GMAT® Official Guide 2019 Quantitative Review5.5 Answer Explanations
'DS05149- Does 2x+ 8 = 12?
(1) 2x + 10 = 14
(2) 3x+8= 14Algebra
We need to determine, for each of statements
1 and 2, whether the statement is sufficient for
determining whether 2x + 8 = 12. Solving for x,
we see that the equation 2x + 8 = 12 is equivalent
to 2x = 12 - 8 = 4 and is thus equivalent to x = 2.
We thus need to find whether the statements are
sufficient for determining whether x = 2.(1) Given that 2x + 10 = 14, it follows that 2x =
14 - 10 = 4, and that x = 2; SUFFICIENT.
(2) Similarly, given that 3x + 8 = 14, it follows
that 3x = 14 - 8 = 6, and that x = 2;
SUFFICIENT.
Alternatively, for both statements 1 and 2, it is
only necessary to determine that it is possible to
solve each of 1 and 2 to produce a unique value
for x. Care must be taken with such an approach
( there are cases such as, for example, 3y = 5 + 3y,
that cannot be solved for a unique value of the
variable). However, the approach can save time.The correct answer is D;
each statement alone is sufficient.
DS01503- If M is a set of consecutive even integers, is O in set
M?
(1) -6 is in set M.
(2) -2 is in set M.179.Arithmetic
For a set M of consecutive even integers, can we
determine whether M contains the number O?
(1) Given that -6 is in the set M, M could be a
set of strictly negative integers or a set that
contains both negative integers and zero
(and perhaps positive integers). For example,
it could be the set {-8, -6, -4} or the set {-8,
-6, --4, -2, 0, 2}; NOT sufficient.
(2) Similarly, given that -2 is in M, M could be
a set of strictly negative integers or a set that
contains both negative integers and zero
(and perhaps positive integers). For example,
it could be the set {-4, -2} or the set {-8, -6,
-4, ·-2, 0, 2}; NOT sufficient.
Furthermore we can see that statements 1 and 2
together are not sufficient. For example, {-8, -6,
-4, -2, 0, 2} contains -6, -2, and 0, while {-8, -6,
-4, -2} contains -6 and -2 but not 0.The corn::ct answer is E;
both statiements together are not sufficient.
DS15510
Rita's monthly salary is^2
3Juanita's monthly salary.
What is their combined monthly salary?(1) Rita's monthly salary is $4,000.
(2) Either Rita's monthly salary or Juanita's monthly
salary is $6,000.Arithmetic
Let R andJbe Rita's and Juanita's monthly salaries,
respectively, in dollars. It is given that R = l J
3
Determine the value of their combined salary,
which can be expressed as R + J = l J + J = i J
3 3
*These numbers correlate with the online test bank question number. See the GMAT Quantitative Review Online Index in the back of this book.