GMAT® Official Guide 2019 Quantitative Review
Geometry Are-:i
Note that, in rectangle ABCD, the sides BC and
AD do not share an endpoint and must therefore
be on opposite sides of the rectangle. We thus see
that the point X, which is both on triangle AXD
and on side BC of the rectangle, lies on the side
of the rectangle that is opposite the side AD of
the rectangle. AD is also a side of the triangle.
So if the rectangle is drawn with AD horizontal
and on the bottom (see the diagram, which is
not drawn to scale), the vertical height of the
triangle from the base AD is equal to the length
of the sides on the rectangle that are adjacent to
AD. Given the formula for the area of a triangle,
1.. x base x height, the area of the triangle AXD is
2
thus 1.. x AD x AB (or equivalently 1.. x AD x CD).
2 2Now,AD may be either a length or a width of
the rectangle-equal to 12 or equal to 8. If AD is
equal to 12, then AB is a width and is equal to 8;
the area of the triangle is thus 1.. x 12 x 8. If AD is
2
instead equal to 8, then AB is equal to 12, and the
formula for the area of the triangle results in the
expression 1.. x 8 x 12. In both cases, the area of
2
the triangle is equal to 48.The correct answer is B.
PS07659- A grocer has 400 pounds of coffee in stock,
20 percent of which is decaffeinated. If the grocer
buys another 100 pounds of coffee of which
60 percent is decaffeinated, what percent, by weight,
of the grocer's stock of coffee is decaffeinated?
(A) 28%
(B) 30%
(C) 32%
(D) 34%
(E) 40%Arithmetic rce
The grocer has 400 pounds of coffee in stock, of
which (400)(20%) = 80 pounds is decaffeinated
coffee. Therefore, if the grocer buys 100 pounds of
coffee, of which (100)(60%) = 60 pounds is
decaffeinated coffee, then the percent of the
grocer's stock of coffee that is decaffeinated would
be 80 + 60 = 140 = 28 = 28 %.
400 + 100 500 100The correct answer is A.
PS05 129- The toll T, in dollars, for a truck using a certain bridge
is given by the formula T = 1.50 + 0.50(x - 2), where
x is the number of axles on the truck. What is the toll
for an 18-wheel truck that has 2 wheels on its front
axle and 4 wheels on each of its other axles?
(A) $2.50
(B) $3.00
(C) $3.50
(D) $4.00
(E) $5.00Algebra Opera .1 l!» on rd :>nal number!.
The 18-wheel truck has 2 wheels on its front
axle and 4 wheels on each of its other axles,
and so if A represents the number of axles on
the truck in addition to the front axle, then
2 + 4A = 18, from which it follows that 4A = 16
and A = 4. Therefore, the total number of axles
on the truck is 1 +A= 1 + 4 = 5. Then, using
T = 1.50 + 0.S0(x -2), where xis the number
of axles on the truck and x = 5, it follows that
T= 1.50 + 0.50(5 - 2) = 1.50 + 1.50 = 3.00.
Therefore, the toll for the truck is $3.00.The correct answer is B.
PS13917- For what value of x between -4 and 4, inclusive, is the
value of x^2 - 1 Ox + 16 the greatest?
(A) -4
(B) -2
(C) 0
(D)
(E)2
4