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c and d are positive

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c and d are positive [#permalink] New post 25 Apr 2017, 02:58
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Question Stats:

48% (00:46) correct 51% (01:34) wrong based on 79 sessions


c and d are positive

\(\frac{1}{c} = 1 + \frac{1}{d}\)

Quantity A
Quantity B
c
d


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: c and d are positive [#permalink] New post 26 May 2017, 12:00
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Expert's post
Carcass wrote:


c and d are positive

\(\frac{1}{c} = 1 + \frac{1}{d}\)

Quantity A
Quantity B
c
d


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Given: 1/c = 1 + 1/d
Rewrite 1 as d/d to get: 1/c = d/d + 1/d
Combine fractions to get: 1/c = (d + 1)/d
Flip both fractions to get: c/1 = d/(d+1)
In other words, c = d/(d+1)

In Quantity A, replace c with d/(d+1) to get:
Quantity A: d/(d+1)
Quantity B: d

Since d is positive, we know that d+1 is positive.
So, let's multiply both quantities by (d+1) to get:
Quantity A: d
Quantity B: d² + d

Subtract d from both quantities to get:
Quantity A: 0
Quantity B: d²

Since d is not equal to zero, we know that d² is POSITIVE

Answer:
[Reveal] Spoiler:
B


Cheers,
Brent
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Re: c and d are positive [#permalink] New post 01 Apr 2018, 12:51
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Answer: B
1/c equals 1 + 1/d so 1/c is something bigger than 1/d,
1/c > 1/ d so d > c

EVEN for negative values this correlation is true.
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Re: c and d are positive [#permalink] New post 04 Apr 2018, 07:46
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Fraction 1/c is bigger than fraction 1/d as we have to add something to fraction 1/d to make it equal to fraction 1/c.

So, if 1/c > 1/d then c < d

Ans: B
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Re: c and d are positive [#permalink] New post 16 Sep 2018, 23:10
Plug in +ve fraction values:

----0---1/4----1/4 +1
1/d 1/c

1/4 < 5/4 --< 1/d < 1/c
BUT
4> 4/5 ---> d> c
Qty B > Qty A
Re: c and d are positive   [#permalink] 16 Sep 2018, 23:10
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c and d are positive

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