Which of the positive numbers x or y is greater?

Statement 1:
y = x + x and x is confirmed to be positive, so y > x is true. Sufficient.

Statement 2:
We can have y=0.000001 or y = 2. Insufficient.

Ans: A

Solution:

Question Stem Analysis:

We need to determine whether x or y is greater, given that both are positive.

Statement One Alone:

Since both x and y are positive and y is twice x, then y is the greater of the two. Statement one alone is sufficient.

Statement Two Alone:

Statement two alone is not sufficient. For example, if x = 1 and y = 2 (notice that 2(1) + 5(2) = 12), then y is greater. However, if x = 3.5 and y = 1 (notice that 2(3.5) + 5(1) = 12), then x is greater.

Answer: A

so, number is not the same as integer? i picked D because it i thought x and y have to whole numbers, in which case only one combination is possible: x = 1 and y = 2

Bunuel

No, "number" and "integer" are not synonymous. All integers are numbers but not all numbers are integers.

A number (a real number) can be:
1. An integer: ..., -3, -2, -1, 0, 1, 2, 3, ...;
2. A rational, non-integer, for example, -8878/99, ..., -3/2, ..., 1/2, ..., 67/11, ...
3. An irrational number: \(-2\sqrt{6}\), ..., \(-\sqrt{2}\), ..., \(\sqrt{3}\), ..., \(\pi\)

2. Properties of Integers

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Hope it helps.

I agree that A is sufficient but if you combine A and B sentences and substitute y= 2x in 2x+5y=12, you get X=1 and Y=2 which is a more precise answer to A. Bcz they didn't mention if the number is rational or integer they just mentioned it is a positive number.
ScottTargetTestPrep Bunuel GMATNinja

For data sufficiency, as long as a statement gives enough information to answer the question, it's sufficient.

As you say, statement 1 is sufficient to answer the question "which of the positive numbers x or y is greater?" At that point, we can definitively rule out (C). Why? Because we definitely do NOT need both statements to decide if x is greater than y. If statement 1 is true -- whether x and y are integers, rationals, or irrationals -- y always has to be bigger.

Sure, if we take statements (1) and (2) together, that would give us exact values for x and y. But keep in mind: the question doesn't require exact values. We just need to decide if x is greater than y.

Now, since statement 2 is not sufficient on its own, we can eliminate B and D. So the final answer has to be (A).

I hope that helps!

What if for the numbers are fractions..?