19}+5^{29}+5^{39}+5^{49}$
2. $5^{30}$
3. $5^{149}$
4. $150$
5. $5^{29}$

6. Which of the following is equal to $(5^{6} \times 5^{9})^{10}$?

1. $25^{150}$
2. $25^{540}$
3. $5^{540}$
4. $5^{150}$
5. $5^{15}$

7. What is the value of $3^{\frac{1}{3}} \times 3^{\frac{2}{3}} \times 3^{\frac{3}{3}}$?

1. $3$
2. $9$
3. $27$
4. $30$
5. $81$

8. How many integers satisfy the inequality $|x| < 2 \pi$.

1. $0$

2. $3$

3. $4$

4. $7$

5. More than $7$

9. What is the average of $5^{a} \times 5^{b}=5^{300}$

1. $50$
2. $100$
3. $150$
4. $200$
5. $250$

10. If $5^{a}5^{b}=\frac{5^{c}}{5^{d}}$, what is d in terms of $a$, $b$ and $c$?

1. $\frac{c}{a+b}$
2. $c+ab$
3. $c-a-b$
4. $c+a-b$
5. $\frac{b}{ac}$
 1 B 2 B 3 B 4 E 5 A 6 D 7 B 8 E 9 C 10 C

### GRE Practice Questions - 10 & Answer Key

1. $2(5x-5)+5(2x+2)=$
1. $0$
2. $20x$
3. $20x-10$
4. $20x+10$
5. $10x^{2}+20+x+20$

2. If $x=a+2$, and $y=-8-a$ then $x+y=$

1. $6$
2. $10$
3. $2a-6$
4. $-10$
5. $-6$

3. If $x \ne -5$, then $\frac{x^{2}+3x-10}{x+5}-(x-2)=$

4. If $(a-\frac{1}{a})^{2}=8$, then $a^{2}+\frac{1}{a^{2}}=$

1. $8$
2. $6$
3. $10$
4. $12$
5. $100$

5. $(x+y)^{2}=16$, and $x^{2}+y^{2}=6$ then $xy=$

1. $5$
2. $10$
3. $6$
4. $4$
5. $16$

6. $(x+y)=2$, and $x^{2}-y^{2}=6$ then $x-y=$

1. $12$
2. $4$
3. $6$
4. $\frac{1}{3}$
5. $3$

7. $\frac{15y+3}{3}-5y=$

1. $1$
2. $0$
3. $10y+1$
4. $3$
5. $3y+1$

8. if $b^{2}-a^{2}=9$ then $5(a-b)(a+b)=$

1. $45$
2. $\frac{9}{5}$
3. $4$
4. $50$
5. $-45$

9. When $c \ne 3$, then $\frac{c^{2}-9}{c-3}=$

1. $c-3$
2. $1$
3. $c+3$
4. $3-c$
5. $o$

10. If $b>0$, and $b^{2}-1=10 \times 12$, then $b=$

1. $9$
2. $1$
3. $12$
4. $10$
5. $11$

 1 B 2 E 3 0 4 C 5 A 6 D 7 A 8 E 9 C 10 E

### GRE Practice Questions - 9 & Answer Key

1. Solve $15x-32=18-10x$

1. $-14$
2. $10$
3. $14$
4. $2$
5. $50$

2. Solve $\frac{x}{8}=\frac{x-2}{4}$

1. $12$
2. $4$
3. $6$
4. $-\frac{1}{2}$
5. $-6$

3. Which of the following are the factors of $t^{2}+8t+16$

1. $(t-4)(t-4)$
2. $(t-8)(t-2)$
3. $(t+8)(t+2)$
4. $(t+1)(t+16)$
5. $(t+4)(t+4)$

4. Solve for a in term of b, if $6a+12b=24$

1. $24-12b$
2. $2-\frac{1}{2}b$
3. $4-2b$
4. $24-18b$
5. $2b-4$

5. If $ax+2b=5c-dx$, what does x equal in terms of a, b, c, and d?

1. $5c-d-2b-a$
2. $a-d$
3. $(5c-2b)(a-d)$
4. $\frac{5c-d-2b}{a}$
5. $\frac{5c-2b}{a-d}$

6. If $(z-9)(z+3)=0$, what are the two possible values of z?

1. $z=-9$ abd $z=3$
2. $z=9$ abd $z=0$
3. $z=0$ abd $z=-3$
4. $z=9$ abd $z=-3$
5. $z=-12$ abd $z=12$

7. If $z^{2}-6z=16$, which of the following could be a value of $z^{2}+6z$?

1. $-8$
2. $112$
3. $110$
4. $18$
5. $108$

8. If $3\sqrt{ a}-10=2$, what is the value of a?

1. $16$
2. $4$
3. $32$
4. $64$
5. $12$

9. Given $\frac{(x+6)(x^{2}-2x-3)}{x^{2}+3x-18}=10$, find the value of x.

1. $18$
2. $4$
3. $12$
4. $9$
5. $12$

10. Solve the equation $\frac{5x}{8}-\frac{3x}{5}=2$.

1. $40$
2. $80$
3. $160$
4. $-80$
5. $20$

 1 D 2 B 3 E 4 C 5 E 6 D 7 B 8 A 9 D 10 B

### GRE Practice Questions - 8 & Answer Key

1. Which of the following is equivalent to $5^{9}$

1. $5^{4}+5^{4}+5^{1}$
2. $5^{2} \times 5^{4} \times 5^{3}$
3. $\frac{10^{9}}{2^{10}}$
4. $(5^{4})^{5}$
5. $\frac{5^{5}}{5^{4}}$

