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

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Intern
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If y is 80% greater than x, than x is what % less than y? [#permalink]

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11 Nov 2013, 20:05
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Question Stats:

78% (01:21) correct 22% (01:21) wrong based on 187 sessions

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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
[Reveal] Spoiler: OA

Last edited by PatrickS on 11 Nov 2013, 20:14, edited 2 times in total.

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Re: If y is 80% greater than x [#permalink]

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11 Nov 2013, 20:10
This problem looks simple enough yet i cannot understand what i am doing wrong:

$$y=x*\frac{180}{100}$$

$$y=x*\frac{18}{10}$$

$$y=x*\frac{9}{5}$$

$$x=y*\frac{5}{9}$$

$$x= y* 5* 0.11111$$

$$x= y* 0.555$$ --> $$x= ~ 55.5% of y$$

Help...
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File comment: I fully understand this explanation, i don't get why my logic is wrong

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Re: If y is 80% greater than x [#permalink]

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11 Nov 2013, 22:08
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Expert's post
PatrickS,

Everything you have done is correct, and your answer would be correct if they had asked x is what percent of y, which is indeed 55.55%. However, the question is asking for x is what percent less than y, which is equal to [(y-x)/y]*100 or 44.44 percent.

Dabral

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Re: If y is 80% greater than x [#permalink]

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12 Nov 2013, 06:34
dabral wrote:
PatrickS,

Everything you have done is correct, and your answer would be correct if they had asked x is what percent of y, which is indeed 55.55%. However, the question is asking for x is what percent less than y, which is equal to [(y-x)/y]*100 or 44.44 percent.

Dabral

Silly me... Thank you for clarifying

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Re: If y is 80% greater than x, than x is what % less than y? [#permalink]

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12 Nov 2014, 02:44
$$y = \frac{180}{100} * x$$

$$x = \frac{100}{180} * y$$

Percentage $$= \frac{100*100}{180} = \frac{500}{9} = 55.55$$

Percentage less = 100 - 55.55 = 44.45

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Re: If y is 80% greater than x, than x is what % less than y? [#permalink]

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12 Nov 2014, 06:32
if y=180 x=100
180-100=80

90 is 50% of y.
80 is little less than 90 so answer D 44 4/9

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If y is 80 percent greater than x, then x is what percent less than y? [#permalink]

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23 Mar 2015, 06:40
Expert's post
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If y is 80 percent greater than x, then x is what percent less than y?

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

Kudos for a correct solution.
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If y is 80 percent greater than x, then x is what percent less than y? [#permalink]

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23 Mar 2015, 07:46
1
KUDOS
Bunuel wrote:
If y is 80 percent greater than x, then x is what percent less than y?

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

Kudos for a correct solution.

$$y = 1.8x$$
$$y = \frac{9}{5}*x$$; therefore $$x = \frac{5}{9}*y$$

Therefore, x is five-ninths of y, which means x is four-ninths less than y. . $$\frac{4}{9}$$ equates to 44.44 percent.

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If y is 80 percent greater than x, then x is what percent less than y? [#permalink]

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24 Mar 2015, 22:53
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Expert's post
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Hi All,

This is a perfect question for TESTing VALUES.

We're told that Y is 80% GREATER than X.....

Let's TEST...
X = 100
Y = 180

The question then asks "X is what percent LESS than Y?"

When a question asks for "percent greater" or "percent less", then the Percentage Change Formula is required.

Percentage Change = (New - Old)/Old = Difference/Original

Here, the "new" number is 100 and the "old" number is 180 (you could also say that the difference is 80 and the 'original' number is 180).

Depending on which version of the formula you use, your answer might look a little different, but the end "meaning" is the same....

(100 - 180)/180 = -80/180 = -8/18 = -4/9 = -44.4444% The 'minus' sign means "less"

OR

80/180 = 8/18 = 4/9 = 44.444%

Either way, the "meaning" is the same: X is 44.4444% less than Y.

[Reveal] Spoiler:
D

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If y is 80 percent greater than x, then x is what percent less than y? [#permalink]

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30 Aug 2016, 14:38
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Hi Bunuel

if-y-is-80-greater-than-x-than-x-is-what-less-than-y-163031.html?fl=similar

*** REPEATED QUESTION. IT has already been Discussed
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Re: If y is 80% greater than x, than x is what % less than y? [#permalink]

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30 Aug 2016, 23:05
stonecold wrote:
Hi Bunuel

if-y-is-80-greater-than-x-than-x-is-what-less-than-y-163031.html?fl=similar

*** REPEATED QUESTION. IT has already been Discussed

______________
Done. Thank you.
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Re: If y is 80% greater than x, than x is what % less than y? [#permalink]

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30 Aug 2016, 23:31
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y=180/100 x

x=5/9 y

y-5/9y = 4/9 y

4/9 y *100 = 44 4/9

therefore option d.

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Re: If y is 80% greater than x, than x is what % less than y? [#permalink]

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Re: If y is 80% greater than x, than x is what % less than y? [#permalink]

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19 Sep 2017, 15:46
PatrickS 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.

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Re: If y is 80% greater than x, than x is what % less than y?   [#permalink] 19 Sep 2017, 15:46
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