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# A function "a#b" is defined for integers a and b such that a#b = a+b

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A function "a#b" is defined for integers a and b such that a#b = a+b  [#permalink]

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17 Jul 2018, 23:50
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A function "a#b" is defined for integers a and b such that a#b = a+b if both a and b are odd, and a#b = (a*b)/2 otherwise. For integers x and y, what is x#y?

(1) |y| < 1.

(2) x = 14k, where 'k' is a non negative integer.
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Re: A function "a#b" is defined for integers a and b such that a#b = a+b  [#permalink]

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18 Jul 2018, 00:09
amanvermagmat wrote:
A function "a#b" is defined for integers a and b such that a#b = a+b if both a and b are odd, and a#b = (a*b)/2 otherwise. For integers x and y, what is x#y?

(1) |y| < 1.

(2) x = 14k, where 'k' is a non negative integer.

Instead of trying to figure out what kind of information we need, we'll try simple examples.
This is an Alternative approach.

(1) Since y is an integer, it must equal 0. Then x#y = (x*0)/2 = 0
Sufficient.

(2) So x is definitely even meaning that x#y = xy/2. But since we can choose many different values for both x and y, this is insufficient.
Insufficient.

(A) is our answer.
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Re: A function "a#b" is defined for integers a and b such that a#b = a+b  [#permalink]

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18 Jul 2018, 00:22
A function "a#b" is defined for integers a and b such that a#b = a+b if both a and b are odd, and a#b = (a*b)/2 otherwise. For integers x and y, what is x#y?

(1) |y| < 1.
This means distance of y from 0 is within 1 units so -1<0<1
even by opening modulus..
a) y>0......y<1
b) y<0......-y<1......y>-1
so -1<y<1
so integer value of y possible is 0
and as y is even $$x#y=\frac{x*y}{2}=\frac{x*0}{2}=0$$
sufficient

(2) x = 14k, where 'k' is a non negative integer.
nothing about y
insuff

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: A function "a#b" is defined for integers a and b such that a#b = a+b &nbs [#permalink] 18 Jul 2018, 00:22
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# A function "a#b" is defined for integers a and b such that a#b = a+b

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