percent problem..

[Black Hole]

Sourch: http://iim-cat-questions-answers.2iim.c ... s-profits/

Question: a is x% of b, b is x% more than a, find x.[/b][/i]
A. 50%
B: 62%
C: 75%
D: 70%
E: None

Solution:
from second part:
b/a=x/100
--->b=ax/100
so, the number is :
(ax+100a)/100................(1)

from first part:
a=(x/100)*b
--->a=(x/100)*a(x+100)/100 [putting the value of b]
--->a=ax(x+100)/10000
--->ax(x+100)=10000a
--->x^2+100x-10000=0 [dividing by a from both side]
--->x^2+2.x.50+50^2=12500
--->(x+50)^2=12500
--->x+50=111.80
--->x=111.80-50
so, x=61.80

in addition, if i use plug in method, it also doesn't make sense.

Hi Ron, How are you. i can not solve this math. is there any mistake in this math?? i used plug in method and general method to solve this math. but every efforts in vain. Some students say: the correct answer is 62% . But i did not get the EXACT figure of this solution. Here, i got approximately 61.80 as correct answer. So, should not it be EXACT figure (like 62%, 70%, etc? also, what is your suggestion about THIS math. i'll be very glad, if i can know what is going here (in this math)...
Thanks....

[Linh]

Hi Black Hole,

I think Ron will tell you to provide the source and all 5 answer choices of the question.
But since percent is my weakest area, I felt tempting to try this one and saw that of all 3 answer choices provided, non is the answer:

A. x =50%.
Equation 1: a is x% of b --> a = (x/100)b --> I picked b=100, so a =50
Equation 2: b is x% more than a --> b = (x/100)a + a
--> plugging b=100 and a=50 into equation 2. Not satisfied.

B. x =62%.
Equation 1: a = (x/100)b --> I picked b=100, so a =62
Equation 2: b = (x/100)a + a
--> plugging b=100 and a=62 into equation 2. Not satisfied.

C. x =75%.
Equation 1: a = (x/100)b --> I picked b=100, so a =75
Equation 2: b = (x/100)a + a
--> plugging b=100 and a=75 into equation 2. Not satisfied.


I don’t know any other method more helpful. Doing algebra will be very complicated (to me) in this case. Maybe Ron knows?

[RonPurewal]

your work is correct. the answer is approximately 62 percent, but not exactly.

these are just practice materials, right? you aren't doing anything wrong here; the problem is just sloppy writing/proofreading. your math is perfectly OK, and your answer (≈ 61.8 percent) is the correct answer.

that sort of sloppy writing would most certainly not be tolerated on the gmat exam, so, you've nothing to worry about here.

[Linh]

Dear Ron,

The answer is B, so what's wrong with my approach or calculation?

[tim]

Please note that Ron was completely correct when he said the answer is close to B, but it is NOT B. The correct answer does not appear in the choices, and the problem is broken. Whatever source it came from should not be trusted. Please stick to practice questions from legitimate sources to avoid this sort of frustration with bogus problems.

[Linh]

Thanks Tim,

Yes, I agree. But I find this question is interesting. Like a nice flower with some bad-decorated petals.
"Bogus problems"? I thought there are only 2 kinds: official and unofficial problems
(I see what you meant, ha)

[Black Hole]

your work is correct. the answer is approximately 62 percent, but not exactly.

these are just practice materials, right? you aren't doing anything wrong here; the problem is just sloppy writing/proofreading. your math is perfectly OK, and your answer (≈ 61.8 percent) is the correct answer.

that sort of sloppy writing would most certainly not be tolerated on the gmat exam, so, you've nothing to worry about here.

Thank you so much Ron...

[RonPurewal]

you're welcome.

[tim]

"Bogus problems"? I thought there are only 2 kinds: official and unofficial problems
(I see what you meant, ha)

It's a little more nuanced than that. There are *some* unofficial problems that are worth doing (ours, for instance), but there are a lot of sources out there that will just lead you astray. When in doubt, stick to GMAT materials our MGMAT materials, because (a) you know they are legit and (b) there are more than enough problems from those sources to prepare you for all the math you'll see on the GMAT if you use those resources properly.