2. Which of the following is equivalent to $\sqrt{289}$

1. $14$
2. $15$
3. $16$
4. $17$
5. $18$

3. Which of the following is a perfect square?

1. $120$
2. $121$
3. $122$
4. $123$
5. $124$

4. Which of the following is equivalent to $3\sqrt{10}$

1. $3\sqrt{5} \times \sqrt{5}$
2. $\sqrt{90}$
3. $3\sqrt{5} + 3\sqrt{2}$
4. $3\sqrt{5}+3\sqrt{5}$
5. $\frac{3\sqrt{2}}{\sqrt{5}}$

5. Which of the following is equivalent to $10^{\frac{2}{5}}$

1. $\sqrt[5]{5}$
2. $\sqrt[5]{10}$
3. $\sqrt[5]{20}$
4. $\sqrt[5]{100}$
5. $\sqrt[5]{1000}$

6. Which of the following fractions is equivalent to $\frac{3}{6} \times \frac{2}{5}$?

1. $\frac{6}{30}$
2. $\frac{5}{30}$
3. $\frac{5}{11}$
4. $\frac{15}{12}$
5. $\frac{9}{30}$

7. Which of the following expressions is equivalent to $\frac{7}{6} \div \frac{5}{2}$?

1. $\frac{7}{30}+\frac{2}{30}$
2. $\frac{9}{6}+\frac{9}{5}$
3. $\frac{7}{8}+\frac{5}{8}$
4. $\frac{7}{6}+\frac{2}{5}$
5. $\frac{1}{7}+\frac{2}{35}$

8. If $3^{x}=729$, what is $x^{3}$?

9. What is the value of $||4|-|-7||$

1. $-11$
2. $-3$
3. $0$
4. $3$
5. $11$

10. What is the value of $(\sqrt{3}+\sqrt{5})^{2}-(\sqrt{8})^{2}$

1. $2\sqrt{15}$
2. $\sqrt{15}$
3. $0$
4. $15$
5. $30$

 1 B 2 D 3 B 4 B 5 D 6 A 7 E 8 125 9 D 10 A

### GRE Practice Questions - 7 & Answer Key

1. For how many positive integers, $n$, is true that $n^{2} \leq 3n$

1. $2$
2. $3$
3. $4$
4. $5$
5. more than 5

2. If $a^{4}=16$, then $3^{a}$

1. $3$
2. $9$
3. $16$
4. $27$
5. $81$

3. $\sqrt{20}\sqrt{5}=$

1. $2\sqrt{5}$
2. $10$
3. $4\sqrt{5}$
4. $5\sqrt{10}$
5. $10\sqrt{5}$

4. The sum of three positive consecutive even integers is x.
What is the value of the middle of the three integers?

1. $\frac{x}{3}-1$
2. $\frac{x}{3}+2$
3. $3x$
4. $\frac{x-2}{3}$
5. $\frac{x}{3}$

5. What is the average of $5^{10}$, $5^{20}$, $5^{30}$, $5^{40}$ and $5^{50}$?

1. $5^{9}+5^{19}+5^{29}+5^{39}+5^{49}$
2. $5^{30}$
3. $5^{149}$
4. $150$
5. $5^{29}$

6. Which of the following is equal to $(5^{6} \times 5^{9})^{10}$?

1. $25^{150}$
2. $25^{540}$
3. $5^{540}$
4. $5^{150}$
5. $5^{15}$

7. What is the value of $3^{\frac{1}{3}} \times 3^{\frac{2}{3}} \times 3^{\frac{3}{3}}$?

1. $3$
2. $9$
3. $27$
4. $30$
5. $81$

8. How many integers satisfy the inequality $|x| < 2 \pi$.

1. $0$

2. $3$

3. $4$

4. $7$

5. More than $7$

9. What is the average of $5^{a} \times 5^{b}=5^{300}$

1. $50$
2. $100$
3. $150$
4. $200$
5. $250$

10. If $5^{a}5^{b}=\frac{5^{c}}{5^{d}}$, what is d in terms of $a$, $b$ and $c$?

1. $\frac{c}{a+b}$
2. $c+ab$
3. $c-a-b$
4. $c+a-b$
5. $\frac{b}{ac}$
 1 B 2 B 3 B 4 E 5 A 6 D 7 B 8 E 9 C 10 C

### GRE Practice Questions - 6 & Answer Key

1. If $0.10 < x < 0.12$, which of the following could be a value of $x$?

1. $9 \%$
2. $10 \%$
3. $11 \%$
4. $12 \%$
5. $13 \%$

2. If $\frac{xyz}{t}=w$ and $x$ and $t$ are doubled, what happens to the value of w

1. The value of $w$ is two times smaller.
2. The value of $w$ is halved.
3. The value of $w$ is four times greater.
4. The value of $w$ is doubled
5. The value of $w$ remains the same.

