GMAT Math : GMAT Quantitative Reasoning

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Example Question #2211 : Gmat Quantitative Reasoning

A lawn-mower is initially listed at . Its price is discounted $D\%$ off the full price. An employee uses their discount, $E\%$ , at the register and is charged .

In terms of , in dollars and in percent, what is the formula for the employee discount, in percent?

Possible Answers:

$E=\frac{P}{Q} (1-D/100)$

$E=100\cdot \left(1-\frac{P}{Q\cdot (1-D/100)}\right)$

$E=100\cdot \frac{P}{Q}\cdot (1-D/100)$

$E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$

$E=\frac{Q}{P}\cdot (1-D/100)$

Correct answer:

$E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$

Explanation:

The relationship between the price charged at the register after two discounts is computed by applying the rule for discounts serially.

$Q=P\cdot (1-D/100)\cdot (1-E/100)$

The factor of 100 converts to decimal values.

Rearranging algebraically and solving for , we obtain

$E= 100\cdot \left(1-\frac{Q}{P\cdot (1-D/100)} \right)$

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Example Question #2212 : Gmat Quantitative Reasoning

A sewing machine is initially listed at . Its price is discounted off the full price. It fails to sell and is placed in a location where all items are discounted off the already discounted ticket price. A customer carries it to the register and is charged .

In terms of , and dollars and in percent, what is the formula for the original discount, in percent?

Possible Answers:

$D= 100\cdot \left(1-\frac{Q}{P\cdot E/100} \right)$

$D= \left(1+\frac{Q}{P\cdot (1-E/100)} \right)$

$D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$

$D= \frac{100\cdot Q}{P\cdot (1-E/100)}$

$D= 100\cdot \left(1+\frac{Q}{P\cdot (1+E/100)} \right)$

Correct answer:

$D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$

Explanation:

The relationship between list price , the two serial discounts, and E and the price charged is found by applying the formula for an individual discount serially:

$Q=P\cdot (1-D/100)\cdot (1-E/100)$

The 100 represents the conversion from percent to decimal.

Rearranging to solve for results in

$D= 100\cdot \left(1-\frac{Q}{P\cdot (1-E/100)} \right)$

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Example Question #2213 : Gmat Quantitative Reasoning

A lawn-mower is initially listed at . Its the ticket lists a discount of off the full price. The item is placed in a 'extra discount' location where all prices are listed as being discounted off the listed ticket price.

The customer wants to know how much she saved, , in dollars. In terms of , and , with discounts and expressed in percent, what is the formula for dollar savings off the initial list price, ?

Possible Answers:

$S=P\cdot (D+E)$

$S=P\cdot \left(\frac{D}{100}+\frac{E}{100}\right)$

$S=P\cdot \left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)$

$S=P\cdot \left(1-\frac{D}{100}-\frac{E}{100}\right)$

$S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$

Correct answer:

$S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$

Explanation:

The price charged at the register, after two discounts is computed using the rule for a single discount applied serially.

$Q=P\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)$

The 100 represents the conversion from % to decimal.

The savings, , is the difference between the price charged and the list price. So,

$S=P\left(1-\left(1-\frac{D}{100}\right)\cdot \left(1-\frac{E}{100}\right)\right)$

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Example Question #2211 : Gmat Quantitative Reasoning

A lawn-mower is initially listed as in dollars $(\$)$ but then discounted $D\%$ . A customer wants to know how much she will save.

In terms of in dollars, and the discount in percent, what is the formula for savings, in dollars?

Possible Answers:

$S=P\cdot D/100$

$S= 100\cdot P\cdot (1-D/100)$

$S= P\cdot D$

$S= P\cdot (1-D)$

$S= P\cdot (1-D/100)$

Correct answer:

$S=P\cdot D/100$

Explanation:

When a single discount applies, the savings in dollars is the product of the discount, in $\%$ and the list price, in dolalrs:

$S=P\cdot D/100$

The factor of 100 represents the conversion from $\%$ to decimal.

