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# M08-26

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Math Expert
Joined: 02 Sep 2009
Posts: 58364

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16 Sep 2014, 00:38
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Difficulty:

15% (low)

Question Stats:

85% (00:46) correct 15% (01:59) wrong based on 102 sessions

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If $$x$$ and $$y$$ are positive integer and $$xy$$ is divisible by 4, which of the following must be true?

A. If $$x$$ is even then $$y$$ is odd.
B. If $$x$$ is odd then $$y$$ is a multiple of 4.
C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer.
D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer.
E. $$x^y$$ is even.

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Joined: 02 Sep 2009
Posts: 58364

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16 Sep 2014, 00:38
1
Official Solution:

If $$x$$ and $$y$$ are positive integer and $$xy$$ is divisible by 4, which of the following must be true?

A. If $$x$$ is even then $$y$$ is odd.
B. If $$x$$ is odd then $$y$$ is a multiple of 4.
C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer.
D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer.
E. $$x^y$$ is even.

Notice that the question asks which of the following MUST be true, not COULD be true.

A. If $$x$$ is even then $$y$$ is odd. Not necessarily true, consider: $$x=y=2=\text{even}$$;

B. If $$x$$ is odd then $$y$$ is a multiple of 4. Always true: if $$x=\text{odd}$$ then in order $$xy$$ to be a multiple of 4 $$y$$ must be a multiple of 4;

C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer. Not necessarily true, consider: $$x=1$$ and $$y=4$$;

D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer. Not necessarily true, consider: $$x=2$$ and $$y=4$$;

E. $$x^y$$ is even. Not necessarily true, consider: $$x=1$$ and $$y=4$$;

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Joined: 13 Feb 2014
Posts: 7
Location: India
Schools: HBS '18, ISB '16, IIMA
GMAT Date: 12-14-2014
GPA: 3.5
WE: Engineering (Consumer Electronics)

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31 Aug 2015, 01:03
this question has to be reconsidered to clarify the users confusion on whether xy means x*y or xy a two digit number.
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Joined: 02 Sep 2009
Posts: 58364

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31 Aug 2015, 07:49
ramarao443 wrote:
this question has to be reconsidered to clarify the users confusion on whether xy means x*y or xy a two digit number.

xy always means x multiplied by y, if it's not stated otherwise. If it were two digit number xy, then it would be explicitly mentioned.
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09 Feb 2016, 23:40
Bunuel wrote:
Official Solution:

If $$x$$ and $$y$$ are positive integer and $$xy$$ is divisible by 4, which of the following must be true?

A. If $$x$$ is even then $$y$$ is odd.
B. If $$x$$ is odd then $$y$$ is a multiple of 4.
C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer.
D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer.
E. $$x^y$$ is even.

Notice that the question asks which of the following MUST be true, not COULD be true.

A. If $$x$$ is even then $$y$$ is odd. Not necessarily true, consider: $$x=y=2=\text{even}$$;

B. If $$x$$ is odd then $$y$$ is a multiple of 4. Always true: if $$x=\text{odd}$$ then in order $$xy$$ to be a multiple of 4 $$y$$ must be a multiple of 4;

C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer. Not necessarily true, consider: $$x=1$$ and $$y=4$$;

D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer. Not necessarily true, consider: $$x=2$$ and $$y=4$$;

E. $$x^y$$ is even. Not necessarily true, consider: $$x=1$$ and $$y=4$$;

Hi Buneul,

As per the question, X and Y are positive number and XY is divisible by 4. Then we have to consider numbers which are only divisible by 4.

Then how Choice (B) can be correct.
Math Expert
Joined: 02 Sep 2009
Posts: 58364

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10 Feb 2016, 00:10
msk0657 wrote:
Bunuel wrote:
Official Solution:

If $$x$$ and $$y$$ are positive integer and $$xy$$ is divisible by 4, which of the following must be true?

A. If $$x$$ is even then $$y$$ is odd.
B. If $$x$$ is odd then $$y$$ is a multiple of 4.
C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer.
D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer.
E. $$x^y$$ is even.

Notice that the question asks which of the following MUST be true, not COULD be true.

A. If $$x$$ is even then $$y$$ is odd. Not necessarily true, consider: $$x=y=2=\text{even}$$;

B. If $$x$$ is odd then $$y$$ is a multiple of 4. Always true: if $$x=\text{odd}$$ then in order $$xy$$ to be a multiple of 4 $$y$$ must be a multiple of 4;

C. If $$x+y$$ is odd then $$\frac{y}{x}$$ is not an integer. Not necessarily true, consider: $$x=1$$ and $$y=4$$;

D. If $$x+y$$ is even then $$\frac{x}{y}$$ is an integer. Not necessarily true, consider: $$x=2$$ and $$y=4$$;

E. $$x^y$$ is even. Not necessarily true, consider: $$x=1$$ and $$y=4$$;

Hi Buneul,

As per the question, X and Y are positive number and XY is divisible by 4. Then we have to consider numbers which are only divisible by 4.

Then how Choice (B) can be correct.

We are given that $$x$$ and $$y$$ are positive integer and $$xy$$ (the product of x and y) is divisible by 4.

(B) says that if $$x$$ is odd then $$y$$ is a multiple of 4. Now, if x is odd, then for xy to be divisible by 4, y must be a multiple of 4. So, option B must be true.
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Joined: 16 Dec 2016
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15 Mar 2018, 23:53
if x =1 and y=4 then none of the options r true
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Joined: 02 Sep 2009
Posts: 58364

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16 Mar 2018, 00:00
sushanttinku wrote:
if x =1 and y=4 then none of the options r true

B says: If x is odd then y is a multiple of 4.

If x = 1 = odd and y = 4 = multiple of 4 (recall that an integer IS a multiple of itself).
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Re: M08-26   [#permalink] 16 Mar 2018, 00:00
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# M08-26

Moderators: chetan2u, Bunuel