3. What is the tenth term of the pattern below?
$\frac{3}{2}$, $\frac{9}{4}$, $\frac{27}{8}$, $\frac{81}{16}$,...

1. $\frac{3}{2^{10}}$
2. $\frac{30}{20}$
3. $(\frac{3}{2})^{10}$
4. $\frac{3^{10}}{2}$
5. $\frac{300}{200}$

4. If $a > 0$ and $b < 0$, which of the following is always negative?

1. $-ab$
2. $a+b$
3. $|a|-|b|$
4. $\frac{a}{b}$
5. $b^{a}$

5. Which of the following number pairs is in the ratio $3:7$?

1. $\frac{1}{3}$,$\frac{1}{7}$
2. $\frac{1}{7}$,$\frac{1}{3}$
3. $\frac{1}{7}$,$\frac{3}{7}$
4. $7$,$\frac{1}{3}$
5. $1$,$\frac{1}{7}$

6. If $x=-\frac{1}{4}$, then $(-x)^{-3}+(\frac{1}{x})^{2}=$

1. $-80$
2. $-64$
3. $16$
4. $64$
5. $80$

7. For which of the following values of $x$ is the relationship $x < x^{2} < x^{3}$ true?

1. $-3$
2. $-\frac{2}{3}$
3. $0$
4. $\frac{2}{3}$
5. $3$

8. $x^{2}+2xy+y^{2}=169$, $-|-(x+y)|=$

9. How many distincts factors does 900 have?

1. $2$
2. $3$
3. $4$
4. $5$
5. more than $5$

10. If $x=-\frac{1}{7}$, then which of the following is always positive for $n > 0$?

1. $x^{n}$
2. $n^{x}$
3. $nx$
4. $n-x$
5. $\frac{x}{n}$

 1 C 2 E 3 C 4 D 5 B 6 E 7 3 8 -13 9 A 10 B

### GRE Practice Questions - 5 & Answer Key

1. If $\frac{1}{2}$ of a number is 3, what is $\frac{1}{3}$ of the number?

1. $1$
2. $2$
3. $3$
4. $6$
5. $8$

2. If $x=-1$, then $x^{5}+x^{4}+x^{3}+x^{2}-5=$

1. $-10$
2. $-6$
3. $-5$
4. $-3$
5. $-1$

3. If $f(x)=2^{x}+7x$, then $f(4)=$

1. $24$
2. $36$
3. $44$
4. $54$
5. $64$

4. If $x-3=y$, then $(y-x)^{3}=$

1. $27$
2. $54$
3. $-54$
4. $-27$
5. $81$

5. If $a>b$, and $\frac{a}{b}>0$, which of the following is true?

1. $a>0$
2. $b>0$
3. $ab>0$

1. I only
2. II only
3. III only
4. I and II only
5. I and III only

6. Which of the following is equal to $(\frac{x^{-7}y^{-5}}{x^{-3}y^{3}})^{-2}$

1. $x^{8}y^{16}$
2. $\frac{x^{8}}{y^{16}}$
3. $\frac{y^{16}}{x^{8}}$
4. $x^{4}y^{8}$
5. $x^{8}y^{8}$

7. What is the slope of the line passing through the points (-1,7) and (3,5)?

1. $\frac{1}{2}$
2. $-2$
3. $-\frac{1}{2}$
4. $1$
5. $2$

8. The symbol $\otimes$ represents a binary operation defined as $a \otimes b=3^{a}+2^{b}$, what is the value of $(-2)\otimes (-3)$

