GMAT® Official Guide 2019 Quantitative Review
$3, there would have been 150 x $3 = $450
in contributions from the seniors and 300 x
$1 = $300 in contributions from the juniors,
for a total of $750-more than the figure of
$740 with which the question is concerned.
However, as noted, we cannot make such an
assumption. To test the conditions that we
have actually been given, we can consider
extreme cases, which are often relatively
simple. For example, given the information
provided, it is possible that only two of
the students are seniors and the other 598
students are juniors. If this were the case,
then the contributions from the juniors
would be $598 ($1 per student) and the
contributions from the seniors would be
$3 ($3 for the one senior who contributes,
given that only half of the 2 seniors
contribute). The total contributions would
then be $598 + $3 = $601; NOT sufficient.
(2) Merely with this statement-and not
statement 1-we have no information as
to how much the students contributed.
We therefore cannot determine the total
amount contributed; NOT sufficient.
We still need to consider whether statements
1 and 2 are sufficient together for determining
whether a minimum of$ 7 40 has been
contributed. However, note that the reasoning in
connection with statement 1 applies here as well.
We considered there the possibility that the 600
students included only two seniors, with the other
598 students being juniors. Because this scenario
also satisfies statement 2, we see that statements 1
and 2 taken together are not sufficient.The correct answer is E;
both statements together are still not sufficient.
DS06650- How much did credit-card fraud cost United States
banks in year X to the nearest $10 million?
( 1) In year X, counterfeit cards and telephone and
mail-order fraud accounted for 39 percent of the
total amount that card fraud cost the banks.
(2) In year X, stolen cards accounted for
$158.4 million, or 16 percent, of the total
amount that credit-card fraud cost the banks.Arithmetic Pe ·cents
(1) It is given that certain parts of the total
fraud cost have a total that is 39% of the
totall fraud cost, but since no actual dollar
amounts are specified, it is not possible to
estimate the total fraud cost to the nearest
$10 million; NOT sufficient.
(2) Given that $158.4 million represents 16% of
the total fraud cost, it follows that the total
fraud cost equals $158.4 million divided by
0.16; SUFFICIENT.
The correct answer is B;
statement 2 alone is sufficient.
DSl 7319- Is the positive integer n odd?
(1) n^2 + (n + 1)^2 + (n + 2)^2 is even.
(2) n^2 - (n + 1)^2 - (n + 2)^2 is even.Arithmetic ... j
The positive integer n is either odd or even.
Determine if it is odd.(1) This indicates that the sum of the squares of
three consecutive integers, n^2 , (n + 1)2, and
(n + 2)2, is even. If n is even, then
n + l is odd and n + 2 is even. It follows
that n^2 is even, (n + 1)^2 is odd, and (n + 2)^2
is even and, therefore, that n^2 + (n + 1)^2 +
(n + 2)^2 is odd. But, this contradicts the
given information, and so, n must be odd;
SUFFICIENT.
(2) This indicates that n^2 - (n + 1)^2 - (n + 2)^2 is
even. Adding the even number represented
by 2(n + 1)^2 + 2(n +2)^2 to the even number
represented by n^2 - (n + 1)^2 - (n + 2)^2
gives the even number represented
by n^2 + (n + 1)^2 + (n +2)^2. This is
Statement (1); SUFFICIENT.
The corre:ct answer is D;
each statement alone is sufficient.
DS01130- In the xy-plane, circle Chas center (1,0) and radius
- If line k is parallel to the y-axis, is line k tangent to
circle C?
(1) Line k passes through the point (-1, 0).
(2) Line k passes through the point (-1,-1).