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A certain box contains

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A certain box contains

by saxenarahul021 » Tue Nov 27, 2012 12:16 am
A certain box contains only red pencils and blue pencils. If 1 red pencil is removed, there will be the same number of red pencils as blue pencils in the box. If 1 blue pencil is removed instead, there will be twice as many red pencils as blue pencils in the box. How many pencils are in the box?

A. 3
B. 5
C. 6
D. 7
E. 8
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by Anurag@Gurome » Tue Nov 27, 2012 1:04 am
saxenarahul021 wrote:A certain box contains only red pencils and blue pencils. If 1 red pencil is removed, there will be the same number of red pencils as blue pencils in the box. If 1 blue pencil is removed instead, there will be twice as many red pencils as blue pencils in the box. How many pencils are in the box?
Algebraic Approach:
Say, number of red pencils in the box = R and number of blue pencils in the box = B

Now, (R - 1) = B
And, R = 2(B - 1)

Hence, B = 2(B - 1) - 1 = 2B - 3 ---> B = 3
Hence, R = (B + 1) = 4

The correct answer is D.
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by Anurag@Gurome » Tue Nov 27, 2012 1:07 am
Tricky Approach:

Say, the total number of pencils in the box = N

Now after removing one red pencil, number of blue pencil = number of red
Hence, N must be odd.
Only possible options are A, B, and D.


And after removing one blue pencil, 2*(number of blue pencil) = number of red pencil.
Hence, (N - 1) must be divisible by 3.
Only possible options is D.
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