Is y a positive number? (1) 2x + y > 27 (2) x – 3y < 24

Question: Is y > 0?

Statement 1:2x + y > 27

Case 1: @x = 1, y > 25 YES
Case 2: @x = 15, y > -3 i.e. y may eb Negative as well hence NO

NOT SUFFICIENT

Statement 2: x – 3y < 24

@x = 0, y > -8 so y may be -7 or +7 both hence

NOT SUFFICIENT

Combining the statements


x – 3y < 24 (Multiplying -2 both sides which requires change of sign we get inequation as)
-2x + 6y > -48
and 2x + y > 27

Adding the two inequalities
7y > -21
i.e. y > -3

i.e y may be Positive and negative both hence

NOT SUFFICIENT

Answer: Option E

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You can add the same side of inequality without changing the inequality sign.
7x>3 and 4<2x+3
7x>3 and 2x+3>4
7x+2x+3>3+4

However you can not subtract the same sides of inequality.
For example
7x-(2x+3)>3-(4) may not be true.

VERITAS PREP OFFICIAL SOLUTION:

Some inequality problems, particularly those that ask whether a value is > 0 or < 0, lend themselves well to conceptual understanding. But most of time you will find, as with this problem, that there is too much “action” in the statements to warrant a quick conceptual estimate of what the statements mean. Whenever you are in doubt, it’s generally a good idea to “just do it”—just perform the mathematical operations to solve for a variable or complete a calculation. In many cases you will be able to stop short of the finish line once a few steps have made the picture clearer, but regardless there will be times when you simply need to do the math.

Here, it should be quickly apparent that neither statement alone is sufficient, as each equation allows for any possible value of x. But together, the statements allow you to do the math. Arrange the equations such that the inequalities face the same direction:

2x + y > 27

24 > x – 3y

Then manipulate the second equation to get the variables on the same side:

3y – x > -24

Then double the bottom equation to allow for an elimination of the x term:

6y – 2x > -48

Then you can combine the inequalities:

y + 2x > 27

6y – 2x > -48

7y > -21

y > -3

You’ll find that y could be negative (it could be -2 or -1) or positive (all positive numbers are greater than -3), so the statements together are not sufficient, and answer choice E is correct.

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