1. $-\frac{17}{72}$
2. $\frac{72}{17}$
3. $-72$
4. $72$
5. $\frac{17}{72}$

9. If $\sqrt{\frac{49}{x}}=\frac{7}{3}$

1. $6$
2. $9$
3. $25$
4. $49$
5. $147$

10. A bike that originally sold for $150 \$$was on sale for 120 \$$. What was the rate of discount? 1.$15 \%$2.$21 \%$3.$20 \%$4.$25 \% $5.$30 \% $ 1 B 2 C 3 C 4 D 5 C 6 A 7 C 8 E 9 B 10 C ### GRE Practice Questions - 4 & Answer Key 1. If$3x+7=5x+1$1.$2.5$2.$3.5 $3.$4 $4.$3 $5.$ 4.5$2. What is the next term in the sequence: 6, 3, 10, 7, 14, 11, ...? 1.$19$2.$15 $3.$6 $4.$ 17$5.$ 18$3. The area of the basis of Cylinder A is 8 times the area of the basis of Cylinder B. What is the radius of Cylinder A in terms of the radius of Cylinder B? 1.$r_{A}=\frac{r_{B}}{8}$2.$r_{A}=8r_{B} $3.$r_{A}=4r_{B} $4.$r_{A}=2\sqrt{2}r_{B} $5.$r_{A}=\frac{r_{B}}{4} $4. If$x^{2}-2xy+y^{2}=121$,$x-y=$1.$10$2.$11 $3.$12 $4.$13 $5.$14 $5. If c is equal to the sum b and twice of a, which of the following is the average of b and c? 1.$a$2.$b $3.$c $4.$a+b $5.$b+c $6.$f(x)=4x+8$,$f(c+3)=8$,$f(c)=$1.$-8$2.$0$3.$3$4.$-3$5.$8$7.$5^{n}.125^{m}=78,125$,$n+3m=$1.$5$2.$ 6$3.$ 7$4.$ 8$5.$ 9$8.$\frac{3b^{2}}{a^{3}}=27a^{2}$1.$3a^{3}$2.$9a^{3} $3.$\frac{1}{9a^{3}} $4.$\frac{1}{a^{3}} $5.$\frac{1}{3a^{3}} $9. Which of the following statements must be true about the x and y coordinates that satisfy the equation$ay-ax=0$,$a \ne 0$,$x \ne 0$,$y \ne 0$1.$x>y$2.$xy=1 $3.$x=-y $4.$y>x $5.$x=y $10. What is the length of the side of a cube whose volume is 125 cubic units? 1.$4$2.$ 5$3.$ 6$4.$ 7$5.$ 4.5$ 1 D 2 E 3 D 4 B 5 D 6 D 7 C 8 E 9 E 10 B ### GMAT Practice Questions - 12 & Answer Key 1. If$3x+7=5x+1$1.$2.5$2.$3.5 $3.$4 $4.$3 $5.$ 4.5$2. What is the next term in the sequence: 6, 3, 10, 7, 14, 11, ...? 1.$19$2.$15 $3.$6 $4.$ 17$5.$ 18$3. The area of the basis of Cylinder A is 8 times the area of the basis of Cylinder B. What is the radius of Cylinder A in terms of the radius of Cylinder B? 1.$r_{A}=\frac{r_{B}}{8}$2.$r_{A}=8r_{B} $3.$r_{A}=4r_{B} $4.$r_{A}=2\sqrt{2}r_{B} $5.$r_{A}=\frac{r_{B}}{4} $4. If$x^{2}-2xy+y^{2}=121$,$x-y=$1.$10$2.$11 $3.$12 $4.$13 $5.$14 $5. If c is equal to the sum b and twice of a, which of the following is the average of b and c? 1.$a$2.$b $3.$c $4.$a+b $5.$b+c $6.$f(x)=4x+8$,$f(c+3)=8$,$f(c)=$1.$-8$2.$0 $3.$3 $4.$8 $5.$-3 $7.$5^{n}.125^{m}=78,125$,$n+3m=$1.$5$2.$ 6$3.$ 7$4.$ 8$5.$ 9$8.$\frac{3b^{2}}{a^{3}}=27a^{2}$1.$3a^{3}$2.$9a^{3} $3.$\frac{1}{9a^{3}} $4.$\frac{1}{a^{3}} $5.$\frac{1}{3a^{3}} $9. Which of the following statements must be true about the x and y coordinates that satisfy the equation$ay-ax=0$,$a \ne 0$,$x \ne 0$,$y \ne 0$1.$x>y$2.$xy=1 $3.$x=-y $4.$y>x $5.$x=y $10. What is the length of the side of a cube whose volume is 125 cubic units? 1.$4$2.$ 5$3.$ 6$4.$ 7$5.$ 4.5$ 1 D 2 E 3 D 4 B 5 D 6 D 7 C 8 E 9 E 10 B ### GMAT Practice Questions - 11 & Answer Key 1. If$\frac{1}{2}$of a number is 3, what is$\frac{1}{3}$of the number? 1.$1$2.$2 $3.$ 3$4.$ 6$5.$ 8$2. If$x=-1$, then$x^{5}+x^{4}+x^{3}+x^{2}-5=$1.$-10$2.$-6 $3.$-5$4.$-3$5.$-1$3. If$f(x)=2^{x}+7x$, then$f(4)=$1.$24$2.$ 36$3.$44 $4.$54 $5.$64 $4. If$x-3=y$, then$(y-x)^{3}=$1.$27$2.$54 $3.$ -54$4.$ -27$5.$ 81$5. If$a>b$, and$\frac{a}{b}>0$, which of the following is true? 1.$a>0$2.$b>0$3.$ab>0$1. I only 2. II only 3. III only 4. I and II only 5. I and III only 6. Which of the following is equal to$(\frac{x^{-7}y^{-5}}{x^{-3}y^{3}})^{-2}$1.$x^{8}y^{16}$2.$\frac{x^{8}}{y^{16}} $3.$\frac{y^{16}}{x^{8}} $4.$x^{4}y^{8}$5.$x^{8}y^{8}$7. What is the slope of the line passing through the points (-1,7) and (3,5)? 1.$\frac{1}{2}$2.$-2$3.$-\frac{1}{2} $4.$1$5.$2$8. The symbol$\otimes$represents a binary operation defined as$a \otimes b=3^{a}+2^{b}$, what is the value of$(-2)\otimes (-3)$1.$-\frac{17}{72}$2.$\frac{72}{17} $3.$-72 $4.$ 72$5.$ \frac{17}{72}$9. If$\sqrt{\frac{49}{x}}=\frac{7}{3}$1.$6$2.$9$3.$25$4.$49$5.$147$10. A bike that originally sold for$150 \$$was on sale for 120 \$$. What was the rate of discount?

1. $15 \%$
2. $21 \%$
3. $20 \%$
4. $25 \%$
5. $30 \%$

 1 B 2 C 3 C 4 D 5 C 6 A 7 C 8 E 9 B 10 C

### GMAT Practice Questions - 10 & Answer Key

1. If $0.10 < x < 0.12$, which of the following could be a value of $x$?

1. $9 \%$
2. $10 \%$
3. $11 \%$
4. $12 \%$
5. $13 \%$

2. If $\frac{xyz}{t}=w$ and $x$ and $t$ are doubled, what happens to the value of w

1. The value of $w$ is two times smaller.
2. The value of $w$ is halved.
3. The value of $w$ is four times greater.
4. The value of $w$ is doubled
5. The value of $w$ remains the same.

