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If x is an integer, is y an integer?

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Bunuel
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If x is an integer, is y an integer? [#permalink] New post   19 Nov 2019, 23:43
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If x is an integer, is y an integer?

(1) The average of x and y is not an integer.

(2) The average of x, y, and x + 6, is y.
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B
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Re: If x is an integer, is y an integer? [#permalink] New post   20 Nov 2019, 00:46
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If x is an integer, is y an integer?

(Statement1): \(\frac{(x+y)}{2}\)—not integer
—>\(\frac{( 2+1)}{2 }\)—Yes
—> \(\frac{(2+1.5)}{2}\)—No
Insufficient

(Statement2):( x+y+x+6)= 3y
2x +y+6= 3y
2x+6= 2y
x+ 3= y
—> x= y—3
In order x to be integer, y must be integer.

Sufficient

The answer is B

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Re: If x is an integer, is y an integer? [#permalink] New post   20 Nov 2019, 01:51
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(1) The average of x and y is not an integer.

average of x and y cannot be an integer, even if y is an integer or not.......INSUFFICIENT

(2) The average of x, y, and x + 6, is y

I.E (2x+6+y)/3 = y
then y have to be the median of x, y, and x + 6.... y becomes x+3

since x is an integer, x+3 is an integer...........SUFFICIENT

OA:B
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Re: If x is an integer, is y an integer? [#permalink] New post   20 Nov 2019, 02:16
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#1
The average of x and y is not an integer.
5+2 /2 = sufficient
(1/3+2)/2 = sufficies condition but insufficient
#2
The average of x, y, and x + 6, is y.
x+y+x+6=3y
or say
x+3=y
so if x is an integer , y has to be an integer
IMO B sufficient



If x is an integer, is y an integer?

(1) The average of x and y is not an integer.

(2) The average of x, y, and x + 6, is y.
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Re: If x is an integer, is y an integer? [#permalink] New post   20 Nov 2019, 05:05
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Quote:
If x is an integer, is y an integer?

(1) The average of x and y is not an integer.

(2) The average of x, y, and x + 6, is y.


(1) The average of x and y is not an integer. insufic

\((x,y)=(2,3=int)…average(2+3)/2=2.5=not.integer\)
\((x,y)=(2,2.5≠not)…average(2+2.5)/2=2.25=not.integer\)

(2) The average of x, y, and x + 6, is y. sufic

\(x+y+(x+6)/3=y…2x+6+y=3y…2x+6=2y…x+3=y…(x,3)=integers…y=integer\)

Ans (B)
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Re: If x is an integer, is y an integer? [#permalink] New post   20 Nov 2019, 18:33
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Given that x is an integer, we are to determine whether y is an integer.

Statement 1: The average of x and y is not an integer.
Not sufficient. when x is odd and y is even, then the average of x and y is not an integer. Likewise, when y is a fraction, the average of y and x is not an integer. Statement 1 is therefore insufficient on its own.

Statement 2: The average of x, y, and x + 6, is y.
(x+y+x+6)/3 = y
x+y+x+6=3y
2x+6=2y
x+3=y
since x is an integer, x+3 is an integer, hence y is an integer.
Statement 2 is therefore sufficient on its own.

The answer is option B.
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Re: If x is an integer, is y an integer? [#permalink] New post   20 Nov 2019, 18:51
1
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If x is an integer, is y an integer?

(1) The average of x and y is not an integer.

(2) The average of x, y, and x + 6, is y.

(1) This statement is true regardless y is an integer or not. i.e: x = 3, y =2, average 2.5. or x= 3, y =7.5, average 5.25. insufficient.

(2) 2x + 6 = 2y, or, x = y - 3. since x is an integer, y has to be an integer also. Sufficient.

IMHO B is the right answer.
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Re: If x is an integer, is y an integer? [#permalink] New post   20 Nov 2019, 22:57
1
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If x is an integer, is y an integer?

(1) The average of x and y is not an integer. Insufficient

(2) The average of x, y, and x + 6, is y.
x+y+x+6=3y
2x+6=2y
y-x=3, therefore, if x is an integer, y is also an integer. Sufficient. Ans B
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Re: If x is an integer, is y an integer? [#permalink]
20 Nov 2019, 22:57
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