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Joined: 02 Sep 2009
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Are x and y integers?
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03 Jan 2016, 12:52
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38% (01:28) correct 63% (01:12) wrong based on 84 sessions
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Re: Are x and y integers?
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03 Jan 2016, 18:55
BrainLab wrote: Bunuel wrote: Are x and y integers?
(1) The product xy is an integer. (2) x + y is an integer. (1) 2*2 YES, 2*1/2 NO (2) 2+2 YES, 0.5 + 0.5 NO (1)+(2) hmm... for statement 1 to be an integer we need either 2 integers or reciprocals, but I don't think that there are reciprocals that total an integer, that's why only integer pair satisfies both expressions. Please correct me if I'm wrong... Hi, in these type of Q one should know that there are various complex numbers which can fit in.. say \(x=2+\sqrt{3}\) and \(y=2\sqrt{3}\) so xy=(2+\sqrt{3})*(2\sqrt{3})=1.. and x+y= 2+\sqrt{3}+2\sqrt{3}=4.. here the reason is we can take these two as roots of an equation, then the eq becomes.. z^2+(x+y)z+xy... this will always give you the roots x and y as int ,frac or complex number, even if the product and sum of roots are integer.. hence answer is E
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1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
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Re: Are x and y integers?
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03 Jan 2016, 16:03
Bunuel wrote: Are x and y integers?
(1) The product xy is an integer. (2) x + y is an integer. (1) 2*2 YES, 2*1/2 NO (2) 2+2 YES, 0.5 + 0.5 NO (1)+(2) hmm... for statement 1 to be an integer we need either 2 integers or reciprocals, but I don't think that there are reciprocals that total an integer, that's why only integer pair satisfies both expressions. Please correct me if I'm wrong...
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Re: Are x and y integers?
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03 Jan 2016, 18:10
I tried the following
For statement 1, x = 2 and y = 1/2, x*y = 2*1/2 = 1 (an integer) No x= 2 and y = 1, x*y = 2*1 = 2(also an integer) Yes
For statement 2, x = 2.5,y=1.5, x+y = 2.5+1.5 (an integer) No x= 2, y = 1, x+y = 2+1 = 3( an integer) Yes
Combining 1+2, we might arrive at an answer E, how ever consider the possibility that x = 0 and y = 0 , both are integers and this would satisfy both the conditions and so the answer is C according to me.



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Re: Are x and y integers?
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03 Jan 2016, 18:57
Pragnya87 wrote: I tried the following
For statement 1, x = 2 and y = 1/2, x*y = 2*1/2 = 1 (an integer) No x= 2 and y = 1, x*y = 2*1 = 2(also an integer) Yes
For statement 2, x = 2.5,y=1.5, x+y = 2.5+1.5 (an integer) No x= 2, y = 1, x+y = 2+1 = 3( an integer) Yes
Combining 1+2, we might arrive at an answer E, how ever consider the possibility that x = 0 and y = 0 , both are integers and this would satisfy both the conditions and so the answer is C according to me. Hi, you can always find values of x and y as an integers satisfying the given conditions.. BUT we have to be sure that there are no values fittin as non integer, ecause the Q is a 'must ' Q.. hope it helped
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1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
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Re: Are x and y integers?
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09 Jun 2018, 11:17
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Re: Are x and y integers? &nbs
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