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# What is the sum of a, b, and c ?

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Math Expert
Joined: 02 Sep 2009
Posts: 51185
What is the sum of a, b, and c ?  [#permalink]

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26 Nov 2017, 22:22
00:00

Difficulty:

25% (medium)

Question Stats:

96% (01:00) correct 4% (01:00) wrong based on 36 sessions

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What is the sum of a, b, and c ?

(1) a:b:c = 3:4:7
(2) c - a = 12

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Re: What is the sum of a, b, and c ?  [#permalink]

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26 Nov 2017, 22:27
Bunuel wrote:
What is the sum of a, b, and c ?

(1) a:b:c = 3:4:7
(2) c - a = 12

(1) we know a:b:c = 3:4:7; hence the sum will be 14x
not sufficient

(2) no info abt b..not sufficient

on combining we know a is 9, b is 12,and c is 21 ...sufficient

C
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Re: What is the sum of a, b, and c ?  [#permalink]

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26 Nov 2017, 22:29
Option C

From st1 we get only the ratio. But not the values. Hence insufficient.
From st2 we get a single equation with two unknowns. Hence insufficient

Combining we get a:c=3:7 and c-a=12. two equations and two unknowns. Hence can be solved. Sufficient. a+b+c=9+12+21=42.

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What is the sum of a, b, and c ?  [#permalink]

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26 Nov 2017, 22:36
What is the sum of a, b, and c ?

(1) a:b:c = 3:4:7
Case 1: a=3,b=4,c=7 Here, a+b+c = 14

Case 2: a=6,b=8,c=14 Here, a+b+c = 28 (Insufficient)

(2) c - a = 12
Case 1: b=2, c=13, a=1 Here, a+b+c=16

Case 2: b=3, c=13, a=1 Here, a+b+c=17 (Insufficient)

On combining the two statements, the sum will be unique
a:b:c = 3x:4x:7x (from statement 1)
7x-3x = 12
Therefore, 4x = 12 => x = 3

The sum of the numbers a,b,and c is 14x = 42(Sufficient)(Option C)

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What is the sum of a, b, and c ? &nbs [#permalink] 26 Nov 2017, 22:36
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# What is the sum of a, b, and c ?

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