x percent of what number is equal to y?

[Max@Math Revolution]

x percent of what number is equal to y?
1) x=10y
2) xy=40

*An answer will be posted in 2 days.

[Brent@GMATPrepNow]

x percent of what number is equal to y?

1) x = 10y
2) xy = 40

Target question: x percent of what number is equal to y?
This is a good candidate for rephrasing the target question

x percent of what number is equal to y?
Let k = the number we're trying to determine

We get: "If x percent of k is equal to y, what is the value of k?
In other words, x/100 of k = y
Or....(x/100)(k) = y
To solve for k, multiply both sides by 100/x.
We get: k = 100y/x

Let's REPHRASE the target question.....
Target question: What is the value of 100y/x?
So, all we need to do now is find the value of x/y

Statement 1: x = 10y
Divide both sides by x to get: 1 = 10y/x
Divide both sides by 10 to get: 1/10 = y/x
PERFECT!
If y/x = 1/10, then 100y/x = 100(1/10) = 10
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: xy = 40
This is NOT enough information to find the value of 100y/x
Consider these two conflicting cases:
Case a: x = 2 and y = 20, in which case 100y/x = 100(20)/(2) = 1000
Case b: x = 20 and y = 2, in which case 100y/x = 100(2)/(20) = 10
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

[DavidG@VeritasPrep]

x percent of what number is equal to y?
1) x=10y
2) xy=40

*An answer will be posted in 2 days.

We could also do a little fun number-picking.

Statement 1:

Case 1: y = 1 and x = 10. 10% of what number is equal to 1? 10.
Case 2: y = 2 and x = 20. 20% of what number is equal to 2? 10.

No matter what we pick, we'll get 10. Sufficient


Statement 2:
We can reuse Case 2, as 2*20 = 40. y = 2 and x = 20. 20% of what number is equal to 2? 10.
Case 3: y = 1 and x = 40. 40% if what number is equal to 1? We could solve: .4t = 1 --> t = 1/.4 = 10/4 = 5/2. But it's enough to see that the answer will not be 10. Because we get different results, this statement alone is not sufficient.

Answer is A

[Brent@GMATPrepNow]

x percent of what number is equal to y?
1) x=10y
2) xy=40

One small note: The question should really include some information that tells us that x ≠ 0.
Otherwise, statement 1 is not sufficient.

Cheers,
Brent

[Max@Math Revolution]

If we modify the original condition and the question, we get x(1/100)(some)=y. So we have to find x/y. In case of condition 1), we get x/y=10. The condition is sufficient and the correct answer is A.