GMAT Math : Word Problems

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Example Questions

Example Question #16 : Calculating Compound Interest

Carl's uncle invested money in some corporate bonds for his nephew the day Carl was born; the bonds paid 4% annual interest compounded continuously. No money was deposited or withdrawn over the next fifteen years. The current value of the bonds is $5,000.

Which of the following expressions is equal to the amount of money Carl's uncle invested initially?

Possible Answers:

$\frac{5,000 }{e^{0.6 }}$

$\frac{5,000 }{e^{1.6 }}$

$5,000 e^{0.6 }$

$5,000 \cdot 1 .04 ^{15 }$

$\frac{5,000}{ 1 .04 ^{15 }}$

Correct answer:

$\frac{5,000 }{e^{0.6 }}$

Explanation:

The formula for continuously compounded interest is

$A = P e^{rt}$

where is the current, or accrued, value of the investment, is the initial amount invested, or principal, is the annual rate expressed as a decimal, and is the number of years.

In this scenario,

A = 5,000 , r = 0.04, t = 15

The equation becomes

$5,000 = P e^{0.04 \cdot 15 }$

$5,000 = P e^{0.6 }$

$P = \frac{5,000 }{e^{0.6 }}$

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Example Question #17 : Calculating Compound Interest

An amount of money is invested in corporate bonds that pay 6% interest compounded monthly. Which of the following expressions would give the amount of time it would take for the money to double?

Possible Answers:

$\frac{ \ln 2}{0.06}$

$\frac{ \ln 2}{\ln 1.06}$

$\frac{ \ln 2}{1.06}$

$\frac{12 \ln 2}{\ln 1.005}$

$\frac{ \ln 2}{12 \ln 1.005}$

Correct answer:

$\frac{ \ln 2}{12 \ln 1.005}$

Explanation:

The formula for compound interest is

$A = P \left $1+ \frac{r}{n} \right $^{nt}$ ,

where is the current, or accrued, value of the investment, is the initial amount invested, or principal, is the annual rate expressed as a decimal, is the number of periods per year, and is the number of years.

In this scenario,

A=2P , r = 0.06, n = 12 , and is unknown.

The equation becomes

$2P = P \left $1+ \frac{0.06}{12} \right $^{12 t}$

$\frac{2P }{P}= \frac{P \left $1+ \frac{0.06}{12} \right $^{12 t}}{P}$

$2 = \left $1+ \frac{0.06}{12} \right $^{12 t}$

$2 = \left $1+ 0.005 \right $^{12 t}$

$2 = \left $1 .005 \right $^{12 t}$

$\ln 2 = \ln \left [ \left $1 .005 \right $^{12 t} \right ]$

$\ln 2 =12 t \ln 1.005$

$\frac{ \ln 2}{12 \ln 1.005} =\frac{12 t \ln 1.005}{12 \ln 1.005}$

$t = \frac{ \ln 2}{12 \ln 1.005}$

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Example Question #18 : Calculating Compound Interest

Five years ago today, Jimmy's grandfather deposited $5,000 into a college fund that yielded interest at an annual rate of 4.8% compounded monthly.

Assuming that no money has been deposited or withdrawn, which of the following expressions would have to be evaluated in order to calculate the amount of money in the account now?

Possible Answers:

$\frac{ 5,000 }{1.048^{5}}$

$5,000\cdot e^{0.24}$

$\frac{ 5,000 }{1.004 ^{60}}$

$5,000\cdot 1.004^{60}$

$5,000 \cdot 1.048 ^{5}$

Correct answer:

$5,000\cdot 1.004^{60}$

Explanation:

The formula for compound interest is

$A = P \left $1+ \frac{r}{n} \right $^{nt}$ ,

In this scenario,

P = 5,000, r = 0.048, n = 12, t = 5

Therefore,

$A = 5,000 \left $1+ \frac{0.048}{12} \right $^{12 \cdot 5}$

$= 5,000 \left $1+ 0.004 \right $^{60}$

$=5,000\cdot 1.004^{60}$

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Example Question #141 : Problem Solving Questions

Darin invested $4,000 in some corporate bonds that pay 6% annual interest compounded semiannually. what will be the value of the bonds after one year (nearest dollar)?

Possible Answers:

$\$4\textup{,}494$

$\$4\textup{,}244$

$\$4\textup{,}240$

$\$4\textup{,}120$

$\$4\textup{,}247$

Correct answer:

$\$4\textup{,}244$

Explanation:

The formula for compound interest is

$A = P \left $1+ \frac{r}{n} \right $^{nt}$ ,

In this scenario,

P = 4,000 , r=0.06, n = 2, t = 1 ,

so the equation to solve is

$A = 4,000 \left $1+ \frac{0.06}{2} \right $^{2 \cdot 1}$

$A = 4,000 \cdot 1.03 ^{2}$

$= 4,000 \cdot 1.0609$

=4,243.60

Round this to $4,244.

