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Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Kudos [?]: 2976 , given: 394

a, b, and c are positive [#permalink]
Expert's post 00:00

Question Stats: 76% (00:16) correct 23% (00:27) wrong based on 51 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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Sandy
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Intern Joined: 21 Nov 2017
Posts: 33
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Kudos [?]: 17 , given: 0

Re: a, b, and c are positive [#permalink]
a,b,c > 0

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

--> A = B

Key: C
Manager Joined: 22 Feb 2018
Posts: 163
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Kudos [?]: 138 , given: 22

Re: a, b, and c are positive [#permalink]
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.

_________________

Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2976 , given: 394

Re: a, b, and c are positive [#permalink]
Expert's post
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.

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.

_________________

Sandy
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Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2976 , given: 394

Re: a, b, and c are positive [#permalink]
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.
_________________

Sandy
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Try our free Online GRE Test Re: a, b, and c are positive   [#permalink] 14 Jul 2018, 04:55
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