GMAT® Official Guide 2019 Quantitative Review
(2) It is given that [d] = 0, which is equivalent
to O :::; d < 1. This can be inferred by
examining a few representative examples,
such as [-0.1] = -1, [OJ = 0, [O.l] = 0, [0.9] = 0,
and [1.1] = 1. From O:::; d < l, it follows that
d < l; SUFFICIENT.
The correct answer is D;
each statement alone is sufficient.
DS14052- If N is a positive odd integer, is N prime?
( 1) N = 2k + l for some positive integer k.
(2) N + 2 and N + 4 are both prime.Arithmetic
Determine whether the positive odd integer Nis
prime.(1) This indicates that N = 2k + l for some
positive integer k. If k = l, then N = 21 + 1 = 3
and Nis prime. However, if k = 3, then N =
23 + 1 = 9 and Nis not prime; NOT sufficient.
(2) This indicates that both N + 2 and N + 4 are
prime. If N = 3, then N + 2 = 5 and N + 4 = 7
are both prime and N is prime. However, if
N = 9, then N + 2 = 11 and N + 4 = 13 are both
prime and N is not prime; 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.
DS01140- If m is a positive integer, then m^3 has how many digits?
(1) m has 3 digits.
(2) m^2 has 5 digits.Arithmetic
(1) Given that m has 3 digits, then m could be
100 and m^3 = 1,000,000 would have 7 digits,
or m could be 300 and m^3 = 27,000,000
would have 8 digits; NOT sufficient.
(2) Given that m^2 has 5 digits, then m could be
100 (because 1002 = 10,000 has 5 digits) or
m could be 300 (because 3002 = 90,000 has
5 digits). In the former case, m^3 = 1,000,000has 7 digits and in the latter case,
m^3 == 27,000,000 has 8 digits; NOT sufficient.
Given (1) and (2), it is still possible form to be
100 or for m to be 300, and thus m^3 could have
7 digits or m^3 could have 8 digits.The correct answer is E;
both stat4ements together are still not sufficient.
DS03308- What is the value of x^2 - y^2?
( 1) (x - y)^2 = 9
(2) x+ Y= 6Algebra
Determine the value of x^2 - y^2.(1) This indicates that (x -y)^2 = 9. It follows
that x -y = -3 or x -y = 3, which gives
information about the value of x -y but not
specific information about the value of x,y,or x^2 - y^2. For example, if x = 2. and y = l ,
2 2(^9 3)
2
then(x-y)^2 =
2- 2
=9andx^2 -y^2
=^81 - 2. = 18. But if x = l and y = 2. then
4 4 2 2'(x-y)2 = (1_2.)
2
= 9 andx^2 - y^2 =2.-^81 =
2 2 4 4- 18; NOT sufficient.
(2) This indicates that x + y = 6 but does not give
specific information about the value of x, y, or
x^2 --y^2. For example, if x = 2. and y = l, then
2 2
x + y = 2. + l = 6 and x^2 -y^2 =^81 - 2. =
· 2 2 4 4- But if x = l and y = 2., then x + y =
2 2
1+2. =6andx^2 -y^2 = 2. -^81 =-18·
2 2 4 4 '
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.Alternatively, note that x^2 - y^2 = (x-y)(x+ y). From
(l), x -y == ±3, and from (2), x + y = 6. Therefore,