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# If x is a positive odd integer and y is a negative even integer, which

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Math Expert
Joined: 02 Sep 2009
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If x is a positive odd integer and y is a negative even integer, which  [#permalink]

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14 Apr 2016, 02:27
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If x is a positive odd integer and y is a negative even integer, which of the following must be true?

A. x^3 + y is a positive odd integer
B. x^2 + y^2 is a negative odd integer
C. x^0 + y^11 is a negative odd integer
D. x + y is a positive odd integer
E. x + y is a negative odd integer

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Posts: 6960
Re: If x is a positive odd integer and y is a negative even integer, which  [#permalink]

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14 Apr 2016, 08:35
Bunuel wrote:
If x is a positive odd integer and y is a negative even integer, which of the following must be true?

A. x^3 + y is a positive odd integer
B. x^2 + y^2 is a negative odd integer
C. x^0 + y^11 is a negative odd integer
D. x + y is a positive odd integer
E. x + y is a negative odd integer

Hi,
two points on the type of integers before we see the choices--
1) one is ODD and other EVEN with no coefficients, so their sum will Always be ODD unless the EVEN is raised to power 0..
2) since they are just variables, there is no way to say which has the highest numeric value unless there is some raised to power 0, Or there is som other info given..

Now lets see the choices--

A. x^3 + y is a positive odd integer
WE cannot say anything whether x^3> y or otherwise..

B. x^2 + y^2 is a negative odd integer
both are to power EVEN so SUM should be positive..

C. x^0 + y^11 is a negative odd integer
x^0 = 1, but y^11 will be much greater than y as y is an even integer, so SUM will be -ive.. MUST be true

D. x + y is a positive odd integer
WE cannot say anything whether x > y or otherwise..

E. x + y is a negative odd integer
WE cannot say anything whether x > y or otherwise..
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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: If x is a positive odd integer and y is a negative even integer, which  [#permalink]

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14 Apr 2016, 12:04
1
Anything power 0 is always 1 and given that Y is even and negative, then

1 + (-2) will be negative with odd power values for Y.

Ans: C
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Re: If x is a positive odd integer and y is a negative even integer, which  [#permalink]

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14 Apr 2016, 16:12
If x is a positive odd integer and y is a negative even integer, which of the following must be true?

A. x^3 + y is a positive odd integer
B. x^2 + y^2 is a negative odd integer
C. x^0 + y^11 is a negative odd integer
D. x + y is a positive odd integer
E. x + y is a negative odd integer

If X - positive odd integer and y is a negative even integer.

Lets assume x = 1 and y = -2.

A: Not True - Eliminate.
B: This statement is always positive. Not true. Eliminate.
C: This is true based on assumed values - Keep.
D: 1 + (-2) = -1 Hence not a positive odd no - Eliminate.
E: 1 + (-2) = -1. True. Keep.

So we are left with C and E.

For E - if x is 101 and y is -2; x + y is 99 (positive odd). Hence not always true.

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Re: If x is a positive odd integer and y is a negative even integer, which  [#permalink]

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17 Apr 2017, 03:57
Option C

Odd: O, Even: E & Fraction: F.
x = +O & y = -E

A. x^3 + y is a positive odd integer : (+O)^3 + (-E) = O - E = O or -O
B. x^2 + y^2 is a negative odd integer : (+O)^2 + (-E)^2 = O + E = +O
C. x^0 + y^11 is a negative odd integer : (+O)^0 + (-E)^11 = 1 - E = -O
D. x + y is a positive odd integer : (+O) + (-E) = +O or -O
E. x + y is a negative odd integer : (+O) + (-E) = +O or -O
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Re: If x is a positive odd integer and y is a negative even integer, which  [#permalink]

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20 Apr 2017, 16:54
Bunuel wrote:
If x is a positive odd integer and y is a negative even integer, which of the following must be true?

A. x^3 + y is a positive odd integer
B. x^2 + y^2 is a negative odd integer
C. x^0 + y^11 is a negative odd integer
D. x + y is a positive odd integer
E. x + y is a negative odd integer

We are given that x is a positive odd integer and y is a negative even integer, and we need to determine which answer choice is true. Let’s examine the answer choices.

A) x^3 + y is a positive odd integer

Although x^3 is odd and y is even, since we do not know the relative value of each number, we cannot determine whether x^3 + y is positive. Thus, answer choice A does not have to be true.

B) x^2 + y^2 is a negative odd integer

The sum of two squares can never be negative. Answer choice B cannot be true.

C) x^0 + y^11 is a negative odd integer

Since x^0 = 1 and y is a negative even integer, we know that y^11 is a negative integer less than -1, and thus x^0 + y^11 is a negative odd integer.

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Re: If x is a positive odd integer and y is a negative even integer, which &nbs [#permalink] 20 Apr 2017, 16:54
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