Is x < y ? (1) 2x < 3y (2) xy > 0 GMAT Data Sufficiency

Question - Is x < y ?

(1) 2x < 3y
(2) xy > 0

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE are sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

‘Is x < y ? (1) 2x < 3y (2) xy > 0’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1:

 Let us examine the factors' potential to alter the inequality sign in this kind of query.

Test procedures:

[a] Take the identical positive integer for each variable in.
The variables cannot alter the inequality sign if the inequality holds true (the normal situation); all the credit goes to the provided constants.
There are three situations that could occur there.
both variables must be equal,
must be greater than first
must be greater than second.
If the inequality does not hold (abnormal case), the variables are primarily responsible for changing the inequality's sign; the provided constants are powerless to do so. Only a fixed role, as indicated in the inequality, is possible in that case. Either the first variable is more than second variable or second variable is greater than first variable.

[b] Take the identical negative integer for both variables in.
Three outcomes are conceivable if the inequality maintains true (the standard case), in which case the variables are powerless to alter the inequality's sign.
First, both variables must be equal, second, must be greater than first, and third, must be greater than second.
The variables are primarily responsible for changing the inequality's sign if it does not hold true (an abnormal situation). The specified constants are powerless to alter the inequality's sign. Only a fixed role, as indicated in the inequality, is possible
in that case. Either first variable is more than second variable or second variable is greater than first variable.

Coming to main question-
Looking Statement 1
Make both variables the same positive integer [2].
4<6. The inequality is present here (normal case). In other words, the variables cannot alter the sign of the inequality [all praise goes to the provided constants].

There are three situations that could occur there.
First, both variables must be equal [x=y].
Second, the first variable must be greater than the second (x>y).
Third, the second variable must be greater than the first (xY).
Statement 1 is therefore insufficient,

Looking at statement 2,
xy>0. in other words x and y are both positive or both negative. i.e. (2,3) or (3,2) or (-2,-3) or (-3,-2).
Thus, So statement 2 is insufficient.

Combining: Three scenarios are available if x and y are positive.
First, both variables must be equal [x=y].
Second, the first variable must be greater than the second (x>y).
Third, the second variable must be greater than the first (xY).
C is so eliminated. Therefore answer E.
The answer is E which is Statements (1) and (2) TOGETHER are NOT sufficient.

Correct Answer: E

Approach Solution 2:

There is another approach to answering this question which is pretty simple when we replace arithmetic math with reasoning.

The problem statement is if one thing is smaller (or bigger) than another.

Statement 1 informs you that 2 of one thing is smaller than 3 of another. That is insufficient to determine if one thing is smaller (larger) than the other.

Thus it is Insufficient.

Statement 2 indicates that x and y have the same sign. Then statement 2 is utterly meaningless because it doesn't tell you anything about their relative magnitude.

Thus it is insufficient.

Combining insufficient (1) and insufficient (2) results in an insufficient combination.

The answer is E which is Statements (1) and (2) TOGETHER are NOT sufficient.

Correct Answer: E

Approach Solution 3:

1. if 2x <3y
2x<3y
=> x < 3/2y
If x=1, y=1 ,x < 3/2y, x=y
If x=1, y=10 ,x< 3/2y, x So, we don't know if x=y or x
2. xy > 0
x = y = 1 => xy > 0 but x = y
x = 2, y = 3 => xy > 0 x < y Not Sufficient

Correct Answer: E

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