GMAT Math : Arithmetic

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Example Questions

Example Question #141 : Arithmetic

Jill buys a new tablet for $\$156.45$ . If she used a coupon and received $\$35$ off of the original price, what was the percent discount she received?

Possible Answers:

$18.3\%$

$35.5\%$

$22.4\%$

$77.6\%$

Correct answer:

$18.3\%$

Explanation:

Jill buys a new tablet for $\$156.45$ . If she used a coupon and received $\$35$ off of the original price, what was the percent discount she received?

So, to find percent discount, we need to calculate the original price.

156.45+35=191.45

Then, we need to find the percent of the discount. To do so, simply divide the amount of the discount by the original amount, then multiply by 100

$\frac{35}{191.45}*100=18.3\%$

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Example Question #61 : Percents

$12\%$ of a certain number is 138 . What is the number?

Possible Answers:

11.5

126

1656

1150

16.56

Correct answer:

1150

Explanation:

Here, we need to first convert the percent into a fraction. Then, we will solve the equation. $12\%=\frac{12}{100}.$ Our number is unknown, so I will call it

$\frac{12x}{100}=138.$ $x=\frac{138*100}{12}=1150.$

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Example Question #1691 : Problem Solving Questions

Given a number , which of these is the greatest quantity of the three?

(a) 30% of 40% of 50% of

(b) 40% of 50% of 30% of

Possible Answers:

30% of 40% of 50% of

50% of 30% of 40% of

40% of 50% of 30% of

It is impossible to tell without knowing the value of

All three are equal to one another

Correct answer:

All three are equal to one another

Explanation:

All three are equal.

30% of 40% of 50% of is $\frac{3}{10}$ of $\frac{2}{5}$ of $\frac{1}{2}$ of : that is, $\frac{3}{10} \cdot\frac{2}{5}\cdot\frac{1}{2} \cdot x = \frac{6}{100} x$

40% of 50% of 30% of is $\frac{2}{5}$ of $\frac{1}{2}$ of $\frac{3}{10}$ of : that is, $\frac {2}{5} \cdot\frac{1}{2} \cdot\ \frac{3}{10} \cdot x = \frac{6}{100} x$

50% of 30% of 40% of is $\frac{1}{2}$ of $\frac{3}{10}$ of $\frac{2}{5}$ of : that is $\frac{1}{2} \cdot\ \frac{3}{10} \cdot \frac {2}{5} \cdot x = \frac{6}{100} x$

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Example Question #1 : Ratio & Proportions

The ratio 4 to $\frac{1}{4}$ is equal to which of the following ratios?

Possible Answers:

$\dpi{100} \small 16$ to $\dpi{100} \small 3$

$\dpi{100} \small 8$ to $\dpi{100} \small 1$

$\dpi{100} \small 6$ to $\dpi{100} \small 1$

$\dpi{100} \small 16$ to $\dpi{100} \small 1$

$\dpi{100} \small 12$ to $\dpi{100} \small 1$

Correct answer:

$\dpi{100} \small 16$ to $\dpi{100} \small 1$

Explanation:

The ratio $\dpi{100} \small 4$ to $\frac{1}{4}$ is equal to $\frac{4}{\frac{1}{4}}$ which is $4\left ( \frac{4}{1} \right )= 16$ .

$\dpi{100} \small 16$ can be written as the ratio $\dpi{100} \small 16$ to $\dpi{100} \small 1$ .

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Example Question #1 : Ratio & Proportions

The annual budget for a road construction project is $25,200 budgeted equally over 12 months. If by the end of the third month the actual expenses have been $7,420, how much has the construction project gone over budget?

Possible Answers:

$\dpi{100} \small \$2150$

$\dpi{100} \small \$3340$

$\dpi{100} \small \$ 1120$

$\dpi{100} \small \$ 980$

$\dpi{100} \small \$1640$

Correct answer:

$\dpi{100} \small \$ 1120$

Explanation:

The monthly budget is found by:

$\frac{25,200}{12}=2,100$

which for 3 months is a budget of:

$2,100\cdot 3= 6,300$

To find out how much they are over budget the budgeted amount is subtracted from the actual expenses.
$7,420 - 6,300 = 1,120$

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Example Question #2 : Ratio & Proportions

The ratio $\dpi{100} \small 3$ to $\dpi{100} \small \frac{1}{2}$ is equal to the ratio:

Possible Answers:

