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Equation Advanced (I)

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Equation Advanced (I) [#permalink] New post 04 May 2009, 18:38
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A
B
C
D
E

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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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Re: Equation Advanced (I) [#permalink] New post 04 May 2009, 19:11
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joyseychow wrote:
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?


Answer should be 61 (B)


5c + 8d = 5c+5d+ 3d = 5*11+3d = 55+3d
Here d must any integers from 1 to 10

C --> 55+14 ( 14 is not multiple of 3 ) --> out
D --> 55+28 ( not multiple of 3) out
E --> 55+33 (d must be between 1 and 10 .. here it is 11) -->out


A--> out
B --> 55 +3*2 = 61 (Potential answer)
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Re: Equation Advanced (I) [#permalink] New post 04 May 2009, 19:34
Expert's post
additional way:

1) let's c=10 and d=1 --> 5*c + 8*d = 58
2) When we decrease c by 1 increasing d by 1, we increase 5*c + 8*d by (+8-5) = 3.
3) Let's add 3n to 58: 58, 61, 64, 67, 70, 73, 76, 79, 81, 84.
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Re: Equation Advanced (I) [#permalink] New post 05 May 2009, 17:39
hi X2suresh,

Why d has to b/w one to 10? d is postive integer so i can be any value > 0.

The problem i think is if u take d = 11 then u will get c = 0. Which is not a positive integer so E is out.

Please correct me if i am wrong.
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Re: Equation Advanced (I) [#permalink] New post 05 May 2009, 18:49
tkarthi4u wrote:
hi X2suresh,

Why d has to b/w one to 10? d is postive integer so i can be any value > 0.

The problem i think is if u take d = 11 then u will get c = 0. Which is not a positive integer so E is out.

Please correct me if i am wrong.


Question stem says c and d are positive integers

and c+d = 11 ..
minmum value of c=1 c can't be equal to zero. ( Zero is neighter +Ve nor -ve)
so max value of d = 10
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Re: Equation Advanced (I) [#permalink] New post 05 May 2009, 19:29
Thanks X2suresh.

some times it take the brain a little more help to understand.
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Re: Equation Advanced (I) [#permalink] New post 15 Oct 2009, 01:27
5c+8d=5(c+d)+3d=55+3d=61 => d=2 hence B
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Re: Equation Advanced (I) [#permalink] New post 15 Oct 2009, 10:55
ngoctraiden1905 wrote:
5c+8d=5(c+d)+3d=55+3d=61 => d=2 hence B


sorry but the above equation seems to find the value of d rather than finding a possible value for the expression.
Re: Equation Advanced (I)   [#permalink] 15 Oct 2009, 10:55
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