# GMAT Math : Understanding diagrams

## Example Questions

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### Example Question #201 : Problem Solving Questions

In a room filled with 100 people, 52 are men and 40 are blonde. There were 16 blonde men in the room. How many non-blonde women were there? Use the following diagram.

Explanation:

Of the  people,   were either men or blonde or both. Therefore,  are non-blonde and non-men (women).

### Example Question #1 : Understanding Diagrams

The above circle graph shows the results of 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.

Who was elected Secretary-Treasurer?

There will be a runoff between Wells and Hawley

There will be a runoff between Crieghton and Wells

Hawley

Wells

Crieghton

Wells

Explanation:

The third-largest portion of the graph is the gray portion, which represents Wells. Wells won the office of Secretary-Treasurer outright.

### Example Question #2 : Understanding Diagrams

The above table shows the results of 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.

Who was elected Secretary-Treasurer?

Jones and Smith will have a runoff to determine who will be Secretary-Treasurer.

Smith

Jones

Jones and Wells will have a runoff to determine who will be Secretary-Treasurer.

Smith and Wells will have a runoff to determine who will be Secretary-Treasurer.

Jones and Smith will have a runoff to determine who will be Secretary-Treasurer.

Explanation:

Jones and Smith tied for third (87 each), so by the rules, there will be a runoff election for the office of Secretary-Treasurer between these two.

### Example Question #1 : Understanding Diagrams

The table below gives the population of the city of Renfrow for each of six census years.

Which decade saw a population decline?

Explanation:

The only census year in which Renfrow had fewer people than the previous one is 1970, so the correct choice is 1960-70.

### Example Question #5 : Diagrams

The table below gives the population of the city of Renfrow for each of six census years.

Which decade saw the greatest increase in population?

Explanation:

For each decade, we can subtract the population at the beginning of the decade from that at the end. We omit 1960-70 since there was a population decline.

1950-60 saw the greatest increase.

### Example Question #6 : Diagrams

The table below gives the population of the city of Renfrow for each of six census years.

The figures for subsequent years are not currently available but it is known that the increase over each decade since 1980 has been at least as great as the increase from 1970 to 1980. What was the minimum population in 2010?

Explanation:

The increase in population from 1970 to 1980 was . Since each of the three ten-year growths from 1980 to 2010 was at least that much, the minimum population of Renfrow in 2010 was

### Example Question #7 : Diagrams

The above is the menu at Monorail Sandwich Shop.

Monorail is running a special today - for each sandwich you buy, you can purchase one large soda for ninety cents or get one small soda for free.

Kevin purchases three beef sandwiches, two large sodas, and two small sodas. Disregarding tax, how much will he pay?

Explanation:

Kevin will pay $5.89 each for the three beef sandwiches. He will pay$0.90 for each of the two large sodas and get one of the small sodas for free; he will pay the full price of \$1.09 for one small soda. Therefore, Kevin will pay

### Example Question #8 : Diagrams

Five candidates ran for the office of student body president at Garfield High School. According to the rules, the student who gets the most votes wins the office, with ties resulting in a runoff. However, Garfield has an unusual rule that states that seniors' votes count double.

This table shows how freshmen, sophomores, and juniors voted:

This table shows how seniors voted:

Who won the election?

Smith

Crane

Jones

Crane and Jones will face each other in a runoff.

Jones

Explanation:

For each candidate, add the number of freshman, sophomore, and junior votes to twice the number of senior votes:

Jones won the election.

### Example Question #1 : Diagrams

Five candidates ran for the office of student body president at Buchanan High School. According to the rules, the student who gets a majority of the votes wins the office; if no student wins a majority, then there will be a runoff between the top two vote-getters. However, Buchanan has an unusual rule that states that seniors' votes count double.

This table shows how freshmen, sophomores, and juniors voted:

This table shows how seniors voted:

Who won the election?

Crane and Trask will face each other in a runoff.

Jones and Trask will face each other in a runoff.

Crane and Jones will face each other in a runoff.

Jones won outright.

Jones and Trask will face each other in a runoff.

Explanation:

For each candidate, add the number of freshman, sophomore, and junior votes to twice the number of senior votes:

Jones got the most votes. However, he clearly did not win a majority, so he and the second-highest vote-getter, Trask, will face each other in a runoff.

### Example Question #10 : Diagrams

Light blue: Goodman

Orange: Ferris

Gray: Inman

Yellow: Jones

Dark blue: Harris

Refer to the diagram. If 3,145 people voted in the school board election, (the results of which are represented in the diagram), then approximately how many people voted for Inman?