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Fractions

by adthedaddy » Thu Sep 24, 2015 7:20 pm
If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, which of the following is true ?

A) 7/15 > x > 1/2
B) 1/2 > x > 1/3
C) 1/3 > x > 1/5
D) 1/5 > x > 1/7
E) 1/7 > x > 1/9

Please suggest an easy way to solve this question.
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by GMATGuruNY » Thu Sep 24, 2015 7:35 pm
adthedaddy wrote:If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, which of the following is true ?

A) 7/15 > x > 1/2
B) 1/2 > x > 1/3
C) 1/3 > x > 1/5
D) 1/5 > x > 1/7
E) 1/7 > x > 1/9

Please suggest an easy way to solve this question.
If all of the fractions were 1/10, then the value of x would be as follows:
1/10 + 1/10 + 1/10 + 1/10 + 1/10 = 5/10 = 1/2.
Sine four of the fractions are actually LESS THAN 1/10, the value of x must be LESS THAN 1/2.

If all of the fractions were 1/15, then the value of x would be as follows:
1/15 + 1/15 + 1/15 + 1/15 + 1/15 = 5/15 = 1/3.
Since four of the fractions are actually GREATER THAN 1/15, the value of x must be GREATER THAN 1/3.

Thus:
1/2 > x > 1/3.

The correct answer is B.
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by Matt@VeritasPrep » Fri Sep 25, 2015 12:16 am
Guru's approach is safer than the one I'm about to give, but given how spread out the answer choices are, you can also just assume that the number is reasonably close to 5 * (1/13).

Since 5/10 > 5/13 > 5/15, we have 1/2 > ≈x > 1/3, and our answer is B.
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