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

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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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1
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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.

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