» GMAT Sample Problems and Solutions: Part II
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:
One day a car rental agency rented 2/3 of its cars, including 3/5 of its cars with CD players. if 3/4 of its cars have CD players, what percentage of the cars that were not rented had CD players?
Answer: This looks like a tough question. So what do we do? We cheat a bit. Instead of working with annoying fractions and percentages, let's just make up real numbers and work with them. There's nothing wrong with that and it will help you beat the GMAT.
So, say we have 120 cars. This means we rented 80 and didn't rent 40 cars. Now, in total, 90 of the cars have CD players, and we rented out 3/5 of them which is 54 cars. We're left with 36 CD cars not rented out of 40. 36 out of 40 is 90%.
See? Working with real numbers got us the answer easy- it's 90%.
Question 2: If
-2<a<11 and 3<b<12, then which of the following is
NOT true?
(A) 1<a+b<23
(B) -14<a-b<8
(C) -7<b-a<14
(D) 1<b+a<23
(E) -24 < ab < 132
Answer: Take a quick
scan of the answers first. You should notice a few things. First,
a and d are the same, as . So we can
cancel them out right away. Also,
, but b
and c are not the same numbers. Thus, either b or c has to be
wrong. Great, we've already narrowed it down a lot without
thinking much.
Which one is it though? A simple check using the end points is
sufficient to find out the answer. Let's try b first. We can get
to ,
,
or
using all the endpoints. Our range is clearly
-14 to 8. So b is right. Without doing anything else, we already
the know the answer is
C.
Question 3: In this figure, we have a circle inside a square. What's the ratio of the area of the circle to the area of the square?
(A)
(B)
(C)
(D)
(E)
Answer: First of all,
take a look at the answers. Keep in mind thet is approximately 3.14.
We're looking for a ratio: the area of the circle to the square.
Clearly, the circle is smaller than the square, so the ratio has
to be a value less than 1. Thus, answer choices A, B and C can't
possible be right. It's either D or E.
Now, what do we do? Let's plug in values again. We know that for
the area of the circle we need a radius, so let's say the radius
is 2. Then the area of the circle is . The square on the
other hand would have a side that's twice the radius- 4, and so
its area would be 16.
Now we just divide for the ratio: . Our answer is just
D.
That's it for now! Check back for more sample problems with solutions.
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