GMAT Math : Problem-Solving Questions

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Example Questions

Example Question #211 : Gmat Quantitative Reasoning

$\begin{matrix} \textrm{\underline{Item}}& \textrm{\underline{Price}}\\ \textrm{Beef} & \$5.89\\ \textrm{Turkey} &\$5.49 \\ \textrm{Ham} & \$5.19\\ \textrm{Chicken} & \$4.79\\ \textrm{Veggie} & \$ 4.39\\\textrm{Sm. Soda} & \$1.09\\ \textrm{Lg. Soda} & \$1.99\end{matrix}$

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?

Possible Answers:

$\$19.66$

$\$ 20.56$

$\$21.65$

$\$19.47$

$\$18.76$

Correct answer:

$\$ 20.56$

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

$\$5.89 \times 3 + \$1.09 + \$0.90 \times 2 = \$17.67 + \$1.09 + \$1.80 = \$20.56$

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Example Question #3 : Understanding 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:

$\begin{matrix} \textrm{Crane}&104 \\ \textrm{Jones}&\; 87\\\textrm{Smith} & \; 87\\ \textrm{Trask} & \; 98\\ \textrm{Wells} & \; 75 \end{matrix}$

This table shows how seniors voted:

$\begin{matrix} \textrm{Crane}&14 \\ \textrm{Jones}&\; 27\\\textrm{Smith} & \; 15\\ \textrm{Trask} & \; 18\\ \textrm{Wells} & \; 10 \end{matrix}$

Who won the election?

Possible Answers:

Jones

Trask

Crane and Jones will face each other in a runoff.

Crane

Smith

Correct answer:

Jones

Explanation:

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

$\begin{matrix} \textrm{Crane}&104+ 2 \times 14 = 132 \\ \textrm{Jones}&\; 87+ 2 \times 27 = 141\\\textrm{Smith} & \; 87+ 2 \times 15 = 117\\ \textrm{Trask} & \; 98+2 \times 18= 134\\ \textrm{Wells} & \; 75+ 2 \times 10 = 95 \end{matrix}$

Jones won the election.

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Example Question #4 : Understanding 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:

$\begin{matrix} \textrm{Crane}&104 \\ \textrm{Jones}&\; 87\\\textrm{Smith} & \; 87\\ \textrm{Trask} & \; 98\\ \textrm{Wells} & \; 75 \end{matrix}$

This table shows how seniors voted:

$\begin{matrix} \textrm{Crane}&14 \\ \textrm{Jones}&\; 27\\\textrm{Smith} & \; 15\\ \textrm{Trask} & \; 18\\ \textrm{Wells} & \; 10 \end{matrix}$

Who won the election?

Possible Answers:

Crane and Jones will face each other in a runoff.

Trask won outright.

Jones and Trask will face each other in a runoff.

Jones won outright.

Crane and Trask will face each other in a runoff.

Correct answer:

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.

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Example Question #5 : Understanding Diagrams

Pie_graph

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?

Possible Answers:

910

790

630

1,050

390

Correct answer:

630

Explanation:

According to the legend, the gray sector represents the portion of the electorate who voted for Inman. This sector is about one-fifth of the circle, so, to find the best estimate of Inman's share of the vote, take one-fifth of 3,145 - or, equivalently, divide 3,145 by 5:

$3,145 \div 5 = 629$

630 is the best estimate of the choices given.

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Example Question #215 : Problem Solving Questions

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?

Possible Answers:

$\$34.13$

$\$35.93$

$\$34.53$

$\$33.03$

$\$ 31.93$

Correct answer:

$\$34.53$

Explanation:

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

$\begin{matrix} \$ 5.89 & \\ \$ 5.89 & \\ \$4.79 & \textrm{Free}\\ \$4.79& \\ \$4.79 & \\ \$4.39 & \textrm{Free} \\ \$4.39& \\ \$4.39& \\ \$4.39& \end{matrix}$

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:

$\begin{matrix} \; \; \$ 5.89 \\ \; \; \$ 5.89 \\ \; \;\$4.79 \\ \; \;\$4.79 \\ \; \;\$4.39 \\ \; \;\$4.39 \\ \; \; \underline{ \$4.39} \\ \$34.53 \end{matrix}$

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Example Question #211 : Gmat Quantitative Reasoning

Venn

Define the universal set $U = \left \{ 1,2,3,4,...50\right \}$ .

