GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #3201 : Gmat Quantitative Reasoning

What is the probability that a patient admitted to a certain hospital will have 2 tests performed upon entering the hospital?

(1) A study conducted in the hospital revealed that  of the patients will have at least two tests performed.

(2) A study conducted in the hospital revealed that 1 in 5 patients will have 2 tests performed.

Possible Answers:

Each Statement ALONE is sufficient.

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

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

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

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

Correct answer:

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

Explanation:

(1) A study conducted in the hospital revealed that   of the patients will have at least two tests performed.

Using the information in Statement (1), we cannot find the probability of patients who have exactly two tests performed upon entering the hospital. The probability given in Statement (1) also includes patients who have more than 2 tests performed.

Therefore, Statement (1) Alone is not sufficient.

(2) A study conducted in the hospital revealed that 1 in 5 patients will have 2 tests performed.

Using Statement (2), we can calculate the probability that a patient entering the hospital will have exactly two tests performed as:

Example Question #112 : Arithmetic

What is the probability that a student guesses the correct answer to each question of a quiz? 

(1) There are only 3 questions on the quiz.

(2) Each question has 4 answer choices and only one choice is correct.

Possible Answers:

Each Statement ALONE is sufficient.

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

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

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not 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) There are only 3 questions on the quiz.

Using Statement (1), we know that the probability that the student guesses the correct answer to each question is the product of the probabilities of getting each individual question right (getting each question right constitutes independent events). That is:

Pr(Question1 Correct) x Pr(Question2 Correct) x Pr(Question3 Correct)

However Statement (1) Alone is not sufficient.

(2) Each question has 4 answer choices and only one choice is correct.

Using Statement (2), we know that the student has the same probability of getting each question right, which we calculate as:

Pr(Correct Answer)=

Still Statement (2) Alone is not Correct.

Combining Both statements, we find the probability of guessing each correct answer on the quiz as:

Therefore Both statements Together are sufficient but neither Statement Alone is sufficient.

 

Example Question #3201 : Gmat Quantitative Reasoning

Bronson has a box of 16 markers. The markers are green, red and yellow.

I) The number of green markers is twice the number of red markers

II) There are 4 yellow markers

What are the odds of pulling a yellow marker followed by a green marker followed by a red marker? (Assume no replacement.)

Possible Answers:

Neither statement is sufficient to answer the question. More information is needed.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Both statements are needed to answer the question.

Correct answer:

Both statements are needed to answer the question.

Explanation:

To find probability, we need to know the number of each color of marker. Statement I gives us a way to put the number of red markers in terms of green markers. Statement II tells us the number of yellow markers. Using Statement II, we can find out how many red and green markers we have together. Then we would have to use Statement I to find the number of red markers and green markers. Then we can calculate probability. There is no way to do it without both statements.

To recap:

Bronson has a box of 16 markers. The markers are green, red and yellow.

I) The number of green markers is twice the number of red markers

II) There are 4 yellow markers

What are the odds of pulling a yellow marker followed by a green marker followed by a red marker? (Assume no replacement.)

So:

So, we have 4 yellow markers, 4 red markers and 8 yellow markers.

To find the odds of three events, we need to multiply the probability of each event together. We assume no replacement, so for each event, our total number of outcomes decreases by one.

So, the odds are 4 in 105.

Example Question #61 : Discrete Probability

Two fair (but possibly, but not necessarily, altered) six-sided dice are tossed, and their sum is noted. Below is a probability table for all possible outcomes.

Which of these choices is a possibility for the numbers on the faces of the dice?

Possible Answers:

Correct answer:

Explanation:

According to the probability table, only an odd number can be rolled. Three of our choices can be eliminated immediately for this reason. 

If the dice have  on their faces, it is possible to roll a double 6 for a 12; if the dice have  or  on their faces, it it possible to roll a double 1 for a 2.

This leaves two possibilites. All we need to look at is the probability of rolling a 3 with each choice.

 

:

A 3 can only be rolled by rolling a 1 on the first die and a 2 on the second. The probability of doing this is 

 

:

Again, a 3 can only be rolled by rolling a 1 on the first die and a 2 on the second. The probability of doing this is 

.

The other probabilities can be confirmed to agree with the ones given in the conditions in the problem. This is the correct choice.

 

Example Question #1092 : Data Sufficiency Questions

Janice has a cooler with bottles of water, cola, and root beer. What are the odds of choosing a water bottle followed by a bottle of root beer?

I) There are 5 times more bottles of root beer than water.