3. What is the tenth term of the pattern below?
$\frac{3}{2}$, $\frac{9}{4}$, $\frac{27}{8}$, $\frac{81}{16}$,...

1. $\frac{3}{2^{10}}$
2. $\frac{30}{20}$
3. $(\frac{3}{2})^{10}$
4. $\frac{3^{10}}{2}$
5. $\frac{300}{200}$

4. If $a > 0$ and $b < 0$, which of the following is always negative?

1. $-ab$
2. $a+b$
3. $|a|-|b|$
4. $\frac{a}{b}$
5. $b^{a}$

5. Which of the following number pairs is in the ratio $3:7$?

1. $\frac{1}{3}$,$\frac{1}{7}$
2. $\frac{1}{7}$,$\frac{1}{3}$
3. $\frac{1}{7}$,$\frac{3}{7}$
4. $7$,$\frac{1}{3}$
5. $1$,$\frac{1}{7}$

6. If $x=-\frac{1}{4}$, then $(-x)^{-3}+(\frac{1}{x})^{2}=$

1. $-80$
2. $-64$
3. $16$
4. $64$
5. $80$

7. For which of the following values of $x$ is the relationship $x < x^{2} < x^{3}$ true?

1. $-3$
2. $-\frac{2}{3}$
3. $0$
4. $\frac{2}{3}$
5. $3$

8. $x^{2}+2xy+y^{2}=169$, $-|-(x+y)|=$

9. How many distincts factors does 900 have?

1. $2$
2. $3$
3. $4$
4. $5$
5. more than $5$

10. If $x=-\frac{1}{7}$, then which of the following is always positive for $n > 0$?

1. $x^{n}$
2. $n^{x}$
3. $nx$
4. $n-x$
5. $\frac{x}{n}$

 1 C 2 E 3 C 4 D 5 B 6 E 7 3 8 -13 9 A 10 B

### GMAT Practice Questions - 9 & Answer Key

1. For how many positive integers, $n$, is true that $n^{2} \leq 3n$

1. $2$
2. $3$
3. $4$
4. $5$
5. more than 5

2. If $a^{4}=16$, then $3^{a}$

1. $3$
2. $9$
3. $16$
4. $27$
5. $81$

3. $\sqrt{20}\sqrt{5}=$

1. $2\sqrt{5}$
2. $10$
3. $4\sqrt{5}$
4. $5\sqrt{10}$
5. $10\sqrt{5}$

4. The sum of three positive consecutive even integers is x.
What is the value of the middle of the three integers?

1. $\frac{x}{3}-1$
2. $\frac{x}{3}+2$
3. $3x$
4. $\frac{x-2}{3}$
5. $\frac{x}{3}$

5. What is the average of $5^{10}$, $5^{20}$, $5^{30}$, $5^{40}$ and $5^{50}$?

1. $5^{9}+5^{19}+5^{29}+5^{39}+5^{49}$
2. $5^{30}$
3. $5^{149}$
4. $150$
5. $5^{29}$

6. Which of the following is equal to $(5^{6} \times 5^{9})^{10}$?

1. $25^{150}$
2. $25^{540}$
3. $5^{540}$
4. $5^{150}$
5. $5^{15}$

7. What is the value of $3^{\frac{1}{3}} \times 3^{\frac{2}{3}} \times 3^{\frac{3}{3}}$?

1. $3$
2. $9$
3. $27$
4. $30$
5. $81$

8. How many integers satisfy the inequality $|x| < 2 \pi$.

1. $0$

2. $3$

3. $4$

4. $7$

5. More than $7$

9. What is the average of $5^{a} \times 5^{b}=5^{300}$

1. $50$
2. $100$
3. $150$
4. $200$
5. $250$

10. If $5^{a}5^{b}=\frac{5^{c}}{5^{d}}$, what is d in terms of $a$, $b$ and $c$?

1. $\frac{c}{a+b}$
2. $c+ab$
3. $c-a-b$
4. $c+a-b$
5. $\frac{b}{ac}$
 1 B 2 B 3 B 4 E 5 A 6 D 7 B 8 E 9 C 10 C

### GMAT Practice Questions - 8 & Answer Key

1. Which of the following is equivalent to $5^{9}$

1. $5^{4}+5^{4}+5^{1}$
2. $5^{2} \times 5^{4} \times 5^{3}$
3. $\frac{10^{9}}{2^{10}}$
4. $(5^{4})^{5}$
5. $\frac{5^{5}}{5^{4}}$

2. Which of the following is equivalent to $\sqrt{289}$

1. $14$
2. $15$
3. $16$
4. $17$
5. $18$

3. Which of the following is a perfect square?

1. $120$
2. $121$
3. $122$
4. $123$
5. $124$

4. Which of the following is equivalent to $3\sqrt{10}$

1. $3\sqrt{5} \times \sqrt{5}$
2. $\sqrt{90}$
3. $3\sqrt{5} + 3\sqrt{2}$
4. $3\sqrt{5}+3\sqrt{5}$
5. $\frac{3\sqrt{2}}{\sqrt{5}}$

