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In a certain business, production index p is directly

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In a certain business, production index p is directly [#permalink] New post 15 Jun 2006, 00:16
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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?

condition 1: e = 0.5 whenever i = 60.

condition 2: p = 2.0 whenever i = 50.

Please explain the rationale behind your answer choice. Thanks.
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 [#permalink] New post 15 Jun 2006, 00:53
p = ae
e = bi
so p=abi

St1:
p = abi
i = 60, e = 0.5, so the factor b must be 1/120. If i = 70, e = 7/12. We can't solve as we cannot derive the factor a.

St2:

p = abi
2 = (a)(b)(50)
ab = 2/50 = 1/25

So if i = 70, p = abi = (1/25)(70). Sufficient.

Ans B
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 [#permalink] New post 15 Jun 2006, 05:56
clearly B.

stmt 1 --insuff gives us no data on how e and i are related

stmt 2-- gives us that relation , basically , (70*2)/50=2.8
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 [#permalink] New post 15 Jun 2006, 12:54
ywilfred wrote:
p = ae
e = bi
so p=abi

St1:
p = abi
i = 60, e = 0.5, so the factor b must be 1/120. If i = 70, e = 7/12. We can't solve as we cannot derive the factor a.

St2:

p = abi
2 = (a)(b)(50)
ab = 2/50 = 1/25

So if i = 70, p = abi = (1/25)(70). Sufficient.

Ans B


Great! thanks for the explanation. A quick question, so when they say directly proportional, just sub any variable "a" into the equation.

p = ae
e = bi

a,b are just random variables assigned to represent the proportional relationship btw p and e and e and i.

Just want to make sure.
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 [#permalink] New post 15 Jun 2006, 18:31
Yes, but you're better off not calling them variables a and b, but denoting them as constants K1, K2 etc....just to avoid confusion.
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 [#permalink] New post 15 Jun 2006, 18:37
mrmikec wrote:
ywilfred wrote:
p = ae
e = bi
so p=abi

St1:
p = abi
i = 60, e = 0.5, so the factor b must be 1/120. If i = 70, e = 7/12. We can't solve as we cannot derive the factor a.

St2:

p = abi
2 = (a)(b)(50)
ab = 2/50 = 1/25

So if i = 70, p = abi = (1/25)(70). Sufficient.

Ans B


Great! thanks for the explanation. A quick question, so when they say directly proportional, just sub any variable "a" into the equation.

p = ae
e = bi

a,b are just random variables assigned to represent the proportional relationship btw p and e and e and i.

Just want to make sure.


yes, I used a and b to represent the proportional constant. you can use anything you like, so long as it doesn't confuse you =)
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 [#permalink] New post 15 Jun 2006, 18:40
B aswell

stmt 1 does not give the ratio between p and i
stmt 2 does.
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 [#permalink] New post 15 Jun 2006, 22:28
Cleary B

P = xe and e =yi
Hence p= xyi

1) e = 0.5 when i =60 But we still don't know x
Henc insuff

2) p =2 when i = 50

Hence p = 2/50 * 70 , when i = 70
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 [#permalink] New post 16 Jun 2006, 07:14
Point to be kept in mind here is -
If x proportional to y and y proportional to z, then x is also proportional to z.

Answer is B.
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 [#permalink] New post 16 Jun 2006, 10:56
Straight B.

p is directly proportional to e and e is directly proportional to i. So p is directly proportional to i.
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  [#permalink] 16 Jun 2006, 10:56
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