Set 25 # 5

[vineetdixit]

If x^3y^4=5,000, is y=5?
(1)y is a positive integer.

(2)x is an integer.

SPOILER: Ans C

5000 = 5^ 4 & 2^3.

I had answered E since if X is negative then the answer will be negative. hence B does not rule out this possibility.

Please help me understand the OA

[tublai]

You have already answered your own question.

x cannot be (-)ve because if x is negetive, then x^3 becomes (-)ve , making the whole expression x^3*y^4 = (-)ve . Why? y^4 is always (+)ve irrespective of y= -ve or +ve

So, in order to stand the equation x^3*y^4 = 5000 , x has to be (+)ve.

And as per (2) x=integer

Hence, both (1) and (2) require to answer this question.

I hope that helps.

[DWarrior]

You're not differentiating between the statement and the question. "If x^3y^4=5,000" is a statement of a fact. x cannot be negative because we know y^4 is always positive and their product must always be positive.

You can now most likely figure out why individual statements are insufficient and why both combined are sufficient.

[vineetdixit]

B says X is an integer. hence it can be positive or negative. it does not rule out the possibility of it being negative.

[tublai]

Well. You have to consider the question stem as TRUE as well.

x^3y^4=5,000 THIS IS TRUE.

LHS = x^3 * y^4 = (+)ve ; as y^4 always (+)ve , x^3 has to be (+)ve to match RHS

RHS = 5000 = (+)ve

[vineetdixit]

DWarrior

by your logic then the answer will D. If the question is a statement of fact then X & Y will be integer by virtue of A & B individually.
1.e. if A then X automatically will be an integer hence need not to be proven separatly
2. Similarly for B

[Cichinel]

vineetdixit,

The answer cannot be D; based only on the second statement, y can be -5,

Hence C

[anil007]

x3.y4 = 5000
from st1 5000 can be written as 125*40; 5^3 * y^3
since y^3 != 40 with y=5, so insufficient.
x is not differtiating clearly btn +ve 7 -ve.
ans is E