GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #221 : Problem Solving Questions

Flight map

Public domain map from The World Factbook, Central Intelligence Agency.

Flight 783 departs from Oslo, Norway when it is 7:12 AM there; it lands in Dallas when it is 10:37 AM there. How long did the flight take?

(Assume Daylight Savings Time is not in effect.)

Possible Answers:

Correct answer:

Explanation:

Refer to the time zone differences printed at the top of the map. The time zone for Dallas is marked ; the time zone for all of Norway is marked . This means that Oslo is  hours ahead of Dallas, so we need to adjust accordingly.

The flight took off when it was  in Oslo; if we subtract , then we find that it took off when it was  in Dallas. Now subtract this from :

Adjust by adding  to :

The flight took .

Example Question #222 : Problem Solving Questions

Flight map

Public domain map from The World Factbook, Central Intelligence Agency.

Flight 122 departed from Washington, DC (green circle) when it was  there. It arrived in Paris, France (red circle)  later. What time was it in Paris upon the flight's arrival there?

(You may assume that Daylight Savings Time is not in effect.)

Possible Answers:

Correct answer:

Explanation:

Refer to the time zone differences printed at the top of the map. The time zone for Washington, DC is marked ; the time zone for Paris, France is marked . This means that Paris is  hours ahead of Washington, so we need to adjust accordingly.

The flight departed from Washington when it was  in Washington, so we add  to this to get , the time it was in Paris. Now we can add :

Now adjust again by subtracting ; this means it was  in Paris when the flight arrived.

Example Question #223 : Problem Solving Questions

Runoff

Three candidates - Craig, Donna, and Elly - ran for student body president. By the rules, the candidate who wins more than half the ballots cast wins the election outright; if no candidate wins more than half, there must be a runoff between the two top vote-getters. You may assume that no other names were written in.

As can be seen in the figure above, which reflects the share of the vote each candidate won, there will be a runoff. Which two candidates will face each other?

Statement 1: Candidate C is Donna.

Statement 2: Craig won 528 votes.

 

Possible Answers:

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

Correct answer:

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

Explanation:

From Statement 1 alone, it can be seen that Donna's share of the vote was the smallest of the three. Therefore, Craig and Elly were the top two votegetters, and they will face each other in the runoff.

Statement 2 alone provides insufficient information; without knowing the total number of voters, the share of the vote won by Craig (or any other candidate) cannot be determined from the number of votes Craig won.

Example Question #221 : Problem Solving Questions

Runoff

Three candidates - Xenia, Yancey, and Zane - ran for student body president. By the rules, the candidate who wins more than half the ballots cast wins the election outright; if no candidate wins more than half, there must be a runoff between the two top vote-getters. You may assume that no other names were written in.

As can be seen in the figure above, which reflects the share of the vote each candidate won, there will be a runoff. Which two candidates will face each other?

Statement 1: Yancey is not Candidate A.

Statement 2: Xenia is not Candidate C.

Possible Answers:

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

Correct answer:

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

Explanation:

From the diagram, it can be seen that Candidates A and B will compete in the runoff. 

Assume both statements to be true. Since Xenia is not Candidate C, she will participate in the runoff. However, we do not know whether she is Candidate A or B. If she is Candidate B, then Yancey, who is not Candidate A, must be Candidate C, and Xenia will face Zane in the runoff. However, if Xenia is Candidate A, Yancey or Zane can be Candidate B. Therefore, while it can be determined that Xenia is in the runoff, her opponent cannot be determined with certainty.

Example Question #1 : Rate Problems

A group of students are making posters to advertise for a bake sale. 12 large signs and 60 small signs are needed. It takes 10 minutes to paint a small sign and 30 minutes to paint a large sign. How many students will be needed to paint all of the signs in 2 hours or less?

Possible Answers:

Correct answer:

Explanation:

In 2 hours, 1 student can paint 4 large signs or 12 small signs. Therefore, 3 students are required to paint the large signs () and 5 students are required to paint the small signs (). In total, 8 students are required.

Example Question #2 : Rate Problems

Jason is driving across the country. For the first 3 hours, he travels 60 mph. For the next 2 hours he travels 72 mph. Assuming that he has not stopped, what is his average traveling speed in miles per hour?

Possible Answers:

Correct answer:

Explanation:

In the first three hours, he travels 180 miles.

In the next two hours, he travels 144 miles.

for a total of 324 miles.

Divide by the total number of hours to obtain the average traveling speed.

Example Question #1 : Rate Problems

Tom runs a 100m race in a certain amount of time.  If John runs the same race, he takes 2 seconds longer.  If John ran at 8m/s, approximately how fast did Tom run?

Possible Answers:

Correct answer:

Explanation:

Tom runs a 100m race in a certain amount of time.  If John runs the same race, he takes 2 seconds longer.  If John ran at 8m/s, how fast did Tom run?

 

Let denote the amount of time that it took Tom to run the race.  Then it took John seconds to run the same race going 8m/s.  At 8m/s, it takes 12.5 seconds to finish a 100m race.  This means it took Tom 10.5 seconds to finish.  Running 100m in 10.5 seconds is the same as

Example Question #2 : Rate Problems

Jim and Julia, a married couple, work in the same building.

One morning, both left at 9:00, but in different cars. Jim arrived at 10:10; Julia arrived 10 minutes later. If Jim's average speed was 54 miles per hour, what was Julia's average speed (nearest whole number)?

Possible Answers:

Correct answer:

Explanation:

Jim arrived at the common destination in 70 minutes, or  hours. His average speed was 54 miles per hour, so their workplace is 

 miles away from Jim and Julia's home.

Julia traveled those 63 miles in 80 minutes, or  hours, so her average speed was

 ,

or, rounded, 47 miles per hour.

 

Example Question #1 : Rate Problems

Andy and his wife Donna both work at the same building. 

One morning, Andy left home at 8:00; Donna left 5 minutes later. Each arrived at their common destination at 8:50. Andy drove at an average speed of 45 miles per hour; what was Donna's average speed, to the nearest mile per hour?

Possible Answers:

Correct answer:

Explanation:

Andy traveled for 50 minutes, or  of one hour, at 45 miles per hour, so the office building is  miles from Andy and Donna's house. Donna traveled this distance for 45 minutes, or  of one hour, so her speed was:

 miles per hour.

Example Question #1 : Rate Problems

Kenny and Marie, a married couple, work in the same building.

One morning, both left at 9:00, but in different cars. Kenny arrived at 10:10; Marie arrived 10 minutes later. If Kenny's average speed was 6 miles per hour faster than Marie's, how far is their work place from their home (nearest whole mile)?

Possible Answers:

Correct answer:

Explanation:

Let  be the rate at which Kenny drove. Then Marie drove at a rate of  miles per hour. The two drove the same distance, so, since Kenny drove 70 minutes, or  hours, and Marie drove for 80 minutes, or  hours, we can use the formula  to set up the equation:

Since Kenny traveled at 48 miles per hour for  hours, the distance each drove is 

 miles.

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