# GMAT Math : Data-Sufficiency Questions

## Example Questions

### Example Question #2131 : Gmat Quantitative Reasoning

Clara spent  of her salary on rent and of the rest on clothes. How much did she have left after paying the rent and buying the clothes?

(1) Her salary was $3000 (2) She spent$1400 on rent and clothes

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

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

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

D. EACH statement ALONE is sufficient.

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

D. EACH statement ALONE is sufficient.

Explanation:

For statement (1), she spent

on rent, and

on clothes.

So she spent  in total.

Therefore, she has  left.

For statement (2), we can set Clara’s salary to be , then we have

Then simplify the equation:

Therefore, .

Now we can just follow what we did for the first statement to calculate the money he had left.

### Example Question #22 : Word Problems

Steve can paint his greenhouse in 4 hours 40 minutes minutes, working alone; his brother Phil can do the same job in 6 hours, working alone. If they work together, to the nearest minute, how long will it take them?

2 hours 22 minutes

3 hours

2 hours 42 miutes

2 hours 54 minutes

2 hours 38 minutes

2 hours 38 minutes

Explanation:

Think of this in terms of "greenhouses per minute", not "minutes per greenhouse". Converting hours and minutes to just minutes, Steve can paint  greenhouses per minute; Phil can paint  greenhouses per minute.

If we let  be the time in minutes that it takes to paint the greenhouse, then Steve and Phil paint   and  greenhouses, respectively; since one greenhouse total is painted, then we can add the labor and set up this equation:

Simplify and solve:

or 2 hours, 38 minutes.

### Example Question #21 : Data Sufficiency Questions

A large water tower can be emptied by opening one or both of two drains of different sizes. On one occasion, both drains were opened at the same time. How long did it take to empty the water tower?

Statement 1: Alone, the larger drain can empty the tower in three hours.

Statement 2: The smaller drain can empty water at 75% of the rate at which the larger drain does.

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.

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.

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

Explanation:

A work problem is actually a rate problem in disguise.

If you know that an object working alone can do a job in  hours, then you know that the object works at a rate of  jobs per hour. After  hours, the object accomplishes  of a job. Similarly, the other object working alone does a job in  hours, and therefore does  of a job. Together, the objects do one whole job, so solve this equation

for .

Statement 1 alone gives us half the picture; , but  is unknown.

Statement 2 alone tells us that  is 75% of . But  is unknown.

From Statement 1 and 2 together, we know

is 75% of  - this allows us to calculate :

75% of  is , so . Since we have both  and , we have the complete equation

and we can calculate .

### Example Question #4 : Dsq: Understanding Work Problems

A large water tower can be emptied by opening one or both of two drains of different sizes. On one occasion, both drains were opened at the same time. How long did it take to empty the water tower?

Statement 1: Alone, the smaller drain can empty the tower in three hours.

Statement 2: Alone, the larger drain can empty the tower in two hours.

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 insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 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 sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

A work problem is actually a rate problem in disguise.

If you know that an object working alone can do a job in  hours, then you know that the object works at a rate of  jobs per hour. After  hours, the object accomplishes  of a job. Similarly, the other object working alone does a job in  hours, and therefore does  of a job. Together, the objects do one whole job, so solve this equation

for .

Statement 1 alone tells us that , and Statement 2 alone tells us that .

Therefore, each statement alone gives us only half the picture, but together, they give us the equation

,

which can be solved to yield the answer.

### Example Question #5 : Dsq: Understanding Work Problems

Three brothers - David, Eddie, and Floyd - mow a lawn together, starting at the same time. How long will it take them to finish?

Statement 1: Working alone, David can mow the lawn in four hours.

Statement 2: Working together, but without David, Eddie and Floyd can mow the lawn in three hours.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER 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.

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 sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

A work problem is actually a rate problem in disguise.

If you know that David working alone can do a job in  hours, then you know that the object works at a rate of  jobs per hour. After  hours, the object accomplishes  of a job. Similarly, Eddie and Floyd, working without David, do a job in  hours, and therefore does  of a job. Together, the objects do one whole job, so solve this equation

for .

Statement 1 alone tells us that , and Statement 2 alone tells us that ; each one alone leaves the other value unknown. However, if both statements are given, the equation

can be solved for  to yield the correct answer.

### Example Question #6 : Dsq: Understanding Work Problems

Last week, Mrs. Smith, Mrs. Edwards, and Mrs. Hume were able to write  invitations to a party in two hours.

Today, Mrs. Smith is sick and cannot help, so Mrs. Edwards, and Mrs. Hume have to work without her. They must write  more invitations to the same party. How long should they take, working together?

Statement 1: Working alone, Mrs. Smith can write  invitations in one and one-half hours.

Statement 2: Working alone, Mrs. Hume can write  invitations in one hour.

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

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

Explanation:

Since the group is now without the help of Mrs. Smith, we look at Mrs. Smith's contribution to the work as a whole, and the sum of the other two ladies' contribution as a whole; Statement 2, which deals with Mrs. Hume alone, is irrelevant and unhelpful.

