» GMAT Sample Problems and Solutions: Part I
To help you crack the Quantitative Section, here are some sample problems and their solutions, step by step. These problems are based on real GMAT questions, so they may be the ones you'll get stuck on.
Before you begin, be sure to review the Quantitative Section lessons and the Basics of Algebra lessons.
Think you know your stuff? Practice using the Question Bank or the GMAT Tests.
» Question 1:
A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rate, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
| A. 64 | B. 36 | C. 12 | D. 29 |
» Answer:
Ok, first of all, what are you looking for?
A quick scan of the question says you're looking for miles per gallon. This is a ratio, so you'll need the total number of miles, and the total number of gallons to find the answer.
Finding the total number of miles is a simple calculation of:
The total number of gallons is trickier. We need to break it down into city and highway:
City: We drove 10 miles using
up
gallons, averaging 25 miles per gallon. A ratio is now set
up:
Cross-multiplying gives:
So in the city we used up 0.4 gallons.
Highway: We work the same way:
Now:
So on the highway we used 1.25 gallons.
Now all we need to do is add these up:
So, now we have 1.65 total gallons. And for our answer, all we have to do is divide:
Then our answer is: B. 36
» Question 2:
A second grade class is writing reports on birds. The students' teacher has given them a list of four birds they can choose to write about. If Lizzy wants to write a report that includes two or three of the birds, how many different reports can she write?
| A. 64 | B. 36 | C. 12 | D. 29 |
» Answer:
This is a combinators problem. We're looking for the number of reports. But really we're looking at the number of ways to choose 2 or 3 out of 4 different birds.
Splitting it up into two cases will help. First, how many ways can we choose 2 birds? Well, we have 4 choices for bird 1. Then, since we already chose 1 bird, we have 3 choices for bird 2. That leaves:
12 different reports with 2 birds.
Now, reports with 3 birds. Same logic applies: 4 choices for bird A, 3 left for bird B and 2 for bird C. That's:
24 reports. (Note that we're assuming order matters in the report, the question is ambiguous about that. But your answer choices should indicate whether you need order or not- if not, divide the 12 by 2 for the order of 2 birds, and the 24 by 6 for the order of 3 birds).
Now we just add these up:
36 reports, so the answer we're looking for is just B. 36
And that's all there is to this question.
» Question 3:
What is the greatest prime factor of:
| A. 2 | B. 5 | C. 7 | D. 9 |
» Answer:
You may be tempted to just pick 2, since that's the only prime in both 2 and 4. But remember that you're looking for factors. You need to factor the expression first.
The best way to do this is to convert the 2 pieces into a common basis:
Simple exponent laws. Now we can factors things out:
All we need to do now is look for that largest prime factor.
But 63 has prime factors of 3 and 7, as:
Now we know that the real answer isn't 2, it's C. 7.
» Additional GMAT Sample Problems:
»» Quantitative: Sample Problems II
»» Quantitative: Sample Problems III
»» Quantitative: Sample Problems IX
All time most popular tags
Post Comments
oLahav said – Tue, 15 Jul 2008 18:08:59 -0000 ( Flag Edit Link )
It makes a difference whether you choose 2 (or 3) out of 4 items in order, or whether you just choose them out of order.
To make it clear with a simple example, say you are trying to choose 2 out of 3 items. There are 3 ways to do it if you don’t care about order- AB, AC or BC. But if you do care about order you get 3 new ways- BA, CA and CB, which changes your result.
The question has to specify whether you care about ordering the objects or not. If it doesn’t specify it, you can figure it out using the answer choices- for example, in the question above if 6 wasn’t the right answer, it has to be 3 and you wouldn’t care about order.
Hope this clarifies matters.