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1. \(2 + x + 5 + y\) is an even integer 2. \(x - y\) is an odd integer
(C) 2008 GMAT Club - m16#18
* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient
I did get the right answer, but I overshot on time. I have a fundamental question that I want to ask you guys: if x + y = Odd and x - y = Odd , then can we conclude that x and y will always be integers? In the question solution we did prove it algebraically and thus I am inclined to "remember" this fact rather than solve it, if encountered again in a problem. Extrapolating from the official explanation: x+y=n ....1 x-y=m.....2 1: x=n-y , subst in 2 2 can be re-written as 2y=(n-m) LHS is always Even - this implies y is an Integer Examine RHS : n-m , now difference of 2 Integers is Even when both are odd or both are even. Thus we can conclude the following: if x+y = Odd and x-y = Odd then both x, and y are integers. if x+y = Even and x-y = Even then both x, and y are integers.
FYI - O.A. is C
Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.
1. \(2 + x + 5 + y\) is an even integer 2. \(x - y\) is an odd integer
(C) 2008 GMAT Club - m16#18
* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient
I did get the right answer, but I overshot on time. I have a fundamental question that I want to ask you guys: if x + y = Odd and x - y = Odd , then can we conclude that x and y will always be integers? In the question solution we did prove it algebraically and thus I am inclined to "remember" this fact rather than solve it, if encountered again in a problem.
O.A. is C
Question: is \(2*x*5*y=even\)? As there is 2 as a multiple, then this expression will be even if \(5xy=integer\). Basically we are asked is \(5xy=integer\) true?
Note that \(x\) and \(y\) may not be integers for \(2*x*5*y\) to be even (example \(x=\frac{7}{9}\) and \(y=\frac{9}{7}\)) BUT if they are integers then \(2*x*5*y\) is even.
(1) \(2+x+5+y=even\) --> \(7+x+y=even\) --> \(x+y=odd\). Not sufficient. (x=1 and y=2 answer YES BUT x=1.3 and y=1.7 answer NO)
(2) \(x-y=odd\). Not sufficient. (x=1 and y=2 answer YES BUT x=1.3 and y=0.3 answer NO)
(1)+(2) Sum (1) and (2) \((x+y)+(x-y)=odd_1+odd_2\) --> \(2x=even\) --> \(x=integer\) --> \(y=integer\) --> Both \(x\) and \(y\) are integers. Hence sufficient.
Answer: C.
As for your question: if \(x+y=odd_1\) and \(x-y=odd_2\) then \(x\) and \(y\) must be integers (see proof above).
Bunuel I didn't have a problem understanding the explanation ,however what i am saying is that shouldn't the following always hold true: if x+y=odd and x-y=odd then both x and y are always integers similarly if x+y=even and x-y=even then both x and y are always integers. This result may come in handy to save time solving some complex number prop problems.
Bunuel I didn't have a problem understanding the explanation ,however what i am saying is that shouldn't the following always hold true: if x+y=odd and x-y=odd then both x and y are always integers similarly if x+y=even and x-y=even then both x and y are always integers. This result may come in handy to save time solving some complex number prop problems.
I thought I answered this question.
If \(x+y=odd_1\) and \(x-y=odd_2\) then \(x\) and \(y\) must be integers: add them up \((x+y)+(x-y)=odd_1+odd_2\) --> \(2x=even\) --> \(x=integer\) --> \(y=integer\) --> Both \(x\) and \(y\) are integers.
If \(x+y=even_1\) and \(x-y=even_2\) then \(x\) and \(y\) must be integers: add them up \((x+y)+(x-y)=even_1+even_2\) --> \(2x=even\) --> \(x=integer\) --> \(y=integer\) --> Both \(x\) and \(y\) are integers.
Hope it's clear.
Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.