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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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lalania1
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If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i [#permalink] New post  18 Nov 2016, 08:40
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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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BrentGMATPrepNow
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If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i [#permalink] New post  Updated on: 05 Oct 2017, 08:10
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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
Answer:
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B

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Originally posted by BrentGMATPrepNow on 18 Nov 2016, 09:10.
Last edited by BrentGMATPrepNow on 05 Oct 2017, 08:10, edited 1 time in total.
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Abhishek009
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Re: If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i [#permalink] New post  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

So, Answer will be (B)...
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Re: If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i [#permalink] New post  18 Nov 2016, 09:43
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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

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] New post  18 Nov 2016, 09:58
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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

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
answer is B.
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If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i [#permalink] New post  05 Dec 2019, 10:17
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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

The source of this question is Ready4GMAT Arithmetic module


We can also solve this question using the theory which states that in an evenly spaced set the mean is equal to the median. And this set very closes mimics an evenly spaced set. As there are 5 terms that sum up to \(x\) the median would be the middle term i.e. \(\frac{1}{13}\)

Now, Sum = Average * Number of Terms,
\(\frac{1}{13}*5\) = \(\frac{5}{13}\) ~ 0.38 which is greater than \(\frac{1}{3}\) (0.33)

Ans. B
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Re: If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i [#permalink] New post  08 Dec 2019, 20:51
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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

The source of this question is Ready4GMAT Arithmetic module


We can create the equation:

2x + 3x + 7x = 156

12x = 156

x = 13

So, there are 13 * 2 = 26 ounces of grape juice.

Answer: B
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Re: If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i [#permalink] New post  08 Dec 2019, 20:51
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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

The source of this question is Ready4GMAT Arithmetic module


Since each fraction is at least 1/15, we can see that x is at least 5 x 1/15 = 5/15 = 1/3. Similarly, since each fraction is at most 1/10, we can see that x is at most 5 x 1/10 = 5/10 = 1/2. Thus, x is between 1/3 and 1/2.

Answer: B
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Re: If x = 1/10 + 1/12 + 1/13 + 1/14 + 1/15, then which of the following i [#permalink] New post  20 Apr 2022, 18:42
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