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.

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?

Because you do not know actually the value of X.

You can pick numbers but not slash of the X

Regards

But we know it,s a variable. And we can eliminate, and add any variable when we need on.

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

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

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.

we can divide by x on both sides?

but if you divide per X on both sides what do you have then ?

right , question is all about x.