An HR manager reviewed the first third of a stack of resumes

Question

An HR manager reviewed the first third of a stack of resumes at a rate of 9 resumes per hour, the second third at a rate of 18 resumes per hour, and the final third at a rate of 36 resumes per hour. If it took the manager 7 hours to review all of the resumes, how many resumes were in the stack?

A) 54
B) 72
C) 90
D) 108
E) 126

A) 54
B) 72
C) 90
D) 108
E) 126

AbdiAR · Answer

Let x = the number of resumes

_____ R ____ T ______ W 
1st _ 9 ___________ x/3
2nd _ 18 ___________ x/3 
3rd _ 36 ___________ x/3

T1+T2+T3 = Time total 
T1: x/3÷9 = x/27
T2: x/3÷18 = x/54
T3: x/3÷36 = x/108

x/27+x/54+x/108 = 7

Multiplying everything by the LCM

4x+2x+x = 756
7x= 756 
x = 108

Answer: D

poojaarora1818 · Answer

Let's apply the matrix approach

Rate 
 Time  
 Work 
 
  First Third 
 9r/h 
 N/9 
 N 
 
  Second Third 
 18r/h 
 N/18 
 N 
 
  Final Third 
 36r/h 
 N/36 
 N

We know the total time took by manager to review all the resumes are 7 hours.

N/9 + N/18 + N/36 = 7

By solving the above equation we get

N = 36

Total number of resumes = 3N = 108

Answer: D

Edskore · Answer

Classic Work and Rate setup. The variable definition is the part that bites most people.

Let the total number of resumes = N. Each third of the stack has N/3 resumes.

1. Time to review the first third: (N/3) / 9 = N/27 hours
2. Time to review the second third: (N/3) / 18 = N/54 hours
3. Time to review the final third: (N/3) / 36 = N/108 hours

Total time = N/27 + N/54 + N/108 = 7

Finding the LCM of 27, 54, 108 — it's 108.

So: 4N/108 + 2N/108 + N/108 = 7
7N/108 = 7
N = 108

Answer is D.

The common trap is setting N equal to one-third of the stack instead of the whole thing, which leads to 36 and then having to remember to multiply back. Defining N as the total from the start avoids that confusion. Also, a lot of people try to work with the rates directly (9+18+36 and some average) which doesn't work for unequal distances — you can only average rates when equal times are spent, not equal amounts of work.

Dereno · Answer

Let the total resumes be 3x.

x resumes at the rate of 9 resumes per hour, 18 resumes per hour, and 36 resumes per hour.

If we assume the total work to be LCM (9,18,36) = 36 units = x.

Efficiency at the respective stacks are 4,2,1 respectively.

Total hours = 4+2+1 = 7 hours.

Total resumes = 3x = 3*36 =  108.

Option D

An HR manager reviewed the first third of a stack of resumes

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	Rate	Time	Work
First Third	9r/h	N/9	N
Second Third	18r/h	N/18	N
Final Third	36r/h	N/36	N

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An HR manager reviewed the first third of a stack of resumes

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