GMAT® Official Guide 2019 Quantitative Review
range for each year was $2,320 - $400 = $1,920.
However, if, last year, Company Y budgeted
$400 for each of 2 projects and $2,320 for each
of the 10 others, and, this year, budgeted $400
for each of 11 projects and $19,600 for 1 project,
then (1) and (2) are true, but the range for last
year was $1,920 and the range for this year was
$19,600- $400 = $19,200.The correct answer is E;
both statements together are still not sufficient.a b C d
DS01633- If a, b, c, and dare numbers on the number line shown
and if the tick marks are equally spaced, what is t he
value of a + c?
(1) a + b =-8
(2 ) a+ d = 0Algebra Seque 1ces
It is given that the distance between a and b
is the same as the distance between b and c,
which is the same as the distance between c
and d. Letting q represent this distance, then
b = a + q, c = a + 2q, and d = a + 3q. The value
of a + c can be determined if the value of
a+ (a+ 2q) = 2a + 2q can be determined.(1) It is given that a + b = -8. Then,
a + (a+ q) = 2a + q = -8. From this, the
value of 2a + 2q cannot be determined. For
example, the values of a and q could be - 5
and 2, respectively, or they could be - 6 and
4, respectively; NOT sufficient.
(2) It is given that a + d = O. Then,
a + (a+ 3q) = 2a + 3q = 0. From this, the
value of 2a + 2q cannot be determined. For
example, the values of a and q could be -3
and 2, respectively, or they could be - 6 and
4, respectively; NOT sufficient.
Taking (1) and (2) together, adding the equations,
2a + q = - 8 and 2a + 3q = 0 gives 4a + 4q = - 8
and so 2a + 2q = -^8 = - 4.
2The correct answer is C;
both statements together are sufficient.0S06067- Is xm < ym?
(1) X>Y
(2 ) m < 0Algebra l'lequ1litiPs
(1) Given that x > y, the inequality xm < ym
can be true (for example, if m = - 1, then
xm < ym becomes - x < - y, or x > y, which
is true by assumption) and it is possible that
the inequality xm < ym can be false (for
example, if m = 0, then xm < ym becomes
0 < 0, which is false); NOT sufficient.(2) Given that m < 0, the inequality xm < ym
can be true (for example, if m = - 1, x = 2,
and y = 1, then xm < ym becomes - 2 < - 1,
which is true) and it is possible that the
inequality xm < ym can be false (for example,
if m = - 1, x = 1, and y = 2, then xm < ym
becomes -1 < - 2, which is false); NOT
sufficient.Taking (1) and (2) together, multiplying both
sides of the inequality x > y by m reverses the
inequality sign (since m < O), which gives
xm<ym.The correct answer is C;
both statements together are sufficient.
DS02899- If y = x^2 - 6x + 9, what is the value of x?
(1) Y = 0
(2) X + .Y = 3Algebra :,econd- egre eq 1 io 1s
Given that y = x2--6x + 9 = (x-3)2, what is the
value of x?(1) Given that y = 0, it follows that (x - 3)^2 = 0,
or x = 3; SUFFICIENT.
(2) Given that x + y = 3, or y = 3 - x, then x = 3
and y = 0 are possible, since y = (x - 3)^2
becomes O = (3 - 3)2, which is true, and
y = 3 -x becomes O = 3 - 3, which is true.
However, x = 2 and y = 1 are also possible,
since y = (x - 3)^2 becomes 1 = (2 - 3)2,
which is true, and y = 3 -x becomes
1 = 3 - 2, which is true; NOT sufficient.