II) There are 75 beverages total in the cooler.

Possible Answers:

Either statement is sufficient to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Both statements are needed to answer the question.

Correct answer:

Neither statement is sufficient to answer the question. More information is needed.

Explanation:

Janice has a cooler with bottles of water, cola, and root beer. What are the odds of choosing a water bottle followed by a bottle of root beer?

I) There are 5 times more bottles of root beer than water.

II) There are 75 beverages total in the cooler.

To calculate probabilty, we need to know the number of desired outcomes and the total number of outcomes. 

II) gives us the number of total possible outcomes.

I) gives us a clue about the number of desired outcomes, but it is insufficient  to find the actual number of root beers and waters.

Therefore 

Neither statement is sufficient to answer the question. More information is needed.

Example Question #61 : Discrete Probability

A coin is flipped five times. What is the probability of it landing tails exactly three times?

Possible Answers:

Correct answer:

Explanation:

Since this problem deals with a probability with two potential outcomes, it is a binomial distribution, and so the probability of an event is given as:

where  is the number of events,  is the number of "successes" (in this case, a "heads" outcome), and  is the probability of success (in this case, fifty percent).

Thus, the probability of three heads in five flips is:

Example Question #62 : Discrete Probability

What is the probability of drawing a card that is blue or has a value of nine from a deck of mystery cards?

1) The probability of drawing a blue card is , and the probability of drawing a nine is 

2) The probability of drawing a blue nine is 

Possible Answers:

Statement 2 alone is sufficient.

Together the two statements are sufficient.

Neither of the statements, separate or together, is sufficient.

Either of the statements is sufficient.

Statement 1 alone is sufficient.

Correct answer:

Together the two statements are sufficient.

Explanation:

The probability of either of two events happening, the union, is given by the formula:

Because we are not told that drawing a blue and drawing a nine are mutually exclusive events, we must know the probability of the intersection, of drawing a blue nine.

Example Question #1101 : Data Sufficiency Questions

Twelve indepent trials are run, testing the reliability of a new engine part. What is the probability that the part will fail less than half of the time?

1) The probability that the part will fail three times in six trials is 

2) The probability of the part not failing is 

Possible Answers:

Either of the statements is sufficient.

Statement 2 alone is sufficient.

Together the two statements are sufficient.

Statement 1 alone is sufficient.

Neither of the statements, separate or together, is sufficient.

Correct answer:

Either of the statements is sufficient.

Explanation:

Since this probability question deals with successes and failures, it regards binomial distributions:

Where   is the number of trials,  is the number of 'successes,'  is the probability of exactly  successes in  trials, and  is the probability of a success occuring.

Statement 1 allows for a calculation of  to be used in the probability calculation for the problem.

Statement 2 outright gives a  to calculate the probability asked of in the problem.

Example Question #62 : Discrete Probability

The problem of an engine part performing succesfully is . A researcher performs a series of tests. Given  trials, P is the probability of the part succeeding at least once. Is  ?

1) 

1) 

Possible Answers:

Statement 2 alone is sufficient.

Either of the statements is sufficient.

Neither of the statements, separate or together, is sufficient.

Statement 1 alone is sufficient.

Together the two statements are sufficient.

Correct answer:

Statement 1 alone is sufficient.

Explanation:

Since this probability question deals with successes and failures, it regards binomial distributions:

Where   is the number of trials,  is the number of 'successes,'  is the probability of exactly  successes in  trials, and  is the probability of a success occuring.

The probability of at least one success is the complement of exactly zero successes. Since we're looking at 3 trials, we can find the probability of zero successes to be  and thus the complement, our .

For fewer than three trials, the probability will always be below , but for three or more, it depends on exactly how many trials there are, since the probability increases with increasing number of trials.

Example Question #116 : Arithmetic

 students are being seated randomly in a row of  chairs. What is the probability, that one of the students, Harold, will be seated in the chair second from the left?

1) There are  students.

2) The probability of Maude, another student, sitting on the leftmost seat, while Dennis, another student, has the rightmost seat is .

Possible Answers:

Neither of the statements, separate or together, is sufficient.

Statement 2 alone is sufficient.

Together, the two statements are sufficient.

Statement 1 alone is sufficient.

Either of the statements is sufficient.

Correct answer:

Either of the statements is sufficient.

Explanation:

Either of these statements can enable finding the probability of Harold sitting in a given seat, i.e. .

Statement 1 outright provides it, while Statement 2 can lead towards it with the relation 

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