GMAT® Official Guide 2019 Quantitative Review
Algebra
If x represents the amount, in liters, of gasoline
poured into the 6-liter container, then
5 - x represents the amount, in liters, of gasoline
poured into the 2-liter container. After the
gasoline is poured into the containers, the 6-liter
container will be filled to (! x 100 )% of its
capacity and the 2-liter container will be filled to
(
5
; x x 100) % of its capacity. Because these two
percents are equal,
-=--X 5-x
6 2
2x= 6(5 - x)
2x= 30-6x
8x= 30
x=3l
4
given
multiply both sides by 12
use distributive property
add 6x to both sides
divide both sides by 8
Therefore, 31 liters of gasoline must be poured
4
into the 6-liter container.
The correct answer is C.
PS02775
- List S consists of 10 consecutive odd integers, and list
T consists of 5 consecutive even integers. If the least
integer in S is 7 more than the least integer in T, how
much greater is the average (arithmetic mean) of the
integers in S than the average of the integers in T?
(A) 2
(B) 7
(C) 8
(D) 12
(E) 22
Arithmetic
Let the integers in S bes, s + 2, s + 4, ... , s + 18,
wheres is odd. Let the integers in The t, t + 2,
t + 4, t + 6, t + 8, where tis even. Given that
s = t + 7, it follows thats -t = 7. The average
o t e f h mtegers. m. S 1s. ---10s +^90 = s + 9, an d ,
10
similarly, the average of the integers in Tis
St+ 20
S = t + 4. The difference in these averages
is (s + 9) - (t + 4) = (s -t) + (9 - 4) = 7 + 5 = 12.
Thus, the average of the integers in Sis 12 greater
than the average of the integers in T.
The correct answer is D.
PS05616
B
4
4
C
A 4 0
- In the figure above, what is the area of triangular
region BCD?
(A) 4./2
(B) 8
(Cl 8./2
(D) 16
(E) 16./2
Geometry n I c• Ar
By the Pythagorean theorem, BD = .J 4 2 + 4 2 = 4Ji.
Then the area of f:iBCD is ~ ( 4Ji) ( 4) = 8Ji.
The corriect answer is C.
PS13882
- What is the larger of the 2 solutions of the equation
x^2 - 4x = 96?
(A) 8
(Bl 12
(C) 16
(D) 32
(El 100
Algebra
It is given that x2 -4x = 96, or x2 -4x - 96 = 0,
or (x - 12)(x + 8) = 0. Therefore, x = 12 or x = -8,
and the larger of these two numbers is 12.
Alternatively, from x2 -4x = 96 it follows that
x(x - 4) == 96. By inspection, the left side is either
the product of 12 and 8, where the value of x is 12,
or the product of -8 and -12, where the value of
x is -8, and the larger of these two values of x is 12.
The correct answer is B.