GMAT® Official Guide 2019 Quantitative Review
DS12187 3
Last year
5of the members of a certain club were
males. This year the members of the club include all
the members from last year plus some new members.
Is the fraction of the members of the club who are
males greater this year than last year?(1) More than half of the new members are male.
(2) The number of members of the club this year
is ~ the number of members last year.Arithmetic Operations with fractions
Let L represent the number of members last
year; N the number of new members added
this year; and x the number of members added
this year who are males. It is given that 1 of the
5
members last year were males. It follows that
the number of members who are male this year
is lL + x. Also, the total number of members
5 3
-L+ x
this year is L + N Determine if 5 > l, or
L + N 5
equivalently, determine if 3L + 5x > 3L + 3N or
simply if x > ¾N(1) This indicates that x > 1-N If, for example,
2
N = 20 and x = 11, then 11 > 1_(20) = 10,
3 2
but 11 )5-
5(20) = 12. On the other hand,
if N = 20 and x = 16, then 16 > 1 (20) = 10,
2
and 16 > 1 (20) = 12; NOT sufficient.
5
(2) This indicates that L + N = 2-L, It follows
5
that N = .!.L, If, for example, L = 100, then
5
N= 1_ (100) = 20. If x = 11, then 11 )5-l
5 5
(20) = 12. On the other hand, if x = 16, then
16 > .!. (20) = 10, and 16 > 1 (20) = 12;
2 5
NOT sufficient.
Taking (1) and (2) together is of no more help
than (1) and (2) taken separately since the same
examples were used to show that neither (1) nor
(2) is sufficient.
The correct answer is E;
both statements together are still not sufficient.DSl3640
296. If a, b, and c are consecutive integers and
0 < a < b < c, is the product abc a multiple of 8?(1) The product ac is even.
(2) The product be is a multiple of 4.Arithmetic Operations with integers
Determine whether the product of three
consecutive positive integers, a, b and e, where
a< b < e, is a multiple of 8.Since a, b, and e are consecutive integers, then
either both a and e are even and b is odd, or both
a and e are odd and b is even.(1) This indicates that at least one of a ore is even,
so both a and e are even. Since, when counting
from 1, every fourth integer is a multiple of
4, one integer of the pair of consecutive even
integ;ers a and e is a multiple of 4. Since the
other integer of the pair is even, the product
ae is a multiple of 8, and, therefore, abe is a
multiple of8; SUFFICIENT
(2) This indicates that be is a multiple of 4. If
b = 3 and e = 4, then a= 2 and be= 12, which is
a multiple of 4. ln this case, abe = (2)(3)(4) =
24, which is a multiple of 8. However, if
b = 4 and e = 5, then a = 3 and be= 20,
which is a multiple of 4. ln this case,
abe = (3)(4)(5) = 60, which is not a multiple
of8; NOT sufficient.
The corre1ct answer is A;
statement: 1 alone is sufficient.
0S13837- Mand N are integers such that 6 < M < N. What is the
value of N ?'
(1) The greatest common divisor of Mand N is 6.
(2) The least common multiple of M and N is 36.Arithmetic, rtie z: m , c-~:::
(1) Given that the greatest common divisor
(GCD) of MandNis 6 and 6 <M <N,
then it is possible that M = (6)(5) = 30 and
N = ( 6)(7) = 42. However, it is also possible
that .M = (6)(7) = 42 and N = (6)(11) = 66;
NOT sufficient.