5. Which of the following is equivalent to $10^{\frac{2}{5}}$

1. $\sqrt[5]{5}$
2. $\sqrt[5]{10}$
3. $\sqrt[5]{20}$
4. $\sqrt[5]{100}$
5. $\sqrt[5]{1000}$

6. Which of the following fractions is equivalent to $\frac{3}{6} \times \frac{2}{5}$?

1. $\frac{6}{30}$
2. $\frac{5}{30}$
3. $\frac{5}{11}$
4. $\frac{15}{12}$
5. $\frac{9}{30}$

7. Which of the following expressions is equivalent to $\frac{7}{6} \div \frac{5}{2}$?

1. $\frac{7}{30}+\frac{2}{30}$
2. $\frac{9}{6}+\frac{9}{5}$
3. $\frac{7}{8}+\frac{5}{8}$
4. $\frac{7}{6}+\frac{2}{5}$
5. $\frac{1}{7}+\frac{2}{35}$

8. If $3^{x}=729$, what is $x^{3}$?

9. What is the value of $||4|-|-7||$

1. $-11$
2. $-3$
3. $0$
4. $3$
5. $11$

10. What is the value of $(\sqrt{3}+\sqrt{5})^{2}-(\sqrt{8})^{2}$

1. $2\sqrt{15}$
2. $\sqrt{15}$
3. $0$
4. $15$
5. $30$

 1 B 2 D 3 B 4 B 5 D 6 A 7 E 8 125 9 D 10 A

### GMAT Practice Questions - 7 & Answer Key

1. Solve $15x-32=18-10x$

1. $-14$
2. $10$
3. $14$
4. $2$
5. $50$

2. Solve $\frac{x}{8}=\frac{x-2}{4}$

1. $12$
2. $4$
3. $6$
4. $-\frac{1}{2}$
5. $-6$

3. Which of the following are the factors of $t^{2}+8t+16$

1. $(t-4)(t-4)$
2. $(t-8)(t-2)$
3. $(t+8)(t+2)$
4. $(t+1)(t+16)$
5. $(t+4)(t+4)$

4. Solve for a in term of b, if $6a+12b=24$

1. $24-12b$
2. $2-\frac{1}{2}b$
3. $4-2b$
4. $24-18b$
5. $2b-4$

5. If $ax+2b=5c-dx$, what does x equal in terms of a, b, c, and d?

1. $5c-d-2b-a$
2. $a-d$
3. $(5c-2b)(a-d)$
4. $\frac{5c-d-2b}{a}$
5. $\frac{5c-2b}{a-d}$

6. If $(z-9)(z+3)=0$, what are the two possible values of z?

1. $z=-9$ abd $z=3$
2. $z=9$ abd $z=0$
3. $z=0$ abd $z=-3$
4. $z=9$ abd $z=-3$
5. $z=-12$ abd $z=12$

7. If $z^{2}-6z=16$, which of the following could be a value of $z^{2}+6z$?

1. $-8$
2. $112$
3. $110$
4. $18$
5. $108$

8. If $3\sqrt{ a}-10=2$, what is the value of a?

1. $16$
2. $4$
3. $32$
4. $64$
5. $12$

9. Given $\frac{(x+6)(x^{2}-2x-3)}{x^{2}+3x-18}=10$, find the value of x.

1. $18$
2. $4$
3. $12$
4. $9$
5. $12$

10. Solve the equation $\frac{5x}{8}-\frac{3x}{5}=2$.

1. $40$
2. $80$
3. $160$
4. $-80$
5. $20$

 1 D 2 B 3 E 4 C 5 E 6 D 7 B 8 A 9 D 10 B

### GMAT Practice Questions -6 & Answer Key

1. $2(5x-5)+5(2x+2)=$
1. $0$
2. $20x$
3. $20x-10$
4. $20x+10$
5. $10x^{2}+20+x+20$

