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Master | Next Rank: 500 Posts
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by joyseychow » Mon May 04, 2009 6:41 pm
If c + d = 11 and c and d are positive integers, which of the following is a possible value for
5c + 8d?

(A) 55
(B) 61
(C) 69
(D) 83
(E) 88

Is there any shortcut to this?
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by m&m » Mon May 04, 2009 7:00 pm
we have 2 eqns

c + d = 11 (1)
5c + 8d = ans (2)



5(11-d) + 8d = ans
55 - 5d + 8d = ans
55 + 3d = ans

so answer with be multiple of 3 starting from first number = 55. Stated otherwise (ans-55)/3 must be between 1 and 10

a) 0
b) 2
c) 14/3
d) 28/3
e) 11

so b is answer. You could have stopped at b once you got it, no need to go through all answer choices if you are pressed for time.
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by Pranay » Tue May 05, 2009 2:30 am
m&m wrote:we have 2 eqns

c + d = 11 (1)
5c + 8d = ans (2)



5(11-d) + 8d = ans
55 - 5d + 8d = ans
55 + 3d = ans

so answer with be multiple of 3 starting from first number = 55. Stated otherwise (ans-55)/3 must be between 1 and 10

a) 0
b) 2
c) 14/3
d) 28/3
e) 11

so b is answer. You could have stopped at b once you got it, no need to go through all answer choices if you are pressed for time.
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