BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Fractions

Expert replies
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.
"Your time is limited, so don't waste it living someone else's life. Don't be trapped by dogma - which is living with the results of other people's thinking. Don't let the noise of others' opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition. They somehow already know what you truly want to become. Everything else is secondary" - Steve Jobs
Join the discussion
Source: — Problem Solving |

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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Join the discussion

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.
Join the discussion