GMAT® Official Guide 2019 Quantitative Review
Arithmetic
If 4 machines, working simultaneously, each work
for 30 hours to fill a production order, it takes
(4)(30) machine hours to fill the order.
If 5 machines are working simultaneously, it. (4)(30)
will take ---= 24 hours. Thus, 5 machines
5
working simultaneously will take 30 - 24 = 6
fewer hours to fill the production order than
4 machines working simultaneously.
The correct answer is C.
PS0l443
5 7. A certain toll station on a highway has 7 tollbooths,
and each tollbooth collects $0. 75 from each vehicle
that passes it. From 6 o'clock yesterday morning
to 12 o'clock midnight, vehicles passed each of the
tollbooths at the average rate of 4 vehicles per minute.
Approximately how much money did the toll station
collect during that time period?
(A) $1,500
(B) $3,000
(C) $11,500
(D) $23,000
(E) $30,000Arithmetic
On average, 4 vehicles pass each tollbooth every
minute. There are 7 tollbooths at the station,
and each passing vehicle pays $0.75. Therefore,
the average rate, per minute, at which money is
collected by the toll station is$ (7 x 4 x 0.75) =
$ (7 x 4 x^3
4) = $ (7 x 3) = $21. From 6 a.m.
through midnight there are 18 hours. And
because 18 hours is equal to 18 x 60 minutes,
from 6 a.m. through midnight there are 1,080
minutes. The total amount of money collected
by the toll station during this period is therefore
1,080 X $21 = $22,680, which is approximately
$23,000.The correct answer is D.PS13829- How many integers between 1 and 16, inclusive, have
exactly 3 different positive integer factors?
(Note: 6 is NOT such an integer because 6 has
4 different positive integer factors: 1, 2, 3, and 6.)
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6Arithmetic
Using the process of elimination to eliminate
integers that do NOT have exactly 3 different
positive integer factors, the integer 1 can be
eliminated since 1 has only 1 positive integer
factor, namely 1 itself Because each prime
number has exactly 2 positive factors, each prime
number between 1 and 16, inclusive, (namely, 2,
3, 5, 7, 11, and 13) can be eliminated. The integer
6 can also be eliminated since it was used as an
example of an integer with exactly 4 positive
integer factors. Check the positive integer factors
of each of the remaining integers.
/
Positive integer Number'
Integer factors of factors
4 1,2,4 3
8 1,2,4,8 4
9 1 ,3,9 3
10 1,2,5,10 4
12 1, 2, 3, 4, 6, 12 6
14 1,2, 7,14 4
15 1,3,5,15 4
16 1,2,4,8,16 5Just the integers 4 and 9 have exactly 3 positive
integer factors.Alternatively, if the integer n, where n > 1, has
exactly 3 positive integer factors, which include
1 and n, then n has exactly one other positive
integer factor, say p. Since any factor of p would
also be a factor of n, then p is prime, and sop is
the only prime factor of n. lt follows that n = pk
for some integer k > 1. But if k 2". 3, then p^2 is
a factor of n in addition to 1, p, and n, which
contradicts the fact that n has exactly 3 positive
integer factors. Therefore, k = 2 and n = p^2 , which