GMAT Math : Problem-Solving Questions
Study concepts, example questions & explanations for GMAT Math
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Example Questions
Example Question #12 : Probability
Sheryl is competing in an archery tournament. She gets to shoot three arrows at a target, and her best one counts.
Sheryl hits the bullseye 42% of the time. What is the probability (two decimal places) that she will hit the bullseye at least once in her three tries?
This is most easily solved by finding the probability that she will not hit the bullseye at all in her three tries. If she hits 42% of the time, she misses 58% of the time, and the probability she misses three times will be
The probability of hitting the bullseye at least once in three tries is the complement of this, or 
Example Question #12 : Calculating Probability
If you have a bag with 15 grey marbles, 15 yellow marbles and 20 green marbles, what is the probability of choosing a green marble followed by a yellow marble? Assume no replacement.
To calculate probability of multiple events, find the probability of each event and multiply them together. We begin with 50 total marbles in the bag.
For the first case, we are asked to pick a green marble. Because there are 20 green marbles and 50 total, our probability of this event is as follows:
For the second case, we need to pick a yellow marble. However, this time there are only 49 marbles left in the bag, because we didn't replace the green marble. Because we have 15 yellow marbles, the probability of this event is as follows:
To find our final answer, we need to multiply these two together.
Example Question #11 : Probability
If you flip a quarter three times, what is the probability of it landing on heads all three times?
Every time you flip a coin, there is a 1 in 2 chance of it landing on heads. So, if we want to know the probability of a coin landing on heads a certain number of times times in a row, we multiply the probability of that occurrence for however many times the coin is flipped. For three flips, this gives us:
So there is a 1 in 8 chance that a coin will land on heads three times in a row.
Example Question #13 : Probability
A drawer has 4 green socks, 6 blue socks, 12 white socks, 8 black socks, and 2 pink socks. If you reach in and pull out a sock at random, what is the probability the sock will be blue?
If you reach in and pull out a sock at random, the probability of it being blue is equal to the number of blue socks divided by the total number of socks in the drawer. First we'll calculate the total number of socks in the drawer:
Now we divide the number of blue socks by the total number of socks to find the probability of picking a blue sock:
Example Question #1 : Understanding Diagrams
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.
Of the 
Example Question #2 : 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?
Crieghton
There will be a runoff between Crieghton and Wells
Wells
Hawley
There will be a runoff between Wells and Hawley
Wells
The third-largest portion of the graph is the gray portion, which represents Wells. Wells won the office of Secretary-Treasurer outright.
Example Question #3 : 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
Jones and Smith will have a runoff to determine who will be Secretary-Treasurer.
Jones and Wells will have a runoff to determine who will be Secretary-Treasurer.
Smith
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.
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 #4 : 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?
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 : Understanding 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?
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 #4 : Understanding 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?
The increase in population from 1970 to 1980 was 
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