Define to be the set of prime numbers, to be the set of integers that end in 2, 5, or 8, and $C = \left \{ 21,22,23,24,...40\right \}$ . 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?

Possible Answers:

Correct answer:

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:

$\left \{ 1,2,3,4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,18, 19, 20, 41,42,43,44, 45, 46, 47, 48, 49, 50\right \}$

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

$\left \{ 1, 3,4, 6, 7, 9, 10, 11, 13, 14,16, 17, 19, 20, 41, 43,44, 46, 47, 49, 50\right \}$ .

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

$\left \{ 1,4, 6,9, 10,14, 16, 20, 44, 46,49, 50\right \}$ ,

a set with 12 elements.

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Example Question #212 : Gmat Quantitative Reasoning

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:

$\$53.01$

$\$41.07$

$\$ 51.02$

$\$48.98$

$\$60.97$

Correct answer:

$\$ 51.02$

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:

$\$5.89 \times 3 + \$5.49 \times 2 + \$5.19 \times 2 + \$1.99 \times 5$

$=\$17.67 + \$10.98+ \$10.38 + \$9.95$

$=\$48.98$

The change from a $100 bill is

$\$100.00 - \$48.98 = \$ 51.02$ .

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Example Question #212 : Word Problems

$\begin{matrix} \textrm{Crane}&124 \\ \textrm{Jones}&\; 87\\\textrm{Smith} & \; 87\\ \textrm{Trask} & \; 98\\ \textrm{Wells} & \; 75 \end{matrix}$

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:

$\begin{matrix} \textrm{Crane}&14 \\ \textrm{Jones}&\; 27\\\textrm{Smith} & \; 15\\ \textrm{Trask} & \; 18\\ \textrm{Wells} & \; 10 \end{matrix}$

Who was elected Vice-President?

Possible Answers:

Jones

Trask and Jones will face each other in a runoff.

Trask

Crane

Crane and Trask will face each other in a runoff.

Correct answer:

Trask

Explanation:

The revised vote count is as follows:

$\begin{matrix} \textrm{Crane}&124 +14 = 138 \\ \textrm{Jones}&\; 87+27=114\\\textrm{Smith} & \; 87+15=102\\ \textrm{Trask} & \; 98+18 = 116\\ \textrm{Wells} & \; 75+10 = 85 \end{matrix}$

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

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Example Question #212 : Problem Solving Questions

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 N + 0.8N = 1.08 N . Charlie can spend at most $30 after sales tax of 8% is counted, so we can set up the equation:

$1.08 N =\$ 30$

$1.08 N \div 1.08= \$30 \div 1.08$

$N = \$ 27.78$

The four turkey sandwiches cost $\$5.49 \times 4 = \$21.96$ , leaving

$\$ 27.78 - \$21.96 = \$ 5.82$

to buy drinks.

$\$1.99$ buys one large soda.

$\$ 5.82 \div \$1.99 \approx 2.9$ , so $\$ 5.82$ 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.

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Example Question #31 : Data Interpretation

Flight map

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.)

Possible Answers:

2:42 PM

2:42 AM

9:42 AM

9:42 PM

6:42 PM

Correct answer:

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 0 - (-6) = 6 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:

$\begin{matrix} 0:12\\ \underline{8:30}\\ 9:42 \end{matrix}$

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

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GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #211 : Gmat Quantitative Reasoning

Example Question #3 : Understanding Diagrams

Example Question #4 : Understanding Diagrams

Example Question #5 : Understanding Diagrams

Example Question #215 : Problem Solving Questions

Example Question #211 : Gmat Quantitative Reasoning

Example Question #212 : Gmat Quantitative Reasoning

Example Question #212 : Word Problems

Example Question #212 : Problem Solving Questions

Example Question #31 : Data Interpretation

All GMAT Math Resources

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