Hi, there. I'm happy to help with this.
Prompt:
What percent of x is 3/4?
Notice there are two variable in this prompt ---- the percentage (call it p), for which the prompt asks, and the variable x. They are related by the equation:
x*p = 3/4
(Assume p is written in decimal form.) Right now, we have one equation and two unknowns.
Statement #1:
x = .5y
This statement introduces an another equation with another variable, so now we have two equations with three unknowns. We still can't solve.
If we plug in:
x*p = 3/4 ---> 0.5y*p = 3/4 (still can't solve for p)
Notice,
pappueshwar, that
(i) you don't get an equation with both x and y in it at the same time
(ii) even if you could determine that y is the percent, which is not, then that would not be an answer to the prompt question, because a DS prompt, unless otherwise stated, is always looking for a
numerical answer.
Statement #1 is
insufficient.
Statement #2:
y=10
Of course, this, by itself, is useless. We want to solve x*p = 3/4 for p, and this statement gives the value of a variable that does not appear in this prompt equation. Statement #2 is
insufficient.
Combined Statements #1 & #2
Now, we have x = .5y and y = 10.
Plug y into the first equation, and we get x = 5.
Now, go back to x*p = 3/4 and plug x=5 into this ---> 5p = 3/4 ----> p = 3/20 = 0.06, or 6%
Combined, the statements allow us to come up with a definitive numerical answer to the prompt question. Combined, they are
sufficient. Answer =
C
Does that make sense? Here's a practice PS question with percents and variables
https://gmat.magoosh.com/questions/34
When you submit your answer to that question, the following page will have a full video explanation.
Let me know if you have any further questions.
Mike
