Quantitative comparison
measures your ability to:
Quantitative
Comparisons
Quantitative comparisons
are basic arithmetic, algebra, and geometry problems, which use the
same concepts we reviewed earlier. We will learn a few special techniques for quantitative
comparisons in this section. Here are the directions for quantitative comparisons as they appear
on the GRE:
Directions: Each of the Questions
consists of two quantities, one in Column A and one
in Column B. You are to compare the two quantities and choose
A if the quantity in Column A is greater;
B if the quantity in Column B is greater;
C if the quantities are equal;
D if the relationship cannot be determined from the information given.
Note: Since there are only four choices, NEVER MARK (E).
Common Information: In a question, information concerning one or both
of the
quantities to be compared is centered above the two columns. A symbol that appears
in both columns represents the same thing in Column A as it does in Column B.
Do not bother to
read these directions. Here are the directions worded more explicitly that you
should memorize before taking the GRE:
Directions: Each of the Questions
consists of two quantities, one in Column A and one
in Column B. You are to compare the two quantities and choose
A if the quantity in Column A is always greater;
B is the quantity in Column B is always greater;
C if the quantities are always equal;
D if none of the other choices is always correct.
The only difference
between these directions and the GRE’s is the fact that the quantity in
Column A must always be greater than the quantity in Column B in order to choose answer A.
The following example illustrates this point.
Example 1:
|
Column
A
|
Column
B
|
|
x
+ 1
|
1
- x
|
Solution: Plug
in the number 1 for x. Then A is greater than B. But what if we plug in (–1).
Then B is greater than A. So, the answer would be D since neither A nor B is always true.
Be very careful
on quantitative comparisons to never mark E. There are only four
answer choices.
If a quantitative
comparison problem contains only numbers, there will be an exact answer.
Therefore, always eliminate choice D on these problems.
Example 2:
|
Column
A
|
Column
B
|
|
2/7
- 1
|
1/3
- 1
|
Solution: Immediately
eliminate choice D because there are only numbers involved. Also, since
(–1) appears in both expressions, we can ignore it. Now we only have to decide which is
bigger, 2/7 or 1/3. Since 1/3 can also be written as 2/6, 2/7 is obviously smaller. Therefore, the
answer is B.
On some problems,
you will be able to visualize the problem and avoid computations.
Example 3:
|
Column
A
|
Column
B
|
|
Area of circle
with diameter 12
|
Surface area of
a
sphere with diameter
12
|
Solution:
Just picture a soccer ball and a paper plate. The answer is B.
Quantitative comparisons
are supposed to be fast. If you find yourself setting up an elaborate
calculation or equation, you are on the wrong track. Look for a shortcut.
Example 4:
|
Column
A
|
Column
B
|
|
9(3 +
24)
|
(9 3) +
(924)
|
Solution: Notice
first that D cannot be the answer. Now notice that A is simply the factored
form of B. The answer is C. You are not expected to multiply out numbers like these.
Treat the two
columns as if they were the two sides of an equation. Anything you can do
to both sides of an equation, you can also do to both columns. You can add or subtract
numbers from both columns; you can multiply or divide both columns by a positive number; you
can multiply one side by some form of 1. Do not, however, multiply or divide both columns by
a negative number. The reason is that we don’t know if the two columns represent an equation
or an inequality. If they represent an inequality, the direction of the inequality will change if you
multiply or divide by a negative number.
You should always simplify
the terms in a quantitative comparison by reducing, factoring,
unfactoring, etc.
Example 5:
|
Column
A
|
Column
B
|
|
25
x 7.39
|
739/4
|
Solution: Notice
that D cannot be the answer. Do not do the division or multiplication in this
problem. Try to simplify it. Multiplying both sides by 4, we get:
|
Column
A
|
Column
B
|
|
100
x 7.39
|
739
|
Now it’s
obvious that the two quantities are equal. The answer is C.
For quantitative
comparisons involving variables, it is usually easier to just plug in
numbers.
Example 6:
|
|
2(k3)6
|
Solution: First
remember that k<0 is a condition that applies to both columns. If you are
comfortable with algebra, you can easily see that Column A is just (k/6)6 = k and Column B is
6k/6 = k. Hence, the answer is C. If you are not comfortable with your algebra, just plug a
number in for k that satisfies the condition k<0. Let’s pick –2 so we can get rid of
the fraction
in Column A.
For Column A we
get:
=
= -6/3
= -2
For Column B:
= 2(-6)6
= -6/3
= -2
As we mentioned
earlier, you must be careful when plugging in on quantitative
comparisons. Because of choice D, you must determine whether a quantity is always
greater than, less than, or equal to another quantity. It’s not enough to determine if it
sometimes is. You must determine whether a choice must be correct, not just whether it could
be correct.
Example 7:
Solution: In
order to satisfy the given condition, plug in 3 for x and 2 for y. Then Column A is
9 and Column B is 4 which means Column A is bigger. But now you must plug in something
different like a negative number. Plug in –2 for A and –3 for B. Now Column B is bigger
than
Column A. So, the answer is D.
When plugging
in on quantitative comparisons, you need to use numbers with special
properties that will reveal situations in which the relationship between two quantities doesn’t
hold.
Numbers to use
are: 0, 1, fractions, negative numbers, and negative fractions. Some
examples of these special properties are:
-
0 times any number
is 0
- 0 is 0
- 1 is 1
- squaring a fraction between 0 and 1 results
in a smaller fraction
- a negative number times a negative number
is a positive number
- a negative fraction squared is a positive
fraction
Example 8:
|
Column
A
|
Column
B
|
|
xy
|
x
+ y
|
Solution: First
plug in some easy numbers like 3 for x and 4 for y. Then Column A is 12 and
Column B is 6. We can now eliminate choices B and C. Now try some of the numbers we
mentioned above that have special properties. Try 0 for x and 0 for y since there is no
condition that x and y must be different. Then Column A and Column B are both 0. By finding
just one situation in which A is not greater than B, we’ve eliminated choice A. Hence, the
answer is D.
Example 9:
Solution: First
plug in an easy number like 2 for x. Then y is 5 which means A is 10 and B is 8.
Hence, A is greater than B, and we can eliminate B and C. Since this is a difficult question, we
can eliminate A also. Therefore, the answer must be D. To see why, plug in –1 for x. Then y is
2, A is –2, and B is –1. Hence, B is greater than A, so the answer is D.
If there is no diagram
on a geometry problem, it may mean that a drawing would make the
answer obvious. So, draw one yourself.
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