Is x > y? (1) |x| > |y| (2) x = |x|

chetan2u

Could you elaborate point 2.

x=|x|
Here modulus will always be positive or 0..
So |x|\(\geq{0}\), and thus x is also \(\geq{0}\)

OA: C
(1)\(|x| > |y|\)
Taking \(x = 2\) and \(y = 1 ,|x| > |y|\) as \(|2| > |1|\)
Is x > y : Yes as \(2>1\)

Taking \(x = -2\) and \(y = -1 ,|x| > |y|\) as \(|-2| > |-1|\)
Is x > y : No as \(-2<-1\)

Statement \(1\) alone is insufficient.

(2) \(x = |x|\)
If we take \(x=-2\), then it will not satisfy the statement \(2\) as \({-2}\neq{|-2|}\)
Only non negative numbers can statisfy \(x = |x|\)
So Statement implies that \(x\geq{0}\), but \(y\) can take any value.

Statement \(2\) alone is insufficient.

Combining 1 and 2 , \(|x| > |y|\) and \(x\geq{0}\) leads to \(x > |y|\)
Is x>y : yes for all \(x > |y|\)
So Combining (1) and (2) will be sufficient.

I have used the basic definition of module to solve this question. If you are fan of doing it on a number line, have a look at this approach

Answer is C
Thank you = Kudos

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 2 variables (\(x\) and \(y\)) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
We have \(x ≥ 0\) since \(x=|x|\).
Thus we have \(x = |x| > |y| ≥ y\) and \(x > y\).

Since both conditions together yield a unique solution, they are sufficient.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
If \(x = 2, y = 1\), then we have \(x > y\) and the answer is 'yes'.
If \(x = -2, y = 1\), then we have \(x < y\) and the answer is 'no'.

Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)
Since we don't have any information about \(y\), condition 2) is not sufficient obviously.

Therefore, C is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

Hi all. I'm new here at GMAT Club. I'd like to ask why there are A, B, C, D, E options when there are only 2 choices in the answer? Thank you in advance!

Hi,

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post ALL YOU NEED FOR QUANT.

Hope this helps.

Hi Bunuel thank you very much for the very detailed explanation! Yes, it helps!