GMAT® Official Guide 2019 Quantitative Review
Geometry
Let L meters and W meters be the length and
width, respectively, of rectangle A. Then (L -10)
meters and (W + 10) meters are the length and
width, respectively, of rectangle B. Since the
perimeter of rectangle A is 200 meters, it follows
that 2L + 2W= 200, or L + W= 100. Since
rectangle Bis a square, it follows that L - 10 =
W + 10, or L - W = 20. Adding the equations
L + W= 100 and L-W = 20 gives 2L = 120, or
L = 60. From L - W = 20 and L = 60, it follows
that W = 40, and so the width of rectangle A is
40 meters.The correct answer is C.- I • I I I I I I I I I I I • I I I I I •
-9 -8 -7 -6 -5 -4 - 3 -2 -1 Q 1 2 3 4 5 6 7 8 9 X
PS08598
- On the number line, the shaded interval is the graph of
which of the following inequalities?
(A) lxl:::; 4
(Bl 1x1:::; 8
(C) 1x-21:::; 4
(D) 1x-21:::; 6
(El Ix+ 21:::; 6
Algebra
The midpoint of the interval from -8 to 4,
inclusive is ---^8 +^4 = - 2 and the lengt h o t e f h
' 2
interval from -8 to 4, inclusive, is 4 -(-8) = 12,
so the interval consists of all numbers within a
distance of12
= 6 from -2. Using an inequality
involving ab!lute values, this can be described by
jx-(-2)! $6,or jx+2j $6.
Alternatively, the inequality -8 ::; x ::; 4 can be
written as the conjunction -8 ::; x and x::; 4.
Rewrite this conjunction so that the lower value,
-8, and the upper value, 4, are shifted to values
that have the same magnitude. This can be done by
adding 2 to each side of each inequality, which gives
-6 ::; x + 2 and x + 2 ::; 6. Thus, x + 2 lies between
-6 and 6, inclusive, and it follows that Ix+ 21 ::; 6.
The correct answer is E.PSl2450- Last year members of a certain professional
organization for teachers consisted of teachers
from 49 different school districts, with an average
(arithmetic mean) of 9.8 schools per district. Last
year the average number of teachers at these schools
who were members of the organization was 22. Which
of the following is closest to the total number of
members of the organization last year?
(A) 107
(B) 106
(C) 105
(D) 104
(El 103Arithmetic
There are 49 school districts and an average
of 9.8 schools per district, so the number of
schools is (49)(9.8)"" (50)(10) = 500. There
are approximately 500 schools and an average
of 22 teachers at each school, so the number
of teachers is approximately (500)(22) "" (500)
(20) = 10,000 = 104 •The correct answer is D.
~~ 1- Of all the students in a certain dormitory,
2
are first-
year studEmts and the rest are second-year students. If
.± 5 of the first-year students have -not declared a major
and if the fraction of second-year students who have
declared a major is 3 times the fraction of first-year
students who have declared a major, what fraction
of all the students in the dormitory are second-year
students who have not declared a major?(A)(Bl(C)(D)(El1
15
1
5
4
15
1
3
2
5