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a, b, and c are positive

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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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a, b, and c are positive [#permalink] New post 10 Jun 2018, 05:20
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Question Stats:

65% (00:10) correct 34% (00:25) wrong based on 23 sessions
a, b, and c are positive

Quantity A
Quantity B
(a + b)% of c
c% of (a + b)


A)The quantity in Column A is greater.
B)The quantity in Column 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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Kudos [?]: 10 [0], given: 0

Re: a, b, and c are positive [#permalink] New post 13 Jun 2018, 18:29
a,b,c > 0

Quantity A = (a+b)%*c
Quantity B = c%*(a+b) =(a+b)*c%

--> A = B

Key: C
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Re: a, b, and c are positive [#permalink] New post 13 Jun 2018, 20:18
Answer: D
A: (a + b) % c
B: c % (a + b)
If a+b = c or : A and B are equal.
If a+b < c : A is equal to a+b and B is equal to c mod a+b. So B is bigger.
If a+b > c : A is equal to a+b mod c and B is equal to c. So A is bigger.

We can apply different values to see this as well.
The answer is D.

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GRE Prep Club Legend
GRE Prep Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1742 [0], given: 397

Re: a, b, and c are positive [#permalink] New post 14 Jun 2018, 04:26
Expert's post
FatemehAsgarinejad wrote:
Answer: D
A: (a + b) % c
B: c % (a + b)
If a+b = c or : A and B are equal.
If a+b < c : A is equal to a+b and B is equal to c mod a+b. So B is bigger.
If a+b > c : A is equal to a+b mod c and B is equal to c. So A is bigger.

We can apply different values to see this as well.
The answer is D.


Lets examine by plugging values in this case a=10 b=30 and c=30

Quantity A is (20+30)% of 30 or \(\frac{50}{100} \times 30\)

Quantity B is 30% of (20+30) or \(\frac{30}{100} \times 50\)

See in both cases the numerator and the denominator is always the same i.e \(30 \times 50\) and \(100\) respectively.

The answer is indeed C.
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GRE Prep Club Legend
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User avatar
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1742 [0], given: 397

Re: a, b, and c are positive [#permalink] New post 14 Jul 2018, 04:55
Expert's post
Explanation

It is always the case that, for two positive quantities, M% of N = N% of M. In this case, (a + b) makes the problem appear more complicated, but the principle still applies. Algebraically:

Quantity A : \(\frac{a+b}{100}\times c\)

Quantity B: \(\frac{c}{100}\times (a+b)\)


Both quantities can be simplified to \(\frac{(a+b) \times c}{100}\). The two quantities are equal.
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Re: a, b, and c are positive   [#permalink] 14 Jul 2018, 04:55
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a, b, and c are positive

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