GMAT® Official Guide 2019 Quantitative Review
Algebra o Ii r ~ lem
If x, where x > 2, represents the number of days
Machine X takes to produce w widgets, then
Machine Y takes x - 2 days to produce w widgets.
It follows that Machines X and Y can produce w
X
and ~ widgets, respectively, in 1 day and
x-2 w w.
together they can produce -;; + x _ 2 widgets
in 1 day. Since it is given that, together, they can
produce i w widgets in 3 days, it follows that,
4
together, they can produce 1(5 )^5
3 4
w =
12
w
widgets in 1 day. Thus,
w+~=j_w
X x-2 12
(.!.+_1 X x-2 )w = j_w 12
(~+ x~2)= :i
12x(x-2)(~+ x~
2
) = 12x(x-2{;
2
)
12[(x-2)+ x] = 5x(x-2)
12(2x - 2) = 5x(x - 2)
24x-24 = 5x^2 -lOx
0 = 5x^2 -34x+ 24
0=(5x-4)(x-6)
x = i or 6
5
Therefore, since x > 2, it follows that x = 6.
Machine X takes 6 days to produce w widgets
and 2(6) = 12 days to produce 2w widgets.
The correct answer is E.
PS07117
- A square wooden plaque has a square brass inlay in
the center, leaving a wooden strip of uniform width
around the brass square. If the ratio of the brass area
to the wooden area is 25 to 39, which of the following
could be the width, in inches, of the wooden strip?
I. 1
II. 3
Ill. 4
(A) I only
(B) II only
(C) I and II only
(D) I and Ill only
(E) I, II, and Ill
Geometry ea
- •---x-----,•.-
Note: Not drawn to scale.
Let x represent the side length of the entire
plaque, let y represent the side length of the brass
inlay, and w represent the uniform width of the
wooden strip around the brass inlay, as shown in
the figure above. Since the ratio of the area of the
brass inlay to the area of the wooden strip is 25 to
39, the ratio of the area of the brass inlay to the
f h.^1. Y
2
areao t eentuepaqueis7=^25 25
25
+
39
=
64
Then 2'.. = {2s' = i and y = ix. Also, x = y + 2w
'X ~64 8 8
and w = x - Y. Substituting .2.. x for y into this
2 8
x--x^5 -x^3
expression. c 1or w gives. w =^8 =JL_=l_x.
2 2
16
Thus,