GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag197

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181. 4 Let d = the number of days it will take the five machines to do the job and 
r = the rate at which one machine could do the job working alone. Ten days times 2 machines 
times r equals 1 job, from which you have =r20 1 (omitting units). Thus, r = 1
20
; that is, 
each machine does 1
20
 of the job per day. Therefore, if 5 machines working together for d 
days complete the job, then =d times 5 machines times 1
20
job per machine 1 job. Omitting 
units and solving for d yields ⋅ ⋅ =d 5 1
20
1 
 =d
4
1 
d = 4 days
182. −−44
−f g( ( 1)) = = −f (3) 4 
183. 2 Observe that in simplified form = − +
− +
=
−
y x x
x x x
( 2) ( 3)
( 2) ( 3)
1
2
2
3
, which will have a vertical 
asymptote when − =x 2 0; that is, when x = 2.
184. 97 = + − = +a a d a d(20 1) (19)20 1 1 , so you need the values of a1 and d to determine 
a20. Write and simultaneously solve the following two equations:
 (1) = = +a a d17 34 1 and (2) = = +a a d47 910 1 . Multiply (2) by −1 and add to 
(1) to obtain − = −d6 30; d = 5. Substitute d = 5 into (1) to obtain =a 21 . Thus, 
= + = + =a a d(19) 2 (19)(5) 9720 1 .
185. 3 Let t = the number of hours in which the two vehicles will be 390 miles apart, 
x = the speed of the first vehicle in miles per hour, and −x 10 = the speed of the second 
vehicle. When the two vehicles are 390 miles apart, the second vehicle has gone a distance 
of 180 miles, so the first vehicle has gone a distance of −390 miles 180 miles = 210 miles. 
Organize the question information.
 Vehicle Rate Time Distance
 1 x t xt = 210 miles
 2 −x 10 t − =x t( 10) 180 miles 
 Together Do not add rates t 390 miles
 From the chart, you can write and solve simultaneously the following two equations:
(1) xt = 210 and (2) − =x t( 10) 180, − =xt t10 180 
 Substitute (1) into (2) and solve for t.
 − =xt t10 180 
 − =t210 10 180 
 − = −t10 30 
t = 3
06_McCune_Answer.indd 188 2/21/22 4:47 PM