GMAT Math : GMAT Quantitative Reasoning

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Example Questions

Example Question #25 : Discrete Probability

Three boxes contain marbles, each one either red or white.

Box 1 contains 20 red marbles and 10 white marbles.

Box 2 contains 30 red marbles and 10 white marbles.

Box 3 conatins 40 red marbles and 10 white marbles.

One of three boxes is selected at random, and one marble is selected from that box at random. What is the probability that a white marble will be selected?

Possible Answers:

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{47}{90}$

$\frac{47}{180}$

$\frac{47}{120}$

Correct answer:

$\frac{47}{180}$

Explanation:

This is a conditional probability problem.

Each box can be selected with probability $\frac{1}{3}$ .

If Box 1 is selected, the probability of selecting a white marble is $\frac{10}{30} =\frac{1}{3}$ . The overall probability of selecting Box 1, then a white marble, is $\frac{1}{3} \cdot \frac{1}{3} = \frac{1}{9}$ .

If Box 2 is selected, the probability of selecting a white marble is $\frac{10}{40} =\frac{1}{4}$ . The overall probability of selecting Box 2, then a white marble, is $\frac{1}{3} \cdot \frac{1}{4} = \frac{1}{12}$ .

If Box 3 is selected, the probability of selecting a white marble is $\frac{10}{50} =\frac{1}{5}$ . The overall probability of selecting Box 2, then a white marble, is $\frac{1}{3} \cdot \frac{1}{5} = \frac{1}{15}$ .

The overall probability of selecting a white marble is the sum of these probabilities:

$\frac{1}{9} +\frac{1}{12} + \frac{1}{15} = \frac{20}{180} +\frac{15}{180} + \frac{12}{180}= \frac{47}{180}$

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Example Question #26 : Discrete Probability

Two fair six-sided dice are altered. One of them has its "6" changed to a "1"; the other has its "1" changed to a "6". The dice are tossed and their sum is noted.

What is the probability that the sum will be 7?

Possible Answers:

$\frac{2}{9}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{7}{36}$

$\frac{1}{6}$

Correct answer:

$\frac{2}{9}$

Explanation:

We will call the faces of the first die (the one with two 1's and no 6) 1A, 1B, 2, 3, 4, 5; we will call the faces of the second die (the one with two 6's and no 1) 2, 3, 4, 5, 6A, 6B.

A seven can be rolled in the following ways - with the outcome of the first die and the second die listed in that order:

$\left \{ 1A, 6A\right \}$

$\left \{ 1A, 6B\right \}$

$\left \{ 1B, 6A\right \}$

$\left \{ 1B, 6B\right \}$

$\left \{ 2,5\right \}$

$\left \{ 3,4\right \}$

$\left \{ 4,3\right \}$

$\left \{ 5,2\right \}$

Note that a 6 cannot be rolled on the first die, nor can a 1 be rolled on the second.

This makes 8 rolls out of 36 that can result in a 7; since the dice are fair, the probability of rolling one of these results is $\frac{8}{36} = \frac{2}{9}$

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Example Question #22 : Calculating Discrete Probability

What is the probability of drawing a red king in a standard card deck?

Possible Answers:

$\frac{1}{13}$

$\frac{1}{26}$

$\frac{4}{13}$

$\frac{1}{52}$

Correct answer:

$\frac{1}{26}$

Explanation:

There are red kings in a standard deck of cards, therefore the probability of drawing red kings is $\frac{2}{52}$ which simplifies to $\frac{1}{26}$ .

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Example Question #1821 : Gmat Quantitative Reasoning

A box contains tickets numbered 01-50 . What is the probability of randomly selecting a ticket that has a in the ones place?

Possible Answers:

$20\%$

$50\%$

$5\%$

$10\%$

Correct answer:

$10\%$

Explanation:

From 01-50 , there are tickets that will have a in the ones place: 2,12,22,32,42 .

Therefore the probability of drawing a ticket with a in the ones place is $\frac{5}{50}$ which is 10%.

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Example Question #27 : Discrete Probability

If N is a number chosen at random from the set [3, -7, 12, 8, 11] , and P is a number chosen at random from the set [1, 2, 0, 9] , what is the probability that

N+P=12 ?

Possible Answers:

0.12

0.15

0.85

0.24

0.25

Correct answer:

0.15

Explanation:

The total possible pairs of numbers for the two sets is 20, since there are 5 numbers in the first set and 4 numbers in the second set. Total possible outcomes are found by multiplying the number of terms in each set together.

5x4=20, so there are 20 possible pairs.

How many pairs sum to 12?

