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# An army’s recruitment process included n rounds of selection tasks. Fo

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An army’s recruitment process included n rounds of selection tasks. Fo  [#permalink]

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20 Jul 2017, 02:15
3
00:00

Difficulty:

65% (hard)

Question Stats:

56% (02:32) correct 44% (05:57) wrong based on 16 sessions

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An army’s recruitment process included n rounds of selection tasks. For the first a rounds, the rejection percentage was 60 percent per round. For the next b rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 100,000 people who applied for the army and 1,400 were finally selected, what was the value of n?

A) 4
B) 5
C) 6
D) 8
E) 10

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Posts: 7334
Re: An army’s recruitment process included n rounds of selection tasks. Fo  [#permalink]

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20 Jul 2017, 02:29
1
duahsolo wrote:
An army’s recruitment process included n rounds of selection tasks. For the first a rounds, the rejection percentage was 60 percent per round. For the next b rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 100,000 people who applied for the army and 1,400 were finally selected, what was the value of n?

A) 4
B) 5
C) 6
D) 8
E) 10

Hi
selected person = $$\frac{4}{10}^a*\frac{1}{2}^b*\frac{7}{10}^c*100000=1400$$
.. = $$\frac{4}{10}^a*\frac{1}{2}^b*\frac{7}{10}^c=\frac{14}{1000}$$...
If you compare left and right side, there is one 7 on each side, so c=1...

$$\frac{4}{10}^a*\frac{1}{2}^b=\frac{2}{100}$$...
There is 100 on RHS and 20 on LHS..., So a =2...
$$\frac{1}{2}^b=\frac{2}{100}*\frac{100}{16}=\frac{1}{8}$$
So b=3..
Total rounds=a+b+c=2+3+1=6
C
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An army’s recruitment process included n rounds of selection tasks. Fo  [#permalink]

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22 Jul 2017, 01:19
duahsolo wrote:
An army’s recruitment process included n rounds of selection tasks. For the first a rounds, the rejection percentage was 60 percent per round. For the next b rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 100,000 people who applied for the army and 1,400 were finally selected, what was the value of n?

A) 4
B) 5
C) 6
D) 8
E) 10

We can judge that there should be a multiplication between 7 and 2 to get 14, accordingly we can start off from the options.
Reduce 100,000 by 60%=40,000
Reduce 40,000 by 60%=16000
Reduce 16,000 by 50%=8000
reduce 8000 by 50%=4000
reduce 4000 by 50%=2000...Option B is gone
70% of 2000=1400...Answer is option C

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Re: An army’s recruitment process included n rounds of selection tasks. Fo  [#permalink]

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22 Jan 2019, 15:11
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Re: An army’s recruitment process included n rounds of selection tasks. Fo   [#permalink] 22 Jan 2019, 15:11
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