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Founder  Joined: 18 Apr 2015
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Kudos [?]: 2030 , given: 8060

c and d are positive [#permalink]
Expert's post 00:00

Question Stats: 48% (00:48) correct 51% (01:16) wrong based on 173 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

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. GRE Instructor Joined: 10 Apr 2015
Posts: 2554
Followers: 91

Kudos [?]: 2718  , given: 40

Re: c and d are positive [#permalink]
1
KUDOS
Expert's post
Carcass Array[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
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Manager Joined: 22 Feb 2018
Posts: 162
Followers: 2

Kudos [?]: 124  , given: 22

Re: c and d are positive [#permalink]
1
KUDOS
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.

_________________ Intern Joined: 20 Mar 2018
Posts: 37
GRE 1: Q164 V150 Followers: 1

Kudos [?]: 30  , given: 8

Re: c and d are positive [#permalink]
1
KUDOS
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
Intern Joined: 19 Mar 2018
Posts: 25
Followers: 1

Kudos [?]: 9 , given: 11

Re: c and d are positive [#permalink]
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 Joined: 02 Dec 2018
Posts: 74
Followers: 0

Kudos [?]: 11 , given: 60

Re: c and d are positive [#permalink]
Carcass Array[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 Joined: 10 Apr 2015
Posts: 2554
Followers: 91

Kudos [?]: 2718  , given: 40

Re: c and d are positive [#permalink]
2
KUDOS
Expert's post
QuantumWonder Array[WROTE]:
Carcass Array[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 Manager Joined: 02 Dec 2018
Posts: 74
Followers: 0

Kudos [?]: 11 , given: 60

Re: c and d are positive [#permalink]
GreenlightTestPrep Array[WROTE]:
QuantumWonder Array[WROTE]:
Carcass Array[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. Manager  Joined: 01 Nov 2018
Posts: 87
Followers: 0

Kudos [?]: 49  , given: 22

Re: c and d are positive [#permalink]
2
KUDOS
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. Intern Joined: 11 Oct 2018
Posts: 3
Followers: 0

Kudos [?]: 1  , given: 5

Re: c and d are positive [#permalink]
1
KUDOS
given:1/c=1+1/d
solving equation gives d=cd+c
This implies D is Cd times greater than C
Manager Joined: 02 Dec 2018
Posts: 74
Followers: 0

Kudos [?]: 11 , given: 60

Re: c and d are positive [#permalink]
vigjna Array[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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