There are three pairs that work: 3 from the first set and 9 from the second, 12 from the first set and 0 from the second, and 11 from the first set and 1 from the second.

Since 3 out of 20 pairs sum to twelve, the probability of N+P=12 is:

$\frac{3}{20}=0.15$

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Example Question #272 : Arithmetic

Jane has toy cars. of them are trucks and are race cars. are blue, are green, are orange, and are red.

What is the probability of having a blue car OR a race car?

Possible Answers:

$\frac{7}{10}$

$\frac{3}{20}$

$\frac{7}{20}$

$\frac{12}{20}$

$\frac{17}{20}$

Correct answer:

$\frac{7}{10}$

Explanation:

P(Blue Car OR Race Car) = P(Blue Car) + P(Race Car) - P(Blue Race Car)

P(Blue Car) = 5/20

P(Race Car) = 12/20

P(Blue Race Car) $= 5/20 \times 12/20 = 1/4 \times 3/5 = 3/20$

So P(Blue Car OR Race Car) = 5/20 + 12/20 - 3/20 = (5+12-3)/20 = 14/20 = 7/10

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Example Question #31 : Discrete Probability

In a 10,000 students university, in students will drop out of college. What is the probability that a randomly selected student will not drop out of college?

Possible Answers:

$\frac{3}{4}$

$\frac{2}{5}$

$\frac{1}{4}$

$\frac{3}{5}$

Correct answer:

$\frac{3}{4}$

Explanation:

The probability of students who will drop out is 1/4.

Therefore, we are looking for the probability that a student will NOT drop out, which is 3/4.

A randomly selected student will not drop out of college with a probability of 3/4.

$p=1-\frac{1}{4}=\frac{3}{4}$

The fact that there is 10,000 students in the school is not relevant to calculate this probability.

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Example Question #32 : Discrete Probability

Of 100 students accepted for a masters degree program this fall semester, 30 do not have any work experience, 10 have two years of work experience, 15 have four years of work experience, and all of the other students have over seven years of work experience. What is the probability that a randomly selected student in the 100 who have been accepted for the program will have at least four years of work experience?

Possible Answers:

0.15

0.6

0.3

0.4

0.45

Correct answer:

0.6

Explanation:

The number of students who have over seven years of experience is:

100-30-10-15=100-55=45

The probability that a randomly selected student has at least four years of experience is:

Formula

Substituting in our values for these variables, we get:

$\frac{15+45}{100}=\frac{60}{100}=0.6$

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Example Question #1821 : Problem Solving Questions

An auto insurer underwrites its 60 customers and classifies them in 3 mutually exclusive risk classes. 15 of the customers are in the high-risk class, 35 are in the moderate-risk class, and 10 are in the low-risk class. What is the probability that a randomly selected customer will be in the moderate- or high-risk class?

Possible Answers:

$\frac{2}{3}$

$\frac{1}{6}$

$\frac{7}{48}$

$\frac{1}{2}$

$\frac{5}{6}$

Correct answer:

$\frac{5}{6}$

Explanation:

The probability that a randomly selected customer is in the moderate- or high-risk class is simply the sum of the number of clients in the moderate-risk class and the number of clients in the high-risk class divided by the total number of clients:

$\frac{15+35}{60}=\frac{50}{60}=\frac{5}{6}$

This is also equivalent to just summing up the probability of being in the high-risk class and the probability of being in the moderate-risk class. Since the 3 classes are mutually exclusive, we do not have to worry about subtracting the probability of mutual elements.

$\frac{15}{60}+\frac{35}{60}=\frac{5}{6}$

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Example Question #31 : Discrete Probability

A university received 1000 applications for their MBA program this semester. Of all applicants, 150 had a GMAT score above 720. 620 applicants had a GMAT score between 640 and 720. 80 applicants had a score between 560 and 640. All other applicants had a score lower than 560. What is the probability that a randomly selected applicant will have a score lower than 560?

Possible Answers:

0.10

0.12

0.15

0.08

0.16

Correct answer:

0.15

Explanation:

The probability that a randomly selected applicant has a score lower than 560 is:

$\frac{1000-150-620-80}{1000}=\frac{150}{1000}=0.15$

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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 #25 : Discrete Probability

Example Question #26 : Discrete Probability

Example Question #22 : Calculating Discrete Probability

Example Question #1821 : Gmat Quantitative Reasoning

Example Question #27 : Discrete Probability

Example Question #272 : Arithmetic

Example Question #31 : Discrete Probability

Example Question #32 : Discrete Probability

Example Question #1821 : Problem Solving Questions

Example Question #31 : Discrete Probability

All GMAT Math Resources

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