GMAT Math : Problem-Solving Questions

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Example Questions

Example Question #145 : Arithmetic

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:

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

$40N \; \textrm{mi}$

$90N \; \textrm{mi}$

$45N \; \textrm{mi}$

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

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 #146 : Arithmetic

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.

$\$ 70.83$

$\$ 141.18$

$\$ 11.76$

$\$ 85.00$

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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Example Question #1 : Ratio & Proportions

In a certain classroom all of the students are either sophomores or juniors. The number of boys and girls in the classroom are equal. Of the girls, $\dpi{80} \frac{3}{7}$ are sophomores, and there are 24 junior boys. If the number of junior boys in the classroom are in the same proportion to the total amount of boys as the number of sophomore girls are to the total number of girls, how many students are in the classroom?

Possible Answers:

168

112

Correct answer:

112

Explanation:

This question seems convoluted but is actually more simple than it seems. We are told that the number of girls and boys in the classroom are equal and that $\frac{3}{7}$ of the girls are sophomores. We are then told that 24 of the boys are juniors, and that they represent a proportion of total boys equal to the proportion of sophomore girls to total girls. This means that:

$\frac{24}{x} = \frac{3}{7}$ ==> x = 56 where is the total number of boys.

If we know that the number of boys and girls in the class are equal, then the total number of students in the class = 112.

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Example Question #1 : Calculating Ratio And Proportion

The Duchy of Grand Fenwick uses an unusual currency system. It takes 24 tiny fenwicks to make a big fenwick.

At current exchange rates, 1 big fenwick can be exchanged for $3.26 American currency. For how much in Grand Fenwick currency can an American tourist exchange $300 (rounded to the nearest tiny fenwick)?

Possible Answers:

92 big fenwicks and 1 tiny fenwick

108 big fenwicks and 16 tiny fenwicks

None of the other choices gives the correct amount of currency.

296 big fenwicks and 16 tiny fenwicks

40 big fenwicks and 18 tiny fenwicks

Correct answer:

92 big fenwicks and 1 tiny fenwick

Explanation:

$3.26 can be exchanged for 1 big fenwick, or, equivalently, 24 tiny fenwicks. We can set up a proportion statement, where is the number of tiny fenwicks for which $300 can be exchanged:

$\frac{F}{300} = \frac{24}{3.26}$

Solve for :

$\frac{F}{300} \cdot 300 = \frac{24}{3.26} \cdot 300$

$F= \frac{24\cdot 300}{3.26} \approx 2,209$

The answer is 2,209 tiny fenwicks, which can be counted up with division:

$2,209 \div 24 = 92 \textrm{ R 1}$

or 92 big fenwicks and 1 tiny fenwick.

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Example Question #2 : Calculating Ratio And Proportion

Five different pizza places offer five different specials. Assuming that all of these pizzas are of the same thickness and that all are of the same quality, which of the following is the best buy?

Possible Answers:

A 9 inch by 9 inch square pizza for $6.99

A 12 inch by 8 inch rectangular pizza for $9.99

A round pizza 12 inches in diameter for $8.99

A round pizza 10 inches in diameter for $5.99

A 10 inch by 10 inch square pizza for $7.99

Correct answer:

A round pizza 10 inches in diameter for $5.99

Explanation:

Since all of the pizzas are of the same thickness and quality, to determine the best bargain, calculate the price per square inch of each. The least amount will mark the best bargain.

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A round pizza 10 inches in diameter for $5.99:

The area of the pizza in square inches is $A = \pi r^{2} = \pi \cdot5^{2} = 25\pi$

The cost per square inch: $5.99\div25\pi =0.076$ or 7.6 cents

A round pizza 12 inches in diameter for $8.99

The area of the pizza in square inches is $A = \pi r^{2} = \pi \cdot6^{2} =36\pi$

The cost per square inch: $8.99\div36\pi =0.079$ or 7.9 cents

A 9 inch by 9 inch square pizza for $6.99

The area of the pizza in square inches is $9 \cdot 9 = 81$

The cost per square inch: $6.99 \div 81 = 0.086$ or 8.6 cents

A 10 inch by 10 inch square pizza for $7.99

The area of the pizza in square inches is $10 \cdot 10 = 100$

The cost per square inch: $7.99 \div 100 = 0.080$ or 8.0 cents

A 12 inch by 8 inch rectangular pizza for $9.99:

The area of the pizza in square inches is $12 \cdot 8 = 96$

The cost per square inch: $9.99 \div 96 = 0.104$ or 10.4 cents

The round pizza 10 inches in diameter for $5.99 is the best buy.

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Example Question #1701 : Problem Solving Questions

A fathom is a unit of underwater depth equal to six feet.

Express two miles in fathoms.

Possible Answers:

$2,060 \textrm{ fathoms}$

$1,860 \textrm{ fathoms}$

$1,760 \textrm{ fathoms}$

$1,660 \textrm{ fathoms}$

$1,960 \textrm{ fathoms}$

Correct answer:

$1,760 \textrm{ fathoms}$

Explanation:

Multiply 2 miles by 5,280 feet per mile, then divide by 6 feet per fathom:

$(2 \times 5,280) \div 6 = 10,560 \div 6 = 1,760 \textrm{ fathoms}$

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Example Question #1702 : Problem Solving Questions

A furlong is a measure of length used in horse racing. Eight furlongs are equal to one mile.

Express 20 furlongs in feet.

Possible Answers:

$15,840 \textrm{ ft }$

$10,700 \textrm{ ft}$

$10,560 \textrm{ ft}$

$13,200 \textrm{ ft}$

$7,920 \textrm{ ft}$

Correct answer:

$13,200 \textrm{ ft}$

Explanation:

Divide 20 furlongs by 8 furlongs per mile, then multiply by 5,280 feet per mile.

$\frac{20}{8} \times 5,280 = 2.5 \times 5,280 = 13,200$

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Example Question #13 : Calculating Ratio And Proportion

127 people signed up for a subscription service. 45 signed up for weekly deliveries, 34 for monthly deliveries, and the rest for annual deliveries. What is the ratio of weekly subscribers to annual subscribers?

Possible Answers:

45:127