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If x is 8/3 percent of y, y is what percent of x?

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If x is 8/3 percent of y, y is what percent of x?

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If x is 8/3 percent of y, y is what percent of x?
A. 3/8 B. 37.5 C. 375 D. 3,750 E. 3.75

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==> according to ivy approach, from x=(8/3)(1/100)y, y=(something)(1/100)x, we get y=(something)(1/100)(8/3)(1/100)y, if we substitute x into y. If we cancel y from both sides of the equation, we get something=3,750. Hence, the correct answer is D.
Answer: D

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Max@Math Revolution wrote:
If x is 8/3 percent of y, y is what percent of x?

A. 3/8
B. 37.5
C. 375
D. 3,750
E. 3.75
x is 8/3 percent of y
Let's plug in some nice values for x and y that satisfy the above conditions.
We know that 8/3 is 8/3 percent of 100.
So, x = 8/3 and y = 100 works

y is what percent of x?
In other words, 100 is what percent of 8/3?
Rewrite as 100 is what percent of 2 2/3?
Well, 100 is about 40 TIMES 2 2/3
If we express 40 as a percent we get 4000%
So, our answer will be close to 4000

Answer: D

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- Working with percent: https://www.gmatprepnow.com/module/gmat-arithmetic/video/1074

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I assume y=300 and hence x=8 to satisfy the given. Now when i back-calculate y (i.e. 300) is what pc of x (i.e 8); I get 37.5%. Should not the answer be B?
Max@Math Revolution wrote:
==> according to ivy approach, from x=(8/3)(1/100)y, y=(something)(1/100)x, we get y=(something)(1/100)(8/3)(1/100)y, if we substitute x into y. If we cancel y from both sides of the equation, we get something=3,750. Hence, the correct answer is D.
Answer: D

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Max@Math Revolution wrote:
If x is 8/3 percent of y, y is what percent of x?
A. 3/8 B. 37.5 C. 375 D. 3,750 E. 3.75
We are given that x = (8/3)/100 * y, we need to express y in terms of x:

x = 8/300 * y

300/8 * x = y

37.5x = y

Since 37.5 = 3,750%, we see that y is 3,750% of x.

Answer: D

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Max@Math Revolution wrote:
If x is 8/3 percent of y, y is what percent of x?
A. 3/8
B. 37.5
C. 375
D. 3,750
E. 3.75
x percent = x/100
So, 8/3 percent = (8/3)/100 = (8/3)/(100/1) = (8/3)(1/100) = 8/300

GIVEN: x is 8/3 percent of y,
We can write: x = 8/300 of y
In other words: x = (8/300)(y)
or......: x = 8y/300

y is what percent of x?
Take: x = 8y/300
Multiply both sides by 300 to get: 300x = 8y
Divide both sides by 8 to get: (300/8)x = y
Rewrite 300/8 as 3750/100 to get: (3750/100)x = y
In other words, y is 3750/100 of x
In other words, y is 3750 PERCENT of x

Answer: D

Cheers,
Brent

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Max@Math Revolution wrote:
If x is 8/3 percent of y, y is what percent of x?
A. 3/8 B. 37.5 C. 375 D. 3,750 E. 3.75
Just as we can convert, say, 42% to a decimal as 42/100, we can convert (8/3)% to a decimal as (8/3)/100. Thus, the relationship between x and y is:

x = (8/3)/100 * y

x = 8/300 * y

y = 300/8 * x

y = 37.5 * x

y = 3750/100 * x

So y is 3750 percent of x.

Answer: D

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