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What is p if i=70?

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by Needgmat » Sat Jul 16, 2016 10:51 pm
In a certain business, production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment index i. What is p if i=70?


1) e=0.5 whenever i=60
2) p=2.0 whenever i=50

OA B

Please explain.
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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Jul 17, 2016 2:10 am
Needgmat wrote:In a certain business, production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment index i. What is p if i=70?


1) e=0.5 whenever i=60
2) p=2.0 whenever i=50
Since all 3 values are directly proportional to one another, p is directly proportional to i.
Thus:
p�/i� = p₂/i₂.

Statement 1:
No information about p.
INSUFFICIENT.

Statement 2:
If we substitute p�=2, i�=50 and i₂=70 into p�/i� = p₂/i₂, we get:
2/50 = pâ‚‚/70.
Since we can solve for pâ‚‚, we can determine the value of p if i=70.
SUFFICIENT.

The correct answer is B.
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by OptimusPrep » Sun Jul 17, 2016 8:50 pm
Needgmat wrote:In a certain business, production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment index i. What is p if i=70?


1) e=0.5 whenever i=60
2) p=2.0 whenever i=50

OA B

Please explain.
Given: p = c1*e - (i) where c1 is a constant
and e = c2*i - (ii) where c2 is a constant

Required: p = ? when i = 70
p = c1*e = c1*c2*i
p = c1*c2*70 - (iii)
Hence we need to find the value of c1 and c2

Statement 1: e=0.5 whenever i=60
From (ii),
0.5 = c2*60
Clearly we cannot solve for c1
INSUFFICIENT

Statement 2: p=2.0 whenever i=50
From (i),
2 = c1*50
and we know that
p = c1*70

Dividing both the equations,
2/p = 50/70
Hence we can solve for p
SUFFICIENT

Correct Option: B
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by Matt@VeritasPrep » Fri Jul 22, 2016 2:12 am
We could also say

p/e = x

e/i = y

S1:

0.5/60 = y, so y = 1/120. This doesn't give us x (which would get us to p) or p itself; NOT SUFFICIENT.

S2:

The ratio p/i = 2/50. Since i = 70, we can multiply both parts of the first ratio by 1.4 (that is, 70/50), to give us p/i = 2.8/70. So when i = 70, p = 2.8; SUFFICIENT.
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