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Find a possible value of a+b given the equations

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Senior Manager
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Joined: 17 Dec 2012
Posts: 394
Location: India
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Kudos [?]: 170 [0], given: 9

Find a possible value of a+b given the equations [#permalink] New post 03 Jan 2013, 03:36
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

33% (04:45) correct 67% (03:03) wrong based on 9 sessions
If ax + by = 17 ,
2ax + 3by = 43

and 3x =2y, which of the following is a possible value of a+b if a and b are integers?

A. 6
B. 10
C. 14
D. 18
E. 20
[Reveal] Spoiler: OA

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Joined: 16 Oct 2010
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Location: Pune, India
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Kudos [?]: 4794 [0], given: 163

Re: Find a possible value of a+b given the equations [#permalink] New post 03 Jan 2013, 09:30
Expert's post
SravnaTestPrep wrote:
If ax + by = 17 ,
2ax + 3by = 43

and 3x =2y, which of the following is a possible value of a+b if a and b are integers?

A. 6
B. 10
C. 14
D. 18
E. 20


Too many variables! I will try to look at the big picture here.
We have two equations:
ax + by = 17 ,
2ax + 3by = 43

Twice of (ax + by) will be 34 so we get that 'by' must be 43 - 34 = 9
If by = 9, ax must be 17 - 9 = 8

Now, x/y = 2/3
ax/by = (a/b)*(2/3) = 8/9
So a/b = 4/3

Since a and b are integers, many such solutions are possible: a = 4, b = 3 OR a = 8, b = 6 etc. a+b will be 7/14/21...
Answer (C)
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Re: Find a possible value of a+b given the equations   [#permalink] 03 Jan 2013, 09:30
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