2. If $x=a+2$, and $y=-8-a$ then $x+y=$

1. $6$
2. $10$
3. $2a-6$
4. $-10$
5. $-6$

3. If $x \ne -5$, then $\frac{x^{2}+3x-10}{x+5}-(x-2)=$

4. If $(a-\frac{1}{a})^{2}=8$, then $a^{2}+\frac{1}{a^{2}}=$

1. $8$
2. $6$
3. $10$
4. $12$
5. $100$

5. $(x+y)^{2}=16$, and $x^{2}+y^{2}=6$ then $xy=$

1. $5$
2. $10$
3. $6$
4. $4$
5. $16$

6. $(x+y)=2$, and $x^{2}-y^{2}=6$ then $x-y=$

1. $12$
2. $4$
3. $6$
4. $\frac{1}{3}$
5. $3$

7. $\frac{15y+3}{3}-5y=$

1. $1$
2. $0$
3. $10y+1$
4. $3$
5. $3y+1$

8. if $b^{2}-a^{2}=9$ then $5(a-b)(a+b)=$

1. $45$
2. $\frac{9}{5}$
3. $4$
4. $50$
5. $-45$

9. When $c \ne 3$, then $\frac{c^{2}-9}{c-3}=$

1. $c-3$
2. $1$
3. $c+3$
4. $3-c$
5. $o$

10. If $b>0$, and $b^{2}-1=10 \times 12$, then $b=$

1. $9$
2. $1$
3. $12$
4. $10$
5. $11$

 1 B 2 E 3 0 4 C 5 A 6 D 7 A 8 E 9 C 10 E

## Wednesday, July 27, 2011

### GRE Practice Questions -3

1. If $m=\frac{\sqrt{5}-3}{\sqrt{2}+1}$, then for which one of the following equals $m-3$

1. $\sqrt{10}-3\sqrt{2}-\sqrt{5}+3$
2. $\sqrt{10}-3\sqrt{2}-\sqrt{5}$
3. $\sqrt{10}-3\sqrt{2}+\sqrt{5}$
4. $\sqrt{10}-3\sqrt{2}-\sqrt{5}-6$
5. $\sqrt{10}+3\sqrt{2}-\sqrt{3}$

2. If $y < 0$ and $x$ is 7 more than the square of $y$, which one of the following expresses $y$ in terms of $x$?

1. $y=-\sqrt{x-7}$
2. $y=\sqrt{x-7}$
3. $y=\sqrt{x+7}$
4. $y=\sqrt{x^{2}-7}$
5. $y=-\sqrt{x^{2}-7}$
3. If $\sqrt[m]{125}=5^{3m}$ and $4^{m} > \frac{1}{2}$, then what is the value of $m$?

1. $-1$
2. $-\frac{1}{5}$
3. $0$
4. $\frac{1}{5}$
5. $1$
4. Column A Column B
$x^{2}(x^{5})^{2}$ $(x^{4})^{3}$

5. Column A Column B
$17^{\frac{1}{x}-\frac{1}{y}}$ $0 < x < y$ $17^{x-y}$

6.  1 A 2 B 3 E 4 C 5 A

## Monday, July 25, 2011

### GMAT Practice Questions -5

1. If $x \ne 3$, then $\frac{3x^{2}+18x+27}{(x+3)^{2}}$

1. $1$
2. $3$
3. $9$
4. $27$
5. $81$

2. If $\frac{x+5}{x-5}=y$, what is the value of $x$ in terms of $y$?

1. $-5-y$
2. $\frac{5}{y}$
3. $\sqrt{y^{2}+5}$
4. $\frac{-5y-5}{1-y}$
5. $\frac{-5y+5}{1-y}$

3. $\frac{1-\frac{1}{3}}{2}$

1. $3$
2. $\frac{2}{3}$
3. $\frac{3}{2}$
4. $\frac{1}{3}$
5. $\frac{1}{5}$

4. $\frac{\frac{1}{x}}{\frac{1}{y}-z}$

1. $\frac{xy}{y-xyz}$
2. $\frac{1}{xy-xyz}$
3. $\frac{y}{xyz+x}$
4. $\frac{y}{x-xyz}$
5. $\frac{x-xyz}{y}$

5. The average of $x$, $\frac{1}{x}$ and $\frac{1}{x^{2}}$ is

1. $\frac{1+x^{2}}{3x}$
2. $\frac{1+x^{2}+x^{3}}{3x^{2}}$
3. $\frac{1+x+x^{2}}{3x^{2}}$
4. $\frac{1-x+x^{2}}{3x}$
5. $\frac{1+x^{2}+x^{3}}{3}$

6. $\frac{1}{5}$ of $.01$ percent equals :

1. $.00002$
2. $.0002$
3. $.002$
4. $.02$
5. $.2$

7. $\frac{2^{a+1}-2^{a-1}}{2^{a+1}+2^{a-1}}$

1. $\frac{1}{4}$
2. $\frac{3}{5}$
3. $2$
4. $\frac{1}{2}$
5. $\frac{5}{3}$

8. If $x$ is $\frac{50}{51}$ of $\frac{51}{52}$ and $y=\frac{50}{51}$, then $\frac{x}{y}=$

1. $\frac{50}{51}$
2. $\frac{50}{52}$
3. $\frac{51}{52}$
4. $\frac{2550}{2500}$
5. $\frac{2601}{2704}$

9. The decimal $.01$ is how many times greater than the decimal $(.0001)^{4}$

1. $10^{6}$
2. $10^{8}$
3. $10^{10}$
4. $10^{12}$
5. $10^{14}$

10. Let $a=.79$, $b=\sqrt{.79}$ and $c=(.79)^{2}$, then which of the following is true?

1. $a < b < c$

2. $c < b < a$

3. $a < b < c$

4. $c < a < b$

5. $b < a < c$

 1 B 2 D 3 D 4 D 5 C 6 A 7 B 8 C 9 E 10 D

## Friday, July 22, 2011

### GMAT Practice Questions -4

1. If $n$ is a positive integer and $(n+3)(n+5)$ is odd, then $(n+4)(n+6)$ must be a multiple of which one of the following?

1. $3$
2. $5$
3. $7$
4. $8$
5. $16$

2. The number of prime numbers divisible par 2 plus the number of prime numbers divisible by 5 is

1. $0$
2. $1$
3. $2$
4. $3$
5. $4$

3. If $13x+17=0$, then $-13|x|$ equals which one of the following?

1. $-\frac{17}{13}$
2. $\frac{17}{13}$
3. $17$
4. $13$
5. $-17$

4. Which one of the following is divisible by both 2 and 3?

1. $1007$
2. $3096$
3. $1616$
4. $2306$
5. $1791$

5. Which one of the following equals the product of exactly two prime numbers?

1. $13.6$
2. $11.9$
3. $17.21$
4. $19.51$
5. $17.23$

6. If $m$, $n$, and $p$ are different prime numbers, then the least common multiple of the the three numbers must equal which one of the following?

