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

Question

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

BrentGMATPrepNow · Accepted Answer

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: B

Abhishek009 · Answer

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)...

Bunuel · Answer

Similar questions to practice: m-is-the-sum-of-the-reciprocals-of-the-consecutive-integers-143703.html if-k-is-the-sum-of-reciprocals-of-the-consecutive-integers-145365.html if-s-is-the-sum-of-the-reciprocals-of-the-consecutive-24847.html

mvictor · Answer

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.

Pritishd · Answer

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

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

ScottTargetTestPrep · Answer

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

ScottTargetTestPrep · Answer

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

MyYear2025 · Answer

Thanks, what a great trick

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

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