M60-08

Question

If  x>y , is  x^2>xy ?

1)  x>0

2)  y>0

MathRevolution · Answer

Official Solution:

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Modifying the question:

x^2>xy

⇔  x^2-xy > 0

⇔  x(x-y) > 0

⇔  x > 0  since  x > y  (which implies that  x - y > 0 ).

So, the question is equivalent to asking 'is  x > 0? '.

Since condition 1) is same as the modified question, it is sufficient.

Condition 2):

Since  x > y , condition 2)  (y > 0)  implies that  x > 0 .

Condition 2) is also sufficient.

Therefore, the answer is D.

Answer: D

Note: The VA approach tells us that the answer is most likely to be D, since this is a CMT(Common Mistake Type) 4B question.

Condition 1) is easy to check, but condition 2) is more difficult to work with. If you can't figure out condition 2), you should choose D as the answer.

Answer: D

manisha1234 · Answer

I think this is a  high-quality  question and I agree with explanation.

KomalT · Answer

Above analysis may not hold true in case of fractions. Question does not say x and y are integers. So we cannot rule out the possibility of fractions.

1 Example:
x = 1/4 y= 1/2

x^2 = 1/16
xy = 1/8

here, x^2<xy

2 Example
x = 4 y= 2

x^2 = 16
xy = 4

here, x^2>xy

I think the solution should be E

Let me know if i am missing out something

Vicentte · Answer

But in your first example, 1/4 < 1/2, which contradicts the stem.

xyzzy94 · Answer

given x>y

If x =2 and y =1, then x2 = 4 and xy = 2.

Thus x2>xy (TRUE FOR ALL POSITIVE NUMBERS SUCH THAT X>Y). SO THE ANSWER IS YES

But if x = -1 & y =-2, then x2 = 1 and xy = 2.

Thus x2<xy. SO THE ANSWER IS NO.

So how is Statement 1 sufficient ????

Please help me out

Bunuel · Answer

___________________________
Notice that (1) says that x > 0.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

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