$\dpi{100} \small 3\ to\ 2$

$\dpi{100} \small 5\ to\ 1$

$\dpi{100} \small 1\ to\ 6$

$\dpi{100} \small 6\ to\ 1$

$\dpi{100} \small 2\ to\ 3$

Correct answer:

$\dpi{100} \small 6\ to\ 1$

Explanation:

The ratio $\dpi{100} \small 3$ to $\dpi{100} \small \frac{1}{2}$ is the same as $\dpi{100} \small \frac{3}{\frac{1}{2}}=3\times \frac{2}{1}=6$ ,
which equals a ratio of $\dpi{100} \small 6$ to $\dpi{100} \small 1$ .

Also, if you double both sides of the ratio, you get $\dpi{100} \small 6$ to $\dpi{100} \small 1$ .

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Example Question #1 : Calculating Ratio And Proportion

Nishita has necklaces, bracelets, and rings in a ratio of 7:5:4. If she has 64 jewelry items total, how many bracelets does she have?

Possible Answers:

Correct answer:

Explanation:

7x + 5x+4x= 64

16x=64

x=4

bracelets: 5x=5(4)=20

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Example Question #4 : Ratio & Proportions

A box contains red and blue marbles. The probablity of picking a red is $\frac{1}{3}$ . There are 30 blue marbles. How many total marbles are there?

Possible Answers:

Correct answer:

Explanation:

If $\frac{1}{3}$ are red, then $\frac{2}{3}$ are blue, and the number of blue marbles can be written as

$blue=\frac{2}{3}*total marbles$

Plug in the number of blue marbles, 30, and solve for the total marbles.

$30 = \frac{2}{3}*total\rightarrow total = \frac{30}{\frac{2}{3}} =45 marbles$

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Example Question #1 : Ratio & Proportions

On a map, one and a half inches represents sixty actual miles. In terms of , what distance in actual miles is represented by inches on the map?

Possible Answers:

$40N \; \textrm{mi}$

$\frac{40 }{N}\; \textrm{mi}$

$\frac{90 }{N}\; \textrm{mi}$

$90N \; \textrm{mi}$

$45N \; \textrm{mi}$

Correct answer:

$40N \; \textrm{mi}$

Explanation:

Let be the number of actual miles. Then the proportion statement to be set up, with each ratio being number of actual miles to number of map inches, is:

$\frac{60}{1\tfrac{1}{2}} = \frac{x}{N}$

Simplify the left expression and solve for

$\frac{x}{N} = \frac{60}{1\tfrac{1}{2}} = 60 \div \frac{3}{2} =60 \cdot \frac{2}{3}$

$\frac{x}{N} = 40$

x = 40N

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Example Question #5 : Ratio & Proportions

The Kingdom of Zenda uses an unusual currency system. It takes 16 kronkheits to make a grotnik and 12 grotniks to make a gazoo.

At current, $1 can be exchanged for 8 grotniks and 8 kronkheits. For how much American currency can a visitor from Zenda exchange a 100-gazoo bill, to the nearest cent?

Possible Answers:

None of the other choices is the correct amount.

$\$ 85.00$

$\$ 11.76$

$\$ 141.18$

$\$ 70.83$

Correct answer:

$\$ 141.18$

Explanation:

$1 can be exchanged for 8 grotniks and 8 kronkheits, or, equivalently, 8.5 grotniks (8 kronkheits is one-half of a grotnik). 100 gazoos is equal to $100 \cdot 12 = 1,200$ grotniks. Therefore, if is the number of dollars that can be exchanged for the 100-gazoo bill, we can set up the proportion:

$\frac{D}{1,200} = \frac{1}{8.5}$

Solve for :

$\frac{D}{1,200} \cdot 1,200 = \frac{1}{8.5}\cdot 1,200$

$D = \frac{1,200}{8.5} \approx 141.18$

That is, the 100-gazoo bill can be exchanged for $141.18.

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GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #141 : Arithmetic

Example Question #61 : Percents

Example Question #1691 : Problem Solving Questions

Example Question #1 : Ratio & Proportions

Example Question #1 : Ratio & Proportions

Example Question #2 : Ratio & Proportions

Example Question #1 : Calculating Ratio And Proportion

Example Question #4 : Ratio & Proportions

Example Question #1 : Ratio & Proportions

Example Question #5 : Ratio & Proportions

All GMAT Math Resources

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