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If y is 80% greater than x, than x is what % less than y?

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by DavidG@VeritasPrep » Thu Sep 14, 2017 6:27 am
ardz24 wrote:If y is 80% greater than x, than x is what % less than y?

(A) 20
(B) 25
(C) 33 1/3
(D) 44 4/9
(E) 80

OA: D

Experts, please share an approach in solving this problem. Thank you
We could pick a simple number for x. Say x = 100. If y is 80% greater, y = 180. Now we want to know how much less 100 is than 180.

If we plug our values into our trusty % change = (New-Old)/Old * 100 formula, we get (180-100)/180 = 80/180 = (4/9) * 100 = 44.44%. The answer is D

(And once we see that we need to find 80/180, it's clear that 80 is too big, as that would be 80/100, and 33 1/3 is too small, as that would be 60/180, so we can derive that the answer must be D without doing the math. )
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by [email protected] » Thu Sep 14, 2017 11:15 am
Hi ardz24,

This question is perfect for TESTing VALUES (the approach used by David). You can also approach it algebraically (although either way you will also need to use the Percentage Change Formula).

We're told that Y is 80% greater than X....
Y = 1.8X

We're asked what percent LESS is X than Y, so we're asked to compare X to 1.8X

Percent Change = (Difference)/(Original) = .8X/1.8X = 8X/18X = 8/18 = 4/9 = 44 4/9%

Final Answer: D

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by Scott@TargetTestPrep » Thu Jan 04, 2018 8:56 am
ardz24 wrote:If y is 80% greater than x, than x is what % less than y?

(A) 20
(B) 25
(C) 33 1/3
(D) 44 4/9
(E) 80
We can create the following equation:

y = 1.8x

Thus:

(x - y)/y * 100 = (x - 1.8x)/1.8x * 100 = -0.8x/1.8x * 100 = -8/18 * 100 = -4/9 * 100 = -44 4/9

We see that x is 44 4/9 percent less than y.

Answer: D

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