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Example Question #2215 : Gmat Quantitative Reasoning

What is the new price on a car after a certain promotional offer is applied?

(1) The promotional offer is equivalent to a $4000 cash back card.

(2) The original price of the car is 1.2 times the new price after the promotional offer.

Possible Answers:

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are not sufficient.

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.

Each Statement ALONE is sufficient.

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.

Correct answer:

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Explanation:

(1) The promotional offer is equivalent to a $4000 cash back card.

Statement (1) alone is not sufficient because we do not know the original price of the car.

(2) The original price of the car is 1.2 times the new price after the promotional offer.

Using the information statement (2), we can write:

Let x be the original price of the car and y the price after the promotional offer

x=1.2y

Statement (2) alone is not sufficient.

Combining both statements:

y=x-4000

x=1.2(x-4000)

We can calculate the original price as:

x=1.2x-4800

-0.2x=-4800

x=24000

So we can find the new price:

y=24000-4000=20000

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Example Question #1 : Dsq: Understanding Measurement

A really backward country does not use inches, feet, yards, or meters to measure distance, it uses units called wumps and zumps. These units can also be used to form units of area and volume (i.e. square wumps, cubic zumps).

How many wumps are in one zump?

Statement 1: There are 361 square wumps in one square zump.

Statement 2: There are 6,859 cubic wumps in one cubic zump.

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

If there are wumps in a zump, then there are $N^{2}$ square wump in a square zump, and $N^{3}$ cubic wump in a cubic zump. Therefore, given the first statement, you can take the square root of the conversion factor to get the number of wumps in a zump; given the second, you can take the cube root of that conversion factor to the same end. In both cases you get 19.

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Example Question #1 : Dsq: Understanding Measurement

You are given a metal cube whose volume can be given by a whole number of cubic meters. What is its volume?

Statement 1: Each edge of the cube has length between 160 and 180 centimeters, inclusive.

Statement 2: The surface area of the cube is between 1,350 square decimeters and 1,944 square decimeters, inclusive.

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone. Each edge of the cube has length between 160 centimeters and 180 centimeters; since one meter is equal to 100 centimeters, the length of one edge falls between 1.6 meters and 1.8 meters. Its volume therefore falls between

$1.6^{3} = 4.096$ cubic meters

and

$1.8 ^{3}= 5.832$ cubic meters.

The only whole number of meters that falls between these boundaries is 5 meters, so the question is answered.

Assume Statement 2 alone. The minimum surface area of the cube is 1,350 square decimeters, so, to find the minumum length of an edge, use the surface area formula, setting A = 1,350 :

$6s^{2} = A$

$6s^{2} = 1,350$

$s^{2} = 225$

s = 15 decimeters; divide by 10 (decimeters per meter) to convert to 1.5 meters.

Similarly, to get the maximum edge length, set A= 1,944 :

$6s^{2} = A$

$6s^{2} = 1,944$

$s^{2} = 324$

s = 18 decimeters; divide by 10 to get 1.8 meters.

The volume of the cube therefore falls between

$1.5^{3} = 3.375$ cubic meters

and

$1.8 ^{3}= 5.832$ cubic meters.

This leaves us with two possible whole number answers, 4 and 5, so the question is not answered.

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Example Question #2218 : Gmat Quantitative Reasoning

You are given a square metal sheet whose area can be given by a whole number of square feet. What is the length of each side?

Statement 1: The length of each side is between 24 and 32 inches, inclusive.

Statement 2: The area of the sheet is no greater than one half of a square yard.

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Assume Statement 1 alone.

24 inches is equal to $24 \div 12 = 2$ feet, and 32 inches is equal to $32 \div 12 = 2\frac{2}{3}$ feet. If, as given in Statement 1, the length of each side of a square falls between these measures, the range of the area is as follows:

$2 \le s \le 2\frac{2}{3}$

$2^{2} \le s^{2} \le \left ( 2\frac{2}{3} \right )^{2}$

$4 \le A \le 7 \frac{1}{9}$

This gives us four possible whole numbers of square feet for the area - 4, 5, 6, and 7.