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Example Question #142 : Problem Solving Questions

Phillip invests $5,000 in a savings account at 5.64% per year interest, compounded monthly. If he does not withdraw or deposit any money, how much money will he have in the account at the end of five years?

Possible Answers:

$\$6,628.89$

$\$6,578.27$

$\$6,624.52$

$\$6,410.00$

None of the other answers are correct.

Correct answer:

$\$6,624.52$

Explanation:

Use the compound interest formula

$A = P \left ( 1+ \frac{r}{n} \right )^{nt}$

where P=5,000 , r=0.0564 , t=5 , and n=12

$A = 5,000\cdot \left ( 1+ \frac{0.0564}{12} \right )^{12 \cdot 5}$

$A = 5,000\cdot 1.0047 ^{60}$

$A = 5,000\cdot 1.3249 \approx 6624.52$

Phillip will have $6,624.52 in his account.

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Example Question #1 : Calculating Profit

Mark buys 1,000 shares of stock for the current stock price of $20 per share. If the stock price goes up to $25 per share, by what percentage does Mark increase his money?

Possible Answers:

125%

50%

25%

20%

100%

Correct answer:

25%

Explanation:

Mark spends $20 * 1,000 shares = $20,000. When the stock price increases to $25/share, he makes ($25 – $20) * 1,000 shares = $5,000.

$5,000 / $20,000 = $\dpi{100} \small \frac{1}{4}$ = 25%

He does NOT increase his money by 125%, which would mean an additional $25,000, not $5,000.

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Example Question #2 : Calculating Profit

Mary works at a clothing store. She makes $13/hour and works 40 hours a week. Working at the clothing store gives her a 25% discount on anything they sell. If she buys a sweater that retails for $50 and a jacket that retails for $144, what is her net profit for the week?

Possible Answers:

$\$390.50$

$\$326$

$\$374.50$

$\$400$

$\$520$

Correct answer:

$\$374.50$

Explanation:

Mary makes $13/hour and works 40 hours. So she makes

$\$13\cdot 40\ hours=\$520$ .

However, we need to subtract the cost of the items that she bought. If the sweater retails for $50, Mary buys it for $.75\cdot \50=\$37.50$ because of her 25% discount. Similarly, she buys the jacket for $.75\cdot 144=\$108$ . So her net profit is

$520-37.50-108=\$374.50$ .

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Example Question #1 : Calculating Profit

The profit equation for a certain manufacturing process is P(x)=500x-10,000 , where is the number of units.

How much money will the plant make/lose if it sells 100 units?

Possible Answers:

40,000

-40,000

-10,000

50,000

Correct answer:

40,000

Explanation:

P(x)=500x-10,000

P(x)=500(100)-10,000

P(x)=50,000-10,000

P(x)=40,000

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Example Question #2 : Calculating Profit

Company B produces toy trucks for a shopping mall at a cost of $7.00 each for the first 500 trucks and $5.00 for each additional truck. If 600 trucks were produced by Company B and sold for $15.00 each, what was Company B’s gross profit?

Possible Answers:

$\$0$

$\$4000$

$\$14,000$

$\$9000$

$\$5000$

Correct answer:

$\$5000$

Explanation:

First of all, we need to know that

$Gross\ Profit=Revenue-Total\ Cost$ .

There are 600 trucks produced. According to the question, the first 500 trucks cost $7.00 each. Therefore, the total cost of the first 500 trucks is $\$7.00\cdot 500=\$3500$ .

The other 100 trucks cost $5.00 each for a cost of $\$5.00\cdot 100=\$500$ .

Add these together to find the cost of the 600 trucks: $\$3500+\$500=\$4000$

The total profit is easier to calculate since the selling price doesn't change: $\$15.00\cdot 600=\$9000$

At this point we have both revenue and total cost, so the answer for gross profit is $\$9000-\$4000=\$5000$ .

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Example Question #3 : Calculating Profit

Abe is a big gambler. He is equally likely to win, lose, or break even. When he loses, his loss is $\$ 1000$ . When he wins, he either makes $\$ 500$ or $\$ 1000$ with equal probability. How much money does Abe win or lose on average?

Possible Answers:

Abe loses $100.

Abe wins $83.

Abe breaks even.

Abe loses $83.

Abe wins $200.

Correct answer:

Abe loses $83.

Explanation:

To find the average, multiply each expected profit or loss by its probability:

$\dpi{100} \small average = \frac{1}{3}\times (-1000)+\frac{1}{3}\times 0 + \frac{1}{6}\times 500 + \frac{1}{6}\times 1000 \approx -\$ 83$

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GMAT Math : Word Problems

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #16 : Calculating Compound Interest

Example Question #17 : Calculating Compound Interest

Example Question #18 : Calculating Compound Interest

Example Question #141 : Problem Solving Questions

Example Question #142 : Problem Solving Questions

Example Question #1 : Calculating Profit

Example Question #2 : Calculating Profit

Example Question #1 : Calculating Profit

Example Question #2 : Calculating Profit

Example Question #3 : Calculating Profit

All GMAT Math Resources

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