If x and y are integers, which of the following can be true?

Question

If x and y are integers and x>y, which of the following can be true?
(I)  |y|*x\geq{y^2} 
(II)  |y|*x\leq{y^2} 
(III)  |y|*x={y^2}

(A) (I) only
(B) (II) only
(C) (I) and (II) only
(D) (I) and (III) only
(E) (I), (II) and (III)

Chetan's  questions

tamal99 · Answer

If we consider Y as negative, then all of three are possible. Hence, IMHO answer is E.

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Archit3110 · Answer

test the condition with x=3 and y=2 and x=-1 and y=-2
we get all three given conditions as can be true 
IMO E

Pritishd · Answer

As the question asks for 'can be true' we can take  x  and  y  as  1  and  0 . These two numbers also satisfy the two conditions that  x>y  and  x  and  y  are integers.

Now,
 |y|*x   =   0*1   =   0  and  y^2   =   0

Applying the above to the three statements we get zero on both sides of the equal to sign.
(I)  |y|*x\geq{y^2} 
(II)  |y|*x\leq{y^2} 
(III)  |y|*x={y^2}

Ans.  E

ankitprad · Answer

Hi Archit,
Is there any way of knowing what values to test, so that one can solve these kind of problems quickly, instead of spending time to test out each equation with different positive / negative values for each variable?

Archit3110 · Answer

ankitprad well particularly for DS based questions for integers/ fractions you can you following range as reference to test and validate the statemets (-2,-3/2,-1,-1/2,0,1/2,1,3/2,2)

SaquibHGMATWhiz · Answer

Solution:

x and y are integers and  x>y

(I)  |y|*x\geq{y^2} 
   Can be true  when  x=3  and  y=2

(II)  |y|*x\leq{y^2} 
   Can be true  when  x=-2  and  y=-3

(III)  |y|*x={y^2} 
   Can be true  when  x=3  and  y=-3

Hence the right answer is    Option E

mvgkannan · Answer

OK. This is a tricky question, because of the difference between, "can be true" & "must be true".

Must be true = the  All   x/unknowns  from the question stem is  True  for the condition.
 
 for eg: if question stem says x<2, then if the answer choices x<5, then it satisfies because, the any value of X from x<2 will be true for x<5. While for the same, 0<x<7 cannot be true because, because x can be 6. Question stem shall be completely inside the answer range.

Can be true =  Some of x/unknowns   from the question stem is true for the condition.

for the above example, 0<x<7 can be true because, x can be 4 also. And x<5 is also true. but x>7 will be false because there is no overlap. Hence for can be true, some overlap is enough for it to be true.

so for  Must be true = Complete overlap,  
for  can be true = some overlap.

Thanks  chetan2u .

vibhorrokstar19 · Answer

can someone please post the explaination not using the plugin approach and solve each equations to prove x>y.. 
Thanks in advance!

Krunaal · Answer

We don't have to prove x>y, that is already given to us. With that information in mind, we have to verify if the below statements could or couldn't hold valid in any case.

If x and y are integers, which of the following can be true?

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GMAT Problem Solving (PS) Questions

If x and y are integers, which of the following can be true?

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