Assume Statement 2 alone. One yard comprises three feet, so one square yard comprises nine square feet. One half of a square yard is equal to half of nine, or four and a half, square feet. This allows us to narrow down the area to four whole numbers of square feet - 1, 2, 3, or 4.

Neither statement alone is sufficient, but both are - since 4 square feet is the only possibility that satisfies both statements, it can be found to be the answer to the question if both are assumed.

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Example Question #102 : Data Sufficiency Questions

You are given a metal cube whose volume can be given as a whole number of cubic yards. What is its volume?

Statement 1: Each edge has length between 6 feet and 7 feet, inclusive.

Statement 2: The area of each face of the cube is between $30\frac{1}{4}$ square feet and $42 \frac{1}{4}$ square feet, inclusive.

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume both statements are true. If we let be the length of one side in yards, then from Statement 1, we can divide maximum and minimum lengths by 3 to obtain

$2 \le s \le 2\frac{1}{3}$

From Statement 2 alone, We can take the square root of the maximum and minmum areas to obtain the maximum and minimum areas in feet, then divide by three to convert these to yards:

$30\frac{1}{4} \le A \le 42 \frac{1}{4}$

$\frac{121}{4} \le A \le \frac{169}{4}$

$\sqrt{\frac{121}{4}} \le\sqrt{ A} \le\sqrt{ \frac{169}{4}}$

$\frac{11}{2} \le s' \le \frac{13}{2}$

$\frac{11}{2} \div 3 \le s \le \frac{13}{2} \div 3$

$\frac{11}{6} \le s \le \frac{13}{6}$

$1\frac{5}{6} \le s \le 2 \frac{1}{6}$

(NOTE: is being used for sidelength in feet).

From the two statements together, we obtain

$2\le s \le 2 \frac{1}{6}$

The maximum and minimum values of the volume are the cubes of those of the sidelengths:

$2^{3} \le s^{3} \le \left (2 \frac{1}{6} \right )^{3}$

$8 \le V \le 10 \frac{37}{216}$

The volume must be a whole number of cubic yards, so it must be 8, 9, or 10 - but without additional information, we cannot narrow it down further.

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Example Question #2220 : Gmat Quantitative Reasoning

You are given a square metal sheet whose area can be given by a whole number of square feet. What is the length of each side?

Statement 1: The area of the sheet is between 3 square yards and 4 square yards inclusive.

Statement 2: Each side of the sheet measures between 60 and 72 inches inclusive.

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Examine Statement 1. One yard comprises three feet, so one square yard comprises nine square feet. Three square yards is equal to $3 \times 9 = 27$ square feet, and four square yards is equal to $4 \times 9 = 36$ square feet. Therefore, the area in feet is one of the whole numbers 27, 28, 29,...36 .

Examine Statement 2. 60 inches is equal to $60 \div 12 = 5$ feet, and 72 inches is equal to $72 \div 12 = 6$ square feet. The range of areas of the square sheet can be found as follows:

$5 \le s \le 6$

$5 ^{2} \le s ^{2} \le 6 ^{2}$

$25 \le A \le 36$

Therefore, the area in feet is one of the whole numbers 25,26,27 ,...36 .

Therefore, the two statements together yield ten possible answers - the whole numbers from 27 to 36.

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GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2211 : Gmat Quantitative Reasoning

Example Question #2212 : Gmat Quantitative Reasoning

Example Question #2213 : Gmat Quantitative Reasoning

Example Question #2211 : Gmat Quantitative Reasoning

Example Question #2215 : Gmat Quantitative Reasoning

Example Question #1 : Dsq: Understanding Measurement

Example Question #1 : Dsq: Understanding Measurement

Example Question #2218 : Gmat Quantitative Reasoning

Example Question #102 : Data Sufficiency Questions

Example Question #2220 : Gmat Quantitative Reasoning

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