# GMAT Math : Understanding diagrams

## Example Questions

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### Example Question #11 : Diagrams

The above is the menu at Monorail Sandwich Shop.

Today, Monorail is running a special - buy any two sandwiches and get an additonal sandwich of equal or lesser value for free, with a limit of two free sandwiches per customer per day.

A father wants to buy some sandwiches for his family. He orders two beef sandwiches, three chicken sandwiches, and four veggie sandwiches. Disregarding sales tax, what is the least possible amount he will pay for them?

Explanation:

In descending order of cost, he is ordering sandwiches that cost the following:

Note that the father will get one chicken sandwich free with the two beef sandwiches, and that he will get one veggie sandwich free with the other two chicken sandwiches. Therefore, he will pay for the other seven sandwiches:

### Example Question #12 : Diagrams

Define the universal set  .

Define  to be the set of prime numbers,  to be the set of integers that end in 2, 5, or 8, and . If each number in the universal set were to be placed in its correct region in the above Venn diagram, how many integers would lie in the gray region?

Explanation:

The integers that go into the gray region are those that do not fall into any of the three sets , or . We can eliminate the integers by taking the universal set and eliminating the elements that fall in any one of the three.

Out of the 50 integers from 1 to 50, we can eliminate the 20 that are in . This leaves 30 so far:

Now we can eliminate nine integers from  - the ones that end in 2, 5, or 8. The 21 remaining numbers are

.

We now eliminate the primes from  - 3, 7, 11, 13, 17, 19, 41, 43, 47. This leaves us with

,

a set with 12 elements.

### Example Question #13 : Diagrams

The above is the menu at Monorail Sandwich Shop.

Today, Monorail is running a special - buy three sandwiches and get a large soda free. A boss treats her employees to lunch; she orders three beef sandwiches, two turkey sandwiches, two ham sandwiches, and seven large sodas. There is no sales tax. If the boss hands the clerk a $100 bill, how much change will she get back? Possible Answers: Correct answer: Explanation: The boss orders seven sandwiches, so two of the sodas will be free. Therefore, she will pay for three beef sandwiches, two turkey sandwiches, two ham sandwiches, and five large sodas. Their total price: The change from a$100 bill is

.

### Example Question #14 : Diagrams

The above table shows the initial count of the votes for a school election. According to the rules, the students who finish first, second, and third become President, Vice-President, and Secretary-Treasurer, respectively. In the event of any tie, a runoff election will be held.

After the initial count, it is discovered that some ballots were left out of the count by mistake. These votes were distributed as follows:

Who was elected Vice-President?

Crane and Trask will face each other in a runoff.

Jones

Crane

Trask and Jones will face each other in a runoff.

Explanation:

The revised vote count is as follows:

Trask finished second with 116, so he was elected Vice-President.

### Example Question #15 : Diagrams

The above is the menu at Monorail Sandwich Shop. The sales tax is 8%, and with the purchase of two sandwiches, a customer gets one free soda of any size.

Charlie wants to purchase four turkey sandwiches. He only has $30 on him and he has no checks, debit cards, or credit cards. How many large sodas can he get with the sandwiches and stay within his budget? Possible Answers: Correct answer: Explanation: If is the maximum price of the sandwiches before tax, then the price after tax is . Charlie can spend at most$30 after sales tax of 8% is counted, so we can set up the equation:

The four turkey sandwiches cost , leaving

, so  allows for the purchase of two. Also, with the four sandwiches, he gets two free sodas, so he can get a total of four sodas.

### Example Question #16 : Diagrams

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

Flight 984 departed from London (green circle) when it was 6:12 PM there. It arrived in Chicago, IL (red circle) 8 hours, 30 minutes later. What time was it in Chicago upon the flight's arrival there?

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

9:42 AM

2:42 PM

2:42 AM

9:42 PM

6:42 PM

9:42 PM

Explanation:

Refer to the time zone differences printed at the top of the map. The time zone for Chicago is marked ; the time zone for London is marked 0. This means that London is  hours ahead of Chicago, so we need to adjust accordingly.

The flight departed from London when it was 6:12 PM in London, so we subtract six hours from this to get 12:12 PM, the time it was in Chicago. Now we can add 8 hours, 30 minutes, first rewriting 12:12 PM as 0:12:

The flight landed in Chicago when it was 9:42 PM there.

### Example Question #221 : Problem Solving Questions

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.)

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 :

The flight took .

### Example Question #222 : Problem Solving Questions

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.)

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

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.

EITHER STATEMENT ALONE provides 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 do NOT provide 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.

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

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 #224 : Problem Solving Questions

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.

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

EITHER STATEMENT ALONE provides 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.

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 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.

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