Is xy < 8? (1) x < 2 and y < 4 (2) 0 < x < 1/2 and y^2 < 225

Question: Is xy < 8?

Statement 1: x < 2 and y < 4
Case 1: @x=1, y=3, xy=3 i.e. Less than 8
Case 2: @x=-10, y=-3, xy=30 i.e. Greater than 8. Hence,
NOT SUFFICIENT

Statement 2: 0 < x < 1/2 and y^2 < 225
0 < x < 1/2
and
-15 < y < 15
i.e. -15/2 < xy < 15/2
i.e. xy will always be less than 8. Hence,
SUFFICIENT

Answer: option B

0 < x < 1/2 and y^2 < 225

Statement 1
x < 2 and y < 4
if x=1,y=3, xy<8
But if x=-5 , y=-6, xy>8
So not sufficient

Statement 2
Y^2<225
=>|y|<15
=> -15<y<15

Max 15*1/2=7.5
Min -15*1/2=-7.5
In any case, xy< 8
So Sufficient

Answer is B

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is xy < 8?
(1) x < 2 and y < 4
(2) 0 < x < 1/2 and y^2 < 225

There are 2 variables (x,y) in the original condition, thus we need 2 equations to match the number of variables and equations. As 2 equations are given from the 2 conditions, there is high chance that (D) is going to be our answer, but looking at the conditions closely,
1) The answer to the question becomes “yes” if x=y=1, but “no” if x=y=-10. The condition is insufficient.
2) xy is always less than 8 for -15<y<15, 0<x<1/2, making the condition sufficient. Hence the answer becomes (B)

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/ No. The question asks: “Is xy < 8?”

Statement 1: x < 2 and y < 4. At first glance this might appear sufficient. When you multiply a positive number smaller than 2 by a positive number smaller than 4, the result is smaller than 8; however, you must consider negative numbers. x could equal -3, for example, and y could be -5. Together their product would equal 15. So this statement is not sufficient and you can eliminate choices A and D. Note: This statement is all about avoiding assumptions. Do not assume that x and y are positive as that is not given in the question stem!

Statement 2: 0 < x < 1/2 and y^2 < 225. This means that x is a positive number between 0 and 1/2 and 15 > y > -15. When you multiply a positive number that is smaller than 1/2 by a number that is between 15 and -15, the result must be smaller than 8. Even if you took the values of 1/2 and 15 the product is 7.5. Unlike in Statement 1, it is okay when y is negative because x must be positive, so the product would be negative and less than 8. With this information, you know that xy must be smaller than 8 and this statement is sufficient.

The answer is B.