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

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chetan2u
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If x and y are integers, which of the following can be true? [#permalink] New post   29 Oct 2019, 00:13
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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)


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E
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tamal99
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Re: If x and y are integers, which of the following can be true? [#permalink] New post   29 Oct 2019, 00:28
If we consider Y as negative, then all of three are possible. Hence, IMHO answer is E.

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Archit3110
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Re: If x and y are integers, which of the following can be true? [#permalink] New post   29 Oct 2019, 09:41
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chetan2u wrote:
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


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
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Pritishd
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Re: If x and y are integers, which of the following can be true? [#permalink] New post   29 Oct 2019, 23:17
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chetan2u wrote:
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


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
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ankitprad
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Re: If x and y are integers, which of the following can be true? [#permalink] New post   03 Nov 2019, 06:15
Archit3110 wrote:
chetan2u wrote:
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


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


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?
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Archit3110
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Re: If x and y are integers, which of the following can be true? [#permalink] New post   03 Nov 2019, 06:21
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)
:)
ankitprad wrote:
Archit3110 wrote:
chetan2u wrote:
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


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


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?
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SaquibHGMATWhiz
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Re: If x and y are integers, which of the following can be true? [#permalink] New post   30 May 2023, 01:37
Expert Reply
chetan2u wrote:
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)

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
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Re: If x and y are integers, which of the following can be true? [#permalink]
30 May 2023, 01:37
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