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Updated on: 12 May 2021, 09:59
Originally posted by Fdambro294 on 09 May 2021, 01:23.
Last edited by Fdambro294 on 12 May 2021, 09:59, edited 1 time in total.
Last edited by Fdambro294 on 12 May 2021, 09:59, edited 1 time in total.
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There is an underlying concept that tangentially has to deal with weighted averages and is a bit rare.....but several companies have covered it (TargetTestPrep )
First, notice that every fraction is a positive proper fraction (between 0 and 1) and each fraction is greater than > (1/2)
Second, if you look at the first 4 answers given, you’ll notice that the NUM and DEN increase by constant amounts from answer to answer (+ 1 is added to NUM and +2 is added to DEN)
The concept is as follows:
If we start out with a Positive fraction such as (X) / (Y)
And we add + 1 to the NUM and + 2 to the DEN
Then the fraction will APPROACH, i.e., get closer to, the fraction (1/2) without ever reaching (1/2)
Case 1: if (X/Y) < (1/2) ————> then (X + 1) / (Y + 2) will be an increase in value when compared to (X/Y) and will move closer to (1/2)
Case 2 (the case involving the first 4 answer choices) (X / Y) > 1/2 ———> then (X + 1) / (Y + 2) will be a decrease in value and move closer towards (1/2) without ever reaching it
Starting from (4/7), which is just a little greater than > (1/2)
(4/7) ———-> (4 + 1) / (7 + 2) = 5/9 ———> which means 5/9 will move closer to 1/2 than 4/7 is
From (5/9) ———-> (5 + 1) / (9 + 2) = 6/11 ——-> which means 6/11 will move closer to 1/2 than 5/9 is
From (6/11) ———> (6 + 1) / (11 + 2) = 7/13——-> which means 7/13 will move closer to 1/2 than 6/11 is
Out of the first four answer choices, (7/13) will be closest to (1/2)
From D to E: (7/13) ——> to (9/16)
We are adding +2 to the NUM and +3 to the DEN of (7/13) to get to (9/16)
By doing this, the new value will move closer to (2/3), which is AWAY from (1/2)
Since (7/13) is less than (2/3), Case 1 from above will apply, and
7/13 < (7 + 2) / (13 + 3) < 2/3
Further, since 7/13 approached (1/2) but never hit it, (7/13) will be the closest value to (1/2)
Answer D (7/13)
Posted from my mobile device
First, notice that every fraction is a positive proper fraction (between 0 and 1) and each fraction is greater than > (1/2)
Second, if you look at the first 4 answers given, you’ll notice that the NUM and DEN increase by constant amounts from answer to answer (+ 1 is added to NUM and +2 is added to DEN)
The concept is as follows:
If we start out with a Positive fraction such as (X) / (Y)
And we add + 1 to the NUM and + 2 to the DEN
Then the fraction will APPROACH, i.e., get closer to, the fraction (1/2) without ever reaching (1/2)
Case 1: if (X/Y) < (1/2) ————> then (X + 1) / (Y + 2) will be an increase in value when compared to (X/Y) and will move closer to (1/2)
Case 2 (the case involving the first 4 answer choices) (X / Y) > 1/2 ———> then (X + 1) / (Y + 2) will be a decrease in value and move closer towards (1/2) without ever reaching it
Starting from (4/7), which is just a little greater than > (1/2)
(4/7) ———-> (4 + 1) / (7 + 2) = 5/9 ———> which means 5/9 will move closer to 1/2 than 4/7 is
From (5/9) ———-> (5 + 1) / (9 + 2) = 6/11 ——-> which means 6/11 will move closer to 1/2 than 5/9 is
From (6/11) ———> (6 + 1) / (11 + 2) = 7/13——-> which means 7/13 will move closer to 1/2 than 6/11 is
Out of the first four answer choices, (7/13) will be closest to (1/2)
From D to E: (7/13) ——> to (9/16)
We are adding +2 to the NUM and +3 to the DEN of (7/13) to get to (9/16)
By doing this, the new value will move closer to (2/3), which is AWAY from (1/2)
Since (7/13) is less than (2/3), Case 1 from above will apply, and
7/13 < (7 + 2) / (13 + 3) < 2/3
Further, since 7/13 approached (1/2) but never hit it, (7/13) will be the closest value to (1/2)
Answer D (7/13)
Posted from my mobile device
12 May 2021, 00:58
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AbdurRakib
Answer: Option D
Video solution by GMATinsight
24 Jul 2021, 13:15
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Given that all answer choices are above 1/2, isn't the question basically asking what is the smallest number in the answer choices? D is the smallest number when comparing each fraction.
