# GMAT Math : GMAT Quantitative Reasoning

## Example Questions

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### Example Question #3441 : Gmat Quantitative Reasoning

By how many years is Jason older than Allison?

(1) Jason is 6 years older than twice David’s age.

(2) In 8 years, Allison will be twice as old as David is now.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

Explanation:

An important Data Sufficiency strategy is to always note when a question is asking you about a combination of variables (here that's "What is J - A?") as opposed to a single variable (either J or A). Almost always, as is the case here, it requires less information to solve directly for the combination than it does to solve for the individual variables and then combine yourself.

Note that neither statement allows you to assess both J and A, so the answer cannot be "Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked", "EACH statement ALONE is sufficient to answer the question asked", or "Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked". But when you take the two statements together, you have:

(1) J = 6 + 2D

(2) A + 8 = 2D

If you then subtract the entire second equation from the first, you'll combine:

J = 6 + 2D -A - 8 = -2D

To get:

J - A - 8 = 6

So when you add 8 to both sides you're finished:

J - A = 14

Because you can solve directly for J - A, even though you do not know the individual variables J or A, this is sufficient information and the correct answer is "Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient".

### Example Question #3441 : Gmat Quantitative Reasoning

Exactly how many show dogs does Sheila have?

1. Of Sheila’s show dogs, exactly 3 have won prizes of at least $500. 2. Of Sheila’s show dogs, exactly 40% have not won a prize of$500 or more.

Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

Explanation:

This question asks for the specific number of show dogs. As with any "what is the value" data sufficiency question, a sufficient statement will ensure that there is one and only one possible value for the number of show dogs. Remember if you are picking numbers to test a statement that just because a statement gives an answer doesn't mean that it gives only ONE answer.

Statement (1) states that “Exactly 3 of the dogs won prizes of at least $500.” This statement is not sufficient alone. Consider a few scenarios: the three dogs that won show prizes could be her only dogs, or Sheila could have 100 dogs - 97 that have not one prizes of at least$500 and 3 that have. There is no way for you to determine the total number of show dogs. Eliminate choices "Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked" and "EACH statement ALONE is sufficient to answer the question asked".

Statement (2) states that “40% of the dogs have not won a prize of $500 or more.” Using this information, you should recognize that this means that 60% of her dogs have won a prize of$500 or more. However, this statement is also not sufficient alone since there is no information about what value you are taking a percentage of.

In evaluating (2), remember that you can't bring down any information from statement (1), so Sheila may not have just 3 dogs that have won prizes. Sheila could have 100 dogs, 60 of which have won prizes, or 10 dogs, six of which have won prizes. As with statement (1), there is no way to determine the total number of dogs. Eliminate choice "Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked".

Taking the two statements, together, you know from statement (1) that 3 dogs have won prizes of $500 or more and you know from statement (2) that 60% of the dogs have won a prize of$500 or more.

You can use these two statements to set up and solve a single-variable equation, since those two statements must equal the same value. So that means “3 dogs = 60% of the total dogs” or

You can either recognize that this is sufficient since it will yield only one value for  , or go ahead and solve this equation by dividing both sides by 0.6. If you solve for , you'll find that

, so she has 5 show dogs total. This information is sufficient and the correct answer is therefore "Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient".

### Example Question #1321 : Data Sufficiency Questions

Julie runs a small art museum. How many paintings does her museum have?

1. Her next acquisition of 4 Monet paintings will increase the number of paintings in the museum’s collection by 10%.
2. The museum currently exhibits 3 impressionist paintings for every 2 non-impressionist paintings.

Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

Explanation:

This question asks you to provide a specific number of paintings in the museum. Since this is a "what is the value" data sufficiency question, remember that you are looking for each statement to give you a consistent value for the number of paintings. If any statement gives multiple possible values, it is insufficient. Additionally, remember to always pick descriptive variables that can clearly be associated with what you're solving for.

Statement (1) states that adding 4 new paintings to the collection will increase the number of paintings in the museum by 10%. You should then recognize that if adding 4 paintings increases the size of the collection by 10%, you can plug in the values you know into what you know about percent change:

New value = (1 + percent change)(Original value)

In the context of this problem, this can be rewritten as

P + 4 = 1.1P,

where P equals the total number of paintings. Because you now have a single variable equation with only one solution, this information will be sufficient to provide a specific answer to the question. There is no need to actually solve this equation. Statement (1) is sufficient, meaning that you can eliminate "Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked", "Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient", and "Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed".

Statement (2) gives that the ratio of impressionist to non-impressionist paintings is 3:2. This information does not allow you to arrive at a specific number since you do not know either the number of impressionist or the number of non-impressionist paintings. There could be 3 impressionist and 2 non-impressionist paintings for a total of 5 paintings. However, because you only have a ratio, the total could also be any multiple of 5 as long as the numbers of non-impressionist and impressionist paintings are in the correct ratio.

Because statement (2) returned two unique values for the number of paintings, it is not sufficient. The answer is "Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked".

### Example Question #3441 : Gmat Quantitative Reasoning

A bake sale sells only individual cupcakes and boxes of cookies. If cupcakes sell for $2 each, and a box of cookies sells for$15, how many boxes of cookies did Kevin buy?

(1) Kevin spent $27 (2) Kevin bought 6 cupcakes Possible Answers: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked EACH statement ALONE is sufficient to answer the question asked Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient Correct answer: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked Explanation: Because this is a "what is the value" data sufficiency problem, for a statement to be sufficient it must yield one and only one value for the number of boxes of cookies Kevin bought. Any time you have a data sufficiency problem couched in real-world terms, think about what the implications of the set up are. In this case, Keven can only buy whole numbers of cupcakes and boxes of cookies. This is important since it limits the number of combinations within the problem. According to the question stem, you know that Kevin bought an unknown number of cupcakes and boxes of cookies for$2 and $15 each, respectively. Statement 1 tells you that Kevin spent$27 total. Cupcakes sell for an even dollar amount, and a box of cookies sells for an odd dollar amount. Kevin cannot have purchased ONLY cupcakes and still have an odd total, since an even number plus an even number will always be even. That means that he must have bought at least one box of cookies.

If he bought one box of cookies for $15, he would have had$12 left over to buy 6 total cupcakes.

However, could he have bought more than one box of cookies? Assume that Kevin bought two boxes of cookies for $15 each and spent$30. There are two problems. First, the number is even, not odd. However, second (and most importantly) the question stem states that Kevin only spent $27, so he can't have spent$30 on two boxes of cookies!

Because there is therefore only one valid combination of cookies and cupcakes, we can determine that he purchased exactly ONE box of cookies. Statement 1 is therefore sufficient. Eliminate "Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked", "Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient", and "Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed".

Statement 2 gives that Kevin purchased 6 cupcakes. However, without any information about how much money spent in total, this statement is insufficient. Keven could have bought six cupcakes and 1 box of cookies, as in statement 1, but he also could have bought any other number of boxes of cookies. Statement 2 is therefore insufficient, eliminating "EACH statement ALONE is sufficient to answer the question asked" and leaving you with correct answer "Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked".

Consider, however, why the testmaker included Statement (2). If you didn't take the time to either consider that there could only be a whole-number number of cupcakes and boxes of cookies sold or you didn't take the time to actually test numbers for statement (1), you may have assumed that statement (1) was insufficient and that you needed to know the value of the number of cupcakes. This would have led you to incorrectly pick "Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient". Remember to always leverage your assets to see if you can "move up" the Data Sufficiency ladder if you are tempted to pick "Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient" without putting the work in first.

Answer is "Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked".

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