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

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BTGmoderatorAT: Moderator; Posts: 426; Joined: Tue Aug 22, 2017 8:48 pmFollowed by: 1 member

by BTGmoderatorAT » Thu Sep 14, 2017 4:38 am

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

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Source: Beat The GMAT — Problem Solving | Thu Sep 14, 2017 4:38 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

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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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

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

GMAT assassins aren't born, they're made,
Rich

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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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