so we are comparing 22% and 2/9 of the same number.
(I) First case - when X is a positive integer.
so 22% = \(\frac{22}{100}\) vs \(\frac{2}{9}\)
cross multiply and the greater quantity will give the greater fraction..
so 22*9 vs 2*100 => 198 vs 200
Since 200 is greater and is at the place of \(\frac{2}{9}\), 2/9 i sgreater
hence B>A
(II) Second case - X is 0..
here both sides will be 0 and A=B

thus we cannot answer unless we know what is X.

D
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Answer: B
It is not written in the correct way but it seems that option B is 2/9
A = 22% = 22/100
B = 2/9
We need to somewhat change them to look similar, thus we multiply both denominator and nominator of B into 10, we will have:
B = 2/9 = 2 * 10 / 9* 10 = 20/90
Now both A and B have the same nominator and we are able to compare them, B is bigger because it has a lower denominator than A.
Answer is B.
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Quantity A	Quantity B
22 percent of x	\(\frac{2}{9}\) of x

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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The biggest question of this century here is that, why we not remove the variable x from both sides whereas we do before in many times on many questions?
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[


Because X can be any number, positive or negative, simply removing it won't suffice for this problem.

If X = 1, then Quantity A = .22 and Quantity B = .2222 etc, making Quantity B bigger.

If X = -1, then Quantity A = -.22 and Quantity B = -.2222 etc, making Quantity A bigger.

Thus, the answer is D.

Take X = 10 and X= -10

You will get 2 Answers.

Hence, D is the option.

Thanks @PIneappleBoy2, and @Sanpreet but my question is why we do not remove the "x" from both side?
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Because you do not know actually the value of X.

You can pick numbers but not slash of the X

Regards
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But we know it,s a variable. And we can eliminate, and add any variable when we need on.
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If you're using the strategy of matching operations (for more on the strategy see the video below), then you can safely:
- add or subtract ANY value from both quantities
- multiply both quantities by any POSITIVE value
- divide both quantities by any POSITIVE value

For this question we have:
QUANTITY A: 0.22x
QUANTITY B: (2/9)x

If you want to eliminate x from both quantities, you must DIVIDE both quantities by x
In order to safely divide both quantities by x, then you must be certain that x is POSITIVE.
In this case, we aren't told whether x is positive, negative or zero.
As such, we can't divide both quantities by x


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A is .22 x, B is .2222... x. If x is positive, answer is B. If negative, it's A. So D.

chetan2u can we consider X as negative, besides x positive and 0 since nothing is given about x !!

When the problem is formulated as above is implied that zero and a negative number is NOT possible.

Having a % of zero does not make any sense.

See here more our quant theory about % https://gre.myprepclub.com/forum/gre-math- ... tml#p81625

regards
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B is greater than A.
Another way to look at this could be - 22% of x = 22/100x
Multiply 2/9 by a number that makes it closest to 100 i.e. 11
When numeratoe and denominator is multiplied by 11, we get 22/99x

As the denominator of B is lesser than that of A, B>A

If the number cannot be zero or positive, then why is the answer D then?

This is not mentioned in the stem, which is why the answer is D.


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we can divide by x on both sides?

but if you divide per X on both sides what do you have then ?
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right , question is all about x.