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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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If the numbers 17/24, 1/2, 3/8, 3/4, and 9/16 were ordered from greatest to least, the middle number of the resulting sequence would be

(A) 17/24 (B) 1/2 (C) 3/8 (D) 3/4 (E) 9/16

17/24, 1/2, 3/8, 3/4, and 9/16 - Multiply all the fractions by 48 we get: 34, 24, 18, 36, 27

So 36 is the greatest which is 3/4 _________________

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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Take LCM of denominators and get common denominator to all fractions so that you can compare the numerators and arrange in the increasing or decreasing order

LCM of denominators is 48

fractions can be rewritten as 34/48,24/48,18/48,36/48,27/48. now arrange them 18/48,24/48,27/48,34/48,36/48 hence the middle element is 27/48=9/16

Re: If the numbers 17/24, 1/2, 3/8, 3/4, and 9/16 were ordered [#permalink]

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20 Jan 2014, 20:27

1

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Easiest way to solve this type of question is to find a common multiplier for denominators of all the given number. As we can see that the Common Factor for all the denominators- 24,2,4,8,16 is 48 . Multiply each number by 48- (17/24)*48 = 34 (1/2)*48 = 24 (3/8)*48 = 18 (3/4)*48 = 36 (9/16)*48 =27

So the given number becomes - 34,24,18,36,27

In descending order - 36,34,27,24,18

So mid-number is 27 . Now again to get the required answer divide it by 48 -> 27/48 = 9/16

So answer is (E)

Note: Although the explanation may look lengthy but when we do it pen-paper it will not take more that 15 sec.

Re: If the numbers 17/24, 1/2, 3/8, 3/4, and 9/16 were ordered [#permalink]

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20 Jan 2014, 21:34

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Approach 1: Here, taking LCM for all the denominators, as others suggested, would be a good idea.

Approach 2: Alternatively, if we are little good at approximation, looking at the numbers, we can say that 3/8 is the least and 3/4 is the greatest. Comparing 17/24 and 9/16 will be the slightly trickiest thing in this problem.

9/16 will be a little more than half(1/2). 17/24 will be a little less than 3/4 as 18/24 will give 3/4.

So, if we arrange from greatest to least, the order will be 3/4, 17/24, 9/16, 1/2, 3/8. Since we are asked for the middle element, 9/16 will be the answer.

Re: If the numbers 17/24, 1/2, 3/8, 3/4, and 9/16 were ordered [#permalink]

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21 Jan 2014, 04:58

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Ans should be (e)..9/16 We can see the other nos relative to 1/2 i.e. 50%. Just by seeing numerator and denominator 3/4 and 3/8 can be placed on either side of 1/2. 17/24 and 9/16 are definitely greater than 1/2. So, to check which no comes in 3rd place, we can individually compute their values and see that 9/16 is smaller than 17/24. So 9/16 must be at the 3rd spot and thus, the middle no.

Re: If the numbers 17/24, 1/2, 3/8, 3/4, and 9/16 were ordered [#permalink]

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26 Apr 2015, 22:16

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Re: If the numbers 17/24, 1/2, 3/8, 3/4, and 9/16 were ordered [#permalink]

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26 Apr 2015, 23:06

Answer is E, I spent a little bit too much time on this though.

I made a number line and put in the obvious ones. The "problem" was deciding between 9/16 and 17 24 -> I realized I could reach a common denominator and it became clear which was bigger.

gmatclubot

Re: If the numbers 17/24, 1/2, 3/8, 3/4, and 9/16 were ordered
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26 Apr 2015, 23:06

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