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# c and d are positive

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

48% (00:51) correct 51% (01:14) wrong based on 192 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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GRE Instructor
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Re: c and d are positive [#permalink]  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

[Reveal] Spoiler:
B

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Re: c and d are positive [#permalink]  01 Apr 2018, 12:51
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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]  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]  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
Manager
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Re: c and d are positive [#permalink]  14 Dec 2018, 19:45
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.

There is an inherent contradiction in the given information, leading me to get the problem wrong. Let me explain.

Let's simplify the equation given. First we multiply everything by c and get

1 = c + c/d
Next we multiply by d
d = cd + c
d-cd = c
d(1-c) = c
d = c/(1-c)

If c is positive, then the 1-c in the denominator will be negative. Thus, d is negative. Thereby leading to a contradiction.
GRE Instructor
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Re: c and d are positive [#permalink]  15 Dec 2018, 06:42
2
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Expert's post
QuantumWonder wrote:
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.

There is an inherent contradiction in the given information, leading me to get the problem wrong. Let me explain.

Let's simplify the equation given. First we multiply everything by c and get

1 = c + c/d
Next we multiply by d
d = cd + c
d-cd = c
d(1-c) = c
d = c/(1-c)

If c is positive, then the 1-c in the denominator will be negative. Thus, d is negative. Thereby leading to a contradiction.

If c is positive, the denominator isn't necessarily negative.
For example, if c = 1/2, then d = 1

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

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Re: c and d are positive [#permalink]  15 Dec 2018, 17:10
GreenlightTestPrep wrote:
QuantumWonder wrote:
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.

There is an inherent contradiction in the given information, leading me to get the problem wrong. Let me explain.

Let's simplify the equation given. First we multiply everything by c and get

1 = c + c/d
Next we multiply by d
d = cd + c
d-cd = c
d(1-c) = c
d = c/(1-c)

If c is positive, then the 1-c in the denominator will be negative. Thus, d is negative. Thereby leading to a contradiction.

If c is positive, the denominator isn't necessarily negative.
For example, if c = 1/2, then d = 1

Cheers,
Brent

Thank you! That must have been from stress, can't believe I didn't see that. It's silly that it slipped me, double major in physics and mathematics and still have things like that slip me haha. GRE really challenges you to think very carefully, I like that aspect.
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Re: c and d are positive [#permalink]  15 Dec 2018, 21:44
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Expert's post
Think of this

c and d are positive numbers

1/c > 1+1/d

this means that C is a positive fraction less than 1, since we can only get a number greater than 1 if 1 is divided by something smaller than 1.
if c is super small, like .01 then

100 > 1+1/d

d cant be less than or equal to .01.. if it is then

100 > 1+1/.01
becomes
100 > 1 + 100... which is not true so we know that if c is equal to .01, then d has to be greater than .01
thus, d is greater than c.

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Re: c and d are positive [#permalink]  17 Dec 2018, 03:39
1
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given:1/c=1+1/d
solving equation gives d=cd+c
This implies D is Cd times greater than C
Manager
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Re: c and d are positive [#permalink]  17 Dec 2018, 07:17
vigjna wrote:
given:1/c=1+1/d
solving equation gives d=cd+c
This implies D is Cd times greater than C

Nice fast solution mate.
Re: c and d are positive   [#permalink] 17 Dec 2018, 07:17
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