D. More practice
questions
Example 1
Is x > 4?
1) x squared = 9
2) x squared =25
Solution
(1) implies that x = +/- 3 (+/- means positive or negative).
Both +3 and -3 are less than 4, so the answer is "NO"
and (1) is sufficient, that is NO, x is not greater than 4. A
"NO" answer is equally acceptable as a "YES"
answer. It is only necessary that there is sufficient information
to answer the question. (2) implies x = positive or negative
5. -5 is less than 4 and + 5 is greater than 4, so the question
cannot be answered with the information given in (2). The correct
response is A.
Example 2
What is x - y?
1) x + y = 8
2) x - 2y = 2
Solution
(1) is not sufficient since (x - y) is the quantity desired.
Likewise, (2) is not sufficient. But (1) and (2) together provide
us with 2 equations and two unknowns from which x - y can be
determined. The correct response is C. (We may solve the problem
by subtracting (2) from (1): 3y = 6, therefore y = 2 and x =
6, so that x - y = 6 - 2 = 4. This calculation is, however, unnecessary.)
Example 3
How old is Gloria?
1) Gloria's age is four times
Alex's age plus Becky's age.
2) Becky was Alex's age fifteen years ago.
Solution
(1) is obviously not sufficient as is (2). Can the question be
answered with (1) and (2)? Let x be Gloria's age, y be Alex's
age, and z be Becky's age. (1) states that x = 4y + z. (2) states
that z - 15 = y. These two equations contain three unknowns;
consequently, we cannot determine x. More information is needed
and the correct response is E.
Example 4
A student group sold only donuts and GMAT books to raise funds.
How many GMAT books were sold?
1) 30% of the 90 items sold were GMAT books.
2) 63 donuts were sold.
Solution
(1) is sufficient since 30% of 90 is 0.3 x 90 = 27. (2) is not
sufficient since we do not know the total number of items sold.
So the correct response is A. A note of caution: Never let information
in (1) influence your decision regarding the information in (2).
In this example we cannot assume that 90 items were sold when
deciding if (2) provides sufficient information. This is the
Amnesia trick that undisciplined test takers
will always fall into. Remember to look at each statement individually
before comparing the two.
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