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

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

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Re: If y is 80% greater than x [#permalink]
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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$$y = \frac{180}{100} * x$$

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

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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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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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.

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Re: If y is 80 percent greater than x, then x is what percent less than y? [#permalink]
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Since we need to find X percent less than Y

y-x/y = (1.8x-x)/1.8x = 44(4/9)

Ans : D
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Re: If y is 80 percent greater than x, then x is what percent less than y? [#permalink]
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Say x = 100, then y = 180

Percent less $$= 100*\frac{80}{180} = 44 \frac{4}{9}$$
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Re: If y is 80 percent greater than x, then x is what percent less than y? [#permalink]
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.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

yis80percentgreaterthanx_text.PNG [ 13.06 KiB | Viewed 72994 times ]
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Re: If y is 80 percent greater than x, then x is what percent less than y? [#permalink]
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.

Let x = 100
So y = 180
We want percentage change.
So, (100-180)/180
= -44.44%
= 44 4/9% lesser tha y.

Hence 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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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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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]
Let x be 100. Therefore, y = 180

=> $$\frac{(y - x) }{ y}$$ * 100 = $$\frac{(180 - 100)}{ 180}$$ * 100

=> $$\frac{80}{180}$$ * 100 = 44.44

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