Since the three ladies together wrote 400 invitations in 120 minutes, we can infer that they would have spent three-fourths of this time, or 90 minutes, writing 300 invitations.

If Statement 1 is true, then Mrs. Smith, who can write 100 invitations in 90 minutes, would take three times this, or 270 minutes, to write 300 invitations.

A work problem is a rate problem in disguise. Think in terms of "jobs per hour", and take the reciprocal of each "hours per job". The three ladies together would have done  job in one hour, and Mrs. Smith alone would have done  job in one hour.

Therefore, in one hour today, the two ladies will do

jobs, and in  hours today, they will do

job.

Solve for  in this equation.

This proves that Statement 1 alone allows us to find the answer - but not Statement 2.

### Example Question #1 : Rate Problems

Data sufficiency question- do not actually solve the question

How many hours did it take to drive from city A to city B without stopping?

1. The drive started at 10 am.

2. The average speed during the trip is 65 miles/hour.

Statement 2 is sufficient, but statement 1 is not sufficient to answer the question

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question

Both statements taken together are sufficient to answer the question but neither statement alone is sufficient

Each statement alone is sufficient to answer the question

Statement 1 is sufficient, but statement 2 is not sufficient to answer the question

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question

Explanation:

The total time is calculated by the equation . Statement 2 provides the rate, but we have no information regarding distance, therefore, the quesiton is impossible to solve without more information.

### Example Question #2 : Rate Problems

The route from Tom's house to his mother's house involves traveling for 55 miles along Interstate 10, then 20 miles along State Route 34. How long does it take for Tom to travel between the two houses, if he drives at precisely the speed limit on each highway?

Statement 1: The speed limit on Interstate 10 is 70 miles per hour for the entire stretch.

Statement 2: The speed limit on State Route 34 is 50 miles per hour for the first half of the distance Tom drives on it, and 40 miles per hour for the second half.

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.

EITHER 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.

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

Explanation:

The rate formula  - or, actually, the equivalent equation  - will help.

Let  be the speed limits along the interstate, the first half of the state route, and the second half of the state route, respectively.

Then Tom can drive I-10 in  hours; the first half of SR 34, ; the second half of SR 34, .

The time  it takes, in hours, for Tom to make the entire trip is the sum of these fractions:

.

To calculate , we need . Statement 1 only tells us ; Statement 2 only tells us  and . Therefore, both together, but neither alone, are enough to allow us to calculate .

### Example Question #3 : Rate Problems

Cassie and Derek must decorate 60 cupcakes. It takes them 150 minutes to complete the task together. How long would it take Derek to decorate the cupcakes by himself?

Statement 1: It would take Cassie 240 minutes to decorate the cupcakes by herself.

Statement 2: Derek can decorate 9 cupcakes in 1 hour.

Each statement alone is sufficient.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Statement 1 alone is sufficient, but Statement 2 alone is not sufficient to answer the question.

Statements 1 and 2 together are not sufficient to answer the question.

Statement 2 alone is sufficient, but Statement 1 alone is not sufficient to answer the question.

Each statement alone is sufficient.

Explanation:

From the first statement, we can calculate the number of cupcakes Cassie can decorate in 150 minutes. From there, we can calculate the rate at which Derek decorates. Therefore, Statement 1 alone is sufficient to answer the question.

The second statement gives the rate at which Derek decorates cupcakes. Therefore, Statement 2 alone is also sufficient to answer the question.

### Example Question #1 : Rate Problems

Two trains (Train A and Train B) leave their stations at exactly 6 pm, travelling towards each other from stations exactly 60 miles apart. There are no other stops between these two stations. What time does Train B arrive at its destination?

1. Train A travels twice as fast as Train B.

2. At 6:40 pm, the two trains pass each other.

Statement 2 alone is sufficient, but Statement 1 alone is not sufficient to answer the question.

Statements 1 and 2 together are not sufficient.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Statement 1 alone is sufficient, but Statement 2 alone is not sufficient to answer the question.

Each statement alone is sufficient.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Explanation:

Statement 1 alone does not tell us enough about the speed of train B to answer the question. Statement 2 alone does not tell us about the rates of either individual train, so it is also not sufficient by itself to answer the question.

But can we figure out the answer using both pieces of information? Yes, we can! If we know that the trains meet at 6:40, then their combined rate of travel is 60 total miles in 40 minutes. Statement 1 says that Train A travels twice as fast as Train B, so we can determine the distances covered by the two trains in those 40 minutes. From there, we can find rates for both trains and then answer the question. Thus, both statements together are sufficient to answer the question, but neither statement alone is sufficient.

Note: We didn't actually answer the question of Train B's arrival time. For data sufficiency questions, don't waste time trying to find the specific answer. All that is necessary is determining whether or not it is POSSIBLE to answer the question with the information given.