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If x is an integer less than or equal to −2 and y is an integer with a

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If x is an integer less than or equal to −2 and y is an integer with a  [#permalink]

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New post 19 Feb 2019, 22:04
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A
B
C
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E

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  45% (medium)

Question Stats:

57% (01:31) correct 43% (01:45) wrong based on 77 sessions

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If x is an integer less than or equal to −2 and y is an integer with an absolute value greater than or equal to 5, which of the following statements must be true of xy ?


I. xy is an integer
II. xy is negative
III. |xy| ≥ 10

A. I only
B. III only
C. I and III only
D. II and III only
E. I, II, and III

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If x is an integer less than or equal to −2 and y is an integer with a  [#permalink]

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New post 20 Feb 2019, 00:34
Bunuel wrote:
If x is an integer less than or equal to −2 and y is an integer with an absolute value greater than or equal to 5, which of the following statements must be true of xy ?


I. xy is an integer
II. xy is negative
III. |xy| ≥ 10

A. I only
B. III only
C. I and III only
D. II and III only
E. I, II, and III


given
x will be <-2 ; -3,-4.. and lyl >5
so only option i & iii are valid
IMO C
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Re: If x is an integer less than or equal to −2 and y is an integer with a  [#permalink]

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New post 20 Feb 2019, 14:44
- The statement says that X is an integer and Y is an integer, so their product should be an integer.... so choice A is correct
- X is negative, but we don't know whether Y is positive or negative, so we cannot confirm choice B
- X is less than or equal -2, and Y (regardless of its sign) is greater than or equal 5, considering the absolute value of the product of XY must be positive, so XY is greater than and equal 10
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Re: If x is an integer less than or equal to −2 and y is an integer with a  [#permalink]

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New post 15 Sep 2019, 12:35
x and y are integer and x≤-2, while |y|≥5, implying either y≤-5 or y≥5.
We are to determine whether the following statements must be true of xy.
I. xy is an integer. This is always true for all values of x and y which are integers. An integer multiplied by another integer always results in another integer. Hence I is always true.

II. xy is negative. Not always true. We know x≤-2, which is always a negative number, but y can be either positive or negative. When y≥5 then xy is negative, however, when y≤-5, then xy is positive. Hence II. is not always true.

III. |xy|≥10. This always true. we know x≤-2 and y is either ≤-5 or ≥5. in either case, the minimum possible value of |xy|=10, hence |xy|≥10 is always true.

Statements I and III are always true, hence the answer must be C.
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Re: If x is an integer less than or equal to −2 and y is an integer with a   [#permalink] 15 Sep 2019, 12:35
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