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Need a better way of solving this

by yumi2012 » Sat Aug 10, 2013 7:14 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

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The MGMAT book answer review is giving me a time-consuming way of solving this. (like plugging positive integers to this equation) Any clearer and faster way of solution?
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by GMATGuruNY » Sat Aug 10, 2013 7:50 pm
yumi2012 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
5C + 8D = 5C + 5D + 3D = 5(C+D) + 3D.

Since C+D = 11, we get:
5(C+D) + 3D = 5*11 + 3D = 55 + 3D.

Since D>0, the correct answer choice must be equal to 55 + (positive multiple of 3).
Keeping adding positive multiples of 3 to 55 until one of the answer choices is yielded:
58, 61...

The correct answer is B.
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by [email protected] » Mon Aug 12, 2013 4:22 pm
Hi yumi2012,

Mitch's approach shows a way to rewrite the information so that you can find the hidden pattern behind this question. Here's another way to do it (especially if you can't come up with Mitch's idea on your own); it's called brute force.

Since C and D are positive integers, there can't be that many ways that C + D = 11

Let's say you tried:
C = 1
D = 10
Then the answer to the question would be 5(1) + 8(10) = 85
This answer is not there, so let's try the next possibility.

C = 2
D = 9
Now we have 5(2) + 8(9) = 82
This answer isn't there either. Notice how the total decreased by 3??? Hmmmm.....

C = 3
D = 8
Now we have 5(3) + 8(8) = 79
This answer isn't there either. NOTICE how the total decreased by 3 AGAIN!!!!

Now we've found the pattern. You can keep subtracting by 3 until you hit the correct answer.

Don't be shy about attacking these types of questions in this way. If you can get the job done quickly (1-2 minutes) by doing some quick calculations, thehn that's much better than staring at the screen and eventually figuring out the algebra shortcut in 3 minutes.

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