OG 2016 Percentage Question

staunchMBAican wrote:If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?

A) 400
B) 420
C) 480
D) 500
E) 600

60 percent of those who receive a questionnaire by mail will respond
Rewrite as: 60 percent of receivers = responders
We want 300 responders, so rewrite as: 60 percent of receivers = 300
60% of what = 300?

Option #1) Check answer choices
A) 400
60% of 400 = 240 (nope, we want 300)
.
.
.
D) 500
60% of 500 = 300...works!!


Or option #2) algebra
60% of x = 300
0.6x = 300
x = 300/0.6
= 500
= D


Or...
60% of x = 300
0.6x = 300
(3/5)x = 300
x = (5/3)300
= 500
= D


Cheers,
Brent

staunchMBAican wrote:If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?

A) 400
B) 420
C) 480
D) 500
E) 600

If we let x = the number of questionnaires that should be mailed, then x must satisfy 0.6x = 300. Then, x = 300/0.6 = 500.

Answer: D

staunchMBAican wrote:If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?

A) 400
B) 420
C) 480
D) 500
E) 600

I feel there's gotta be a nifty quick trick here. Experts?

60 percent of those who receive a questionnaire by mail will respond
Rewrite as: 60 percent of receivers = responders
We want 300 responders, so rewrite as: 60 percent of receivers = 300
60% of what = 300?

Option #1) Check answer choices
A) 400
60% of 400 = 240 (nope, we want 300)
.
.
.
D) 500
60% of 500 = 300...works!!


Or option #2) algebra
60% of x = 300
0.6x = 300
x = 300/0.6
= 500
= D


Or...
60% of x = 300
0.6x = 300
(3/5)x = 300
x = (5/3)300
= 500
= D

Cheers,
Brent

Hi All,

We're told that it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 300 responses are needed. We're asked for the MINIMUM number of questionnaires that should be mailed. We can answer this question with a bit of logic and TESTing THE ANSWERS.

To start, IF only 50% of people responded to the questionnaire, then we would need 600 mailings to generate 300 responses (since 50% of 600 = 300). However, since we're dealing with a 60% response rate, (.6)(600) = 360 - and that's far more responses than we actually 'need.' Thus, 600 is almost certainly NOT the answer. Logically, we need fewer than 600 questionnaires; looking at the answer choices, it would make sense to think about 500 next...

10% of 500 = 50
60% of 500 = (6)(50) = 300

That is an exact match for what we were told, so this MUST be the answer.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich