Inequalities

Question

Is x>y?
A) (x-y) (x-y) >0
B) y>0

My answer is A

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thyagi · Answer

Statement 1 - (x-y)^2 >0

This statement is clearly not sufficient because no matter what values X and y take , (x-y)^2 will always yield a positive value...(except for X=y..(x-y)^2 = 0)

If X =3 and y=1 , (x-y)^2 >0
And X>y , a definite yes...

If X =-3 and y = 7.
(X-y)^2 > 0
X<y , a definite no...so this statement alone is not sufficient to answer the question.. eliminate options A and D..

Statement 2 = y>0... Nothing about X .. this statement is not sufficient as well.... Eliminate option B...

Now we are left with C and E...

Consider both statements together..

(X-y)^2 > 0
Y>0.... This might look sufficient but it isn't...

If X= 1 and y = 3 , X<y and (x-y)^2 > 0... I get a definite no...

If X= 5 and y = 1 , X>y and
(X-y)^2 > 0... I get a definite yes...

Even if we consider both statements together, we cannot answer the target question...

We can eliminate option c and right choice is E...

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eswarchethu135 · Answer

Statement 1) (x-y)(x-y) > 0

For a product of 2 numbers to be greater than 0, either each term should be greater than 0 or each term should be less than 0. So both the cases are possible here.

x can be greater than y and x cannot be greater than y.

For ex: If x = 3 and y = 1, (x-y)(x-y) = 4 > 0, and x > y.
If x = 1 and y = 3, (x-y)(x-y) = 4 > 0, and y > x.

So statement 1 is INSUFFICIENT.

Statement 2) Very little information and we cannot say anything from this statement. INSUFFICIENT.

Combining 1) + 2)
Still both the cases we considered in statement 1) are possible and we cannot get a unique answer. So even combining didn't work.

OPTION:  E

madgmat2019 · Answer

For (x-y) (x-y) >0 either both x-y >0 or x-y<0
Obviously A is insufficient
and with just knowing y>0, its insufficient.
if we combine both, even then we cannot find whether x>y or not ...........So (E)