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# If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i

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Joined: 17 Nov 2013
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If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i  [#permalink]

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18 Nov 2016, 08:40
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45% (medium)

Question Stats:

67% (01:10) correct 33% (01:45) wrong based on 235 sessions

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If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then 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

The source of this question is Ready4GMAT Arithmetic module
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Joined: 12 Sep 2015
Posts: 2706
If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i  [#permalink]

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Updated on: 05 Oct 2017, 08:10
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Top Contributor
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lalania1 wrote:
If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then 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

Let's examine the SMALLEST and LARGEST values in the sum.

1/15 is the SMALLEST value.
So, if all 5 fractions were equal, then the sum would equal (5)(1/15) = 1/3
However, since the other 4 values in the sum are greater than 1/15, we can conclude that x must be greater than 1/3

1/10 is the BIGGEST value.
So, if all 5 fractions were equal, then the sum would equal (5)(1/10) = 1/2
However, since the other 4 values in the sum are less than 1/10, we can conclude that x must be less than 1/2

So, we know that x must be greater than 1/3 AND less than 1/2
In other words, 1/3 < x < 1/2
Or we can write it as 1/2 > x > 1/3
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Originally posted by GMATPrepNow on 18 Nov 2016, 09:10.
Last edited by GMATPrepNow on 05 Oct 2017, 08:10, edited 1 time in total.
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Re: If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i  [#permalink]

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18 Nov 2016, 09:14
lalania1 wrote:
If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then 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

The source of this question is Ready4GMAT Arithmetic module

$$x = \frac{546}{5460} + \frac{455}{5460} + \frac{420}{5460} + \frac{390}{5460} + \frac{364}{5460}$$

So, $$x = \frac{( 546 + 455 + 420 + 390 + 364 )}{5460}$$

Or, $$x = \frac{2175}{5460}$$

Or, $$x = 0.39$$

(A) x > 1/2 = x > 0.50
(B) 1/2 > x > 1/3 = 0.50 > x > 0.33
(C) 1/3 > x = 0.33 > x
(D) 1/5 > x > 1/7 = 0.20 > x > 0.14
(E) 1/7 > x > 1/9 = 0.14 > x > 0.11

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Re: If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i  [#permalink]

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18 Nov 2016, 09:43
lalania1 wrote:
If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then 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

The source of this question is Ready4GMAT Arithmetic module

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Re: If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i  [#permalink]

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18 Nov 2016, 09:58
1
lalania1 wrote:
If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then 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

The source of this question is Ready4GMAT Arithmetic module

the easiest way to find the answer:
suppose all of the fractions are 1/10. we have 5 of them. total sum = 5/10 or 1/2. since it is not the case, we know for sure that x<1/2
next step -> suppose all numbers are 1/15. sum of all of them would be 5/15 or 1/3. since it is not the case, we know for sure that x>1/3
now, use both statements: 1/3 < x < 1/2
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Re: If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i  [#permalink]

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07 Feb 2018, 11:10
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Re: If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i &nbs [#permalink] 07 Feb 2018, 11:10
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