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number problem

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number problem

by rupsk » Fri Jul 22, 2011 3:21 pm
If the terms of a series are either "2" or "24" and the sum of all the terms of the series is 124, then which of the following could be the number of "2s" in the series?

A. 48

B. 35

C. 40

D. 29

E. 26

I could not understand the problem statement itself. please help
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by goalevan » Fri Jul 22, 2011 3:54 pm
The question stem says that a sequence whose sum is 124 is made up of a certain number of 2s and a certain number of 24s. You can rephrase this as follows:

2a + 24b = 124, where a and b are integers. Which of the following could be a value of a?

I would recommend creating a quick table for each value of b (24s in the series) and calculating the number of 2s that would be required for the sum to be 124:

b=1: 24b = 24. 124 - 24 = 100, or 2a = 100, a = 50
b=2: 24b = 48. 124 - 48 = 76, or 2a = 76, a = 38
b=3: 24b = 72. 124 - 72 = 52, or 2a = 52, a = 26
b=4: 24b = 96. 124 - 96 = 28, or 2a = 28, a = 14
b=5: 24b = 120. 124 - 120 = 4, or 2a = 4, a = 2.

We see that the only answer choice that is a possible value for a is E) 26.
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