1. $mn(p+n)$
2. $m+n+p$
3. $m+np$
4. $m+n-p$
5. $pnm$

7. Each of the positive integer $a$ and $b$ ends with the digit 3. With which one of the following numbers does $a-b$ ends?

1. $0$
2. $1$
3. $2$
4. $3$
5. $4$

8. If $p-10$ is divisible by 4, then which one of the following must be divisible by 4?

1. $p$
2. $p-2$
3. $p-6$
4. $p+3$
5. $p+8$

## Wednesday, July 20, 2011

### GMAT Practice Questions -3

1. If $a+5a$ is 6 less than $b+5b$, then $a-b=$

1. $6$
2. $-1$
3. $-\frac{1}{6}$
4. $\frac{1}{6}$
5. $-6$

2. If $w \ne 0$, $w=5x=\sqrt{5}y$, what is the value of $w-x$ in terms of $y$?

1. $5y$
2. $\frac{\sqrt{5}}{5}y$
3. $\sqrt{5y}$
4. $\frac{5}{4\sqrt{5}}y$
5. $\frac{4\sqrt{5}}{5}y$

3. If $(a-1)(a+5)(a-7)=0$, and $a < 0$, then $a=$

1. $-1$

2. $-7$

3. $-5$

4. $-3$

5. $-2$

4. A aytem of equations is as shown below
$x-l=8$
$x+m=7$
$x-p=6$
$x+q=5$
What is the value of $l+m+p+q$?

1. $-4$
2. $-3$
3. $-2$
4. $-1$
5. $0$

5. If $\frac{a^{2}-25}{20a}=\frac{a-5}{a+5}$, $a=5 \ne 0$, and $a \ne 0$, then $a=$

1. $1$
2. $3$
3. $5$
4. $20$
5. $25$

6. If $a$, $b$, $c$,and $d$ are not equal to 0 or 1, and if $a^{x}=b$, $b^{y}=c$, $c^{z}=d$ and $d^{t}=a$, then $xyzt=$

1. $0$
2. $1$
3. $abc$
4. $abcd$
5. $a^{b^{c^{d}}}$

7. If $(x-3y)(x+3y)=-9$ and $(3x-y)(3x+y)=-1$, then $\frac{x^{2}+y^{2}}{x^{2}-y^{2}}=$

1. $-2$
2. $-1$
3. $0$
4. $1$
5. $2$

8. If $p-q=5$ and $pq=11$, then is the value of $\frac{1}{p^{2}}+\frac{1}{q^{2}}$?

1. $\frac{25}{121}$
2. $-\frac{47}{121}$
3. $\frac{5}{11}$
4. $-\frac{5}{11}$
5. $\frac{47}{121}$

## Sunday, July 17, 2011

### GMAT Practice Questions -2

1. If n is an integer, which of the following CANNOT be an integer?

1. $\frac{n+2}{2}$
2. $\sqrt{n+1}$
3. $\frac{3}{n+2}$
4. $\sqrt{n^{2}+5}$
5. $\sqrt{\frac{1}{n^{2}+3}}$

2. If n is an integer, which one of the following is an odd integer?

1. $n^{2}$
2. $\frac{n+3}{2}$
3. $-2n-8$
4. $n^{2}-3$
5. $\sqrt{n^{4}+1}$

3. If $x$, $y$, $z$ and $t$ are positive integers such that $x < y < z < t$ and $x+y+z+t=10$, then what is the value of $t$?

1. $2$

2. $3$

3. $4$

4. $5$

5. $6$

4. The remainder when the positive integer $m$ is divided by $n$ is r. What is the remainder when $3m$ is divided by $3n$?

1. $r$
2. $3r$
3. $3n$
4. $m-3n$
5. $3(m-nr)$

5. If $(x-5)(x+4)=(x-4)(x+5)$, then $x=$

1. $-5$
2. $-4$
3. $0$
4. $4$
5. $5$

6. If $(3x-1)^{2}=121$, then which one of the following COULD equal x?

1. $-4$
2. $\frac{10}{3}$
3. $\frac{13}{3}$
4. $-\frac{10}{3}$
5. $\frac{17}{3}$

7. (The average of 5 consecutive integers starting from 17)-(The average of 6 consecutive integers starting from 17)=

1. $-\frac{1}{8}$
2. $-\frac{1}{2}$
3. $0$
4. $\frac{1}{8}$
5. $\frac{1}{2}$

8. If $n^{3}+n^{2}-n-2=-1$, then which one of the following could be the value of $n$

1. $0$
2. $1$
3. $2$
4. $3$
5. $4$

9. Solve the the system of equations given?
$x+3y=8$
$x+2y=5$

1. $-1,4$
2. $1,3$
3. $2,3$
4. $1,-3$
5. $-1,3$

10. If $(a-b)(a+b)=7 \times 3$ then $a$ and $b$ equals respectively?

1. $-5,-2$
2. $5,3$
3. $7,2$
4. $9,2$
5. $-3,-10$