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Math Expert V
Joined: 02 Sep 2009
Posts: 58316
If x is an integer less than or equal to −2 and y is an integer with a  [#permalink]

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Difficulty:   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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GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 4978
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
If x is an integer less than or equal to −2 and y is an integer with a  [#permalink]

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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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Intern  B
Joined: 09 Jan 2012
Posts: 8
Re: If x is an integer less than or equal to −2 and y is an integer with a  [#permalink]

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- 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
Senior Manager  G
Joined: 18 May 2019
Posts: 343
Re: If x is an integer less than or equal to −2 and y is an integer with a  [#permalink]

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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. 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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