GMAT Math : Problem-Solving Questions
Study concepts, example questions & explanations for GMAT Math
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Example Questions
Example Question #1 : Data Interpretation
What is the probability of sequentially drawing 3 aces from a deck or regular playing cards when the selected cards are not replaced?
The probability of drawing an ace first is 
Assuming an ace is the first card selected, the probability of selecting another ace is 
For the third card, the probability is 
To calculate the probability of all 3 events happening, you must multiply the probabilities:
Example Question #191 : Word Problems
How many even four-digit numbers larger than 4999 can be formed from the numbers 2, 4, 5, and 7 if each number can be used more than once?
Since the number must be larger than 4999, the thousand’s digit has to be 5 or 7. We are also told that the number must be even. Thus, the unit’s digit must be 2 or 4. The middle digits can by any of the numbers 2,4,5, or 7. Therefore, we have a total of 
Example Question #1 : Probability
What is the probability of rolling an even number on a standard dice?
A standard dice has 6 faces numbered 
There are 
Example Question #2 : Data Interpretation
Shawn is competing in an archery tournament. He gets to shoots three arrows at a target, and his best two shots count.
He hits the bullseye with 40% of his shots. What is the probability that he will hit the bullseye at least twice out of the three times?
There are three scenarios favorable to this event.
1: He hits a bullseye with his first two shots; the third shot doesn't matter.
The probability of this happening is
2: He hits a bullseye with his first shot, misses with his second shot, and hits with his third shot.
The probability of this happening is
3: He misses with his first shot and hits a bullseye with his other two shots.
The probability of this happening is
Add these probabilities:
Example Question #195 : Problem Solving Questions
A store uses the above target for a promotion. For each purchase, a customer gets to toss a dart at the target, and the outcome decides his prize. If he hits a pink region, he gets nothing; if he hits a red region, he gets a 10% discount on a future purchase; if he hits a green region, he gets a 20% discount; if he hits a blue region, he gets a 40% discount.
Assume a customer hits the target and no skill is involved. What are the odds against him getting a discount?
The customer gets a discount if he does not hit a pink region. There are ten out of twenty ways to hit a pink region and ten to not hit one - this makes the odds 10 to 10, or, in lowest terms, 1 to 1 against a discount.
Example Question #5 : Probability
It costs $10 to buy a ticket to a charity raffle in which three prizes are given - the grand prize is $3,000, the second prize is $1,000, and the third prize is $500. Assuming that all of 1,000 tickets are sold, what is the expected value of one ticket to someone who purchases it?
If 1,000 tickets are sold at $10 apiece, then $10,000 will be raised. The prizes are $3,000, $1,000, and $500, so $4,500 will be given back, meaning that the 1,000 ticket purchasers will collectively lose $5,500. This means that on the average, one ticket will be worth
This is the expected value of one ticket.
Example Question #3 : Calculating Probability
Daria has 5 plates: 2 are green, 1 is blue, 1 is red, and 1 is both green and blue. What is the probability that Daria randomly selects a plate that has blue OR green on it?
The easiest way to solve this is by using the complement. Only one of the five plates is NOT blue or green. So 
Example Question #11 : Probability
A die is rolled and then a coin is tossed. What is the probability that the die shows an even number AND the coin shows a tail?
We can calculate the two individual probabilities first.
Prob(die shows even) 
Prob(tail) 
Then, Prob(even AND tail) is 
Example Question #12 : Probability
A jar contains 8 blue marbles and 4 red marbles. What is the probability of picking a blue marble followed by a red marble if the first marble chosen is not put back in the jar?
There are 12 marbles total. The probability of picking a blue marble first is 
Example Question #12 : Probability
Refer to the above figure, which shows a target. Each of the squares is of equal size. If a dart is thrown at the target, what are the odds against hitting a red region?
You may assume that the dart hits the target, and you may disregard any skill factor.
There are fifteen ways to not hit a red region, and five ways to hit a red region. This makes the odds 15 to 5, or, in lowest terms, 3 to 1, against hitting a red region with a randomly thrown dart.
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