If A = x% of y and B = y% of x, then which of the following is true?

Question

A. A is smaller than B. 
B. A is greater than B
C. Relationship between A and B cannot be determined. 
D. If x is smaller than y, then A is greater than B.
E. None of the above

Source: Quick Maths by M.Tyra (Indian publication)

sukanyar · Answer

Basically A = B = xy/100

None of the options mentions this; hence E.

EMPOWERgmatRichC · Answer

Hi aimtoteach,

This question can be solved conceptually or by TESTing VALUES. It's not quite written in proper "GMAT style", but the basic concepts will show up on Test Day.

We're told that A = X% of Y and B = Y% of X. We're asked which of the following is true.

IF....
X = 50
Y = 100

A = 50% of 100 = 50
B = 100% of 50 = 50

Answer A: A is smaller than B.This is NOT true.
Answer B: A is greater than B. This is NOT true.
Answer C: Relationship between A and B cannot be determined. While it would take additional TESTs to prove, A always = B, so the relationship IS known. This is NOT true.
Answer D: If x is smaller than y, then A is greater than B. This is NOT true.

Since we've disproved the first four answers, there's only one answer left.

Final Answer:  E

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

aimtoteach · Answer

Hello rich , I got this one, just shared because it does test a very basic principle. You are right this is not 'GMAT style' but good practise never the less

AjChakravarthy · Answer

If there was an answer option  "A=B"  then that would be the correct answer right?

Thanks, 
Aj

EMPOWERgmatRichC · Answer

Hi Aj,

Yes, given the information in the prompt, A DOES = B.

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

CrackverbalGMAT · Answer

Solution: A = x% of y => A = x y/100 B = y% of x => B = y x/100 A = B = x y/100 A,B.C can be eliminated. As A=B. So D can be also eliminated. (option e) Hope this helps

Devmitra Sen(GMAT Quant Expert)

egmat · Answer

Hi AjChakravarthy,

Yes, absolutely! You've got it exactly right.

A = x% of y = (x * y) /  100 
B = y% of x = (y * x) /  100

Both simplify to exactly  xy/100 , so A always equals B.

Since none of the given options say "A = B," the correct answer is  E  (None of the above). But if there had been an option stating "A is equal to B," that would have been the correct choice.

Key takeaway here:  x% of y will ALWAYS equal y% of x.  This is a handy trick to remember — for example,  8 % of  50  is the same as  50 % of  8 , which is  4 . This can save you time on calculations in other problems too!

Answer: E

If A = x% of y and B = y% of x, then which of the following is true?

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GMAT Problem Solving (PS) Questions

If A = x% of y and B = y% of x, then which of the following is true?

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