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X and Y are integers, X is even and negative, Y is odd and positive. W

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X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 22 Jun 2016, 03:04
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

53% (01:48) correct 47% (01:38) wrong based on 184 sessions

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X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?

1. (X + Y) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a positive number.

A. 2 only.
B. 3 only.
C. 1 and 3 only.
D. 2 and 3 only.
E. 1, 2 and 3.

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Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 22 Jun 2016, 04:26
1
Answer is B : 3 only,

Using the properties for even and odd numbers along with positive and negatives,

1. (X + Y) is an odd number : even + odd is always a odd number, so eliminate 1
2. Y^(X + Y) is an integer. : an odd and positive number could be raised to power of either positive or negative, so not conclusive, elimiate 2
3. X^Y is a positive number. : a negative number raised to power of odd number is always negative.






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Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 22 Jun 2016, 04:59
Bunuel wrote:
X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?

1. (X + Y) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a positive number.

A. 2 only.
B. 3 only.
C. 1 and 3 only.
D. 2 and 3 only.
E. 1, 2 and 3.


1. (X + Y) is an odd number. even+odd= odd. True

2. Y^(X + Y) is an integer. odd ^(even+odd)= odd ^odd= odd integer. True

3. X^Y is a positive number.. -ve even ^+ve odd= -ve integer (odd power means the number will retain its sign). Not true.

B is the answer
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Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 22 Jun 2016, 05:08
Bunuel wrote:
X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?

1. (X + Y) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a positive number.

A. 2 only.
B. 3 only.
C. 1 and 3 only.
D. 2 and 3 only.
E. 1, 2 and 3.



X is even and Y is odd. X+Y will always be odd. This will never be false.

so C and E are out of contention.

Now X^Y.

X = (-2)
Y = 3

This will always be negative. So (3) is always False. A is out.

We will have to check (2)

Y^(X+Y)

say
Y = 3
X = (-4)

The X+Y will be negative value and then Y^(X+Y) will not be an integer. so this can be false.

Answer : 2 and 3.

D is the answer.
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X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 22 Jun 2016, 05:11
The question says which of the following could be false

So, if X is -4 and Y is 3 then Statement 2 would be 3^-1 which is 1/3 which isn't an integer.

Since the question specifies could be shouldn't the answer be D, since 2 could be false in certain cases and 3 is false.
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Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 22 Jun 2016, 07:35
Divyadisha wrote:
Bunuel wrote:
X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?

1. (X + Y) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a positive number.

A. 2 only.
B. 3 only.
C. 1 and 3 only.
D. 2 and 3 only.
E. 1, 2 and 3.


1. (X + Y) is an odd number. even+odd= odd. True

2. Y^(X + Y) is an integer. odd ^(even+odd)= odd ^odd= odd integer. True

3. X^Y is a positive number.. -ve even ^+ve odd= -ve integer (odd power means the number will retain its sign). Not true.

B is the answer


for second case take x=-4 and y=3.thats false.

answer is D
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Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 22 Jun 2016, 07:36
AvalonQQ wrote:
The question says which of the following could be false

So, if X is -4 and Y is 3 then Statement 2 would be 3^-1 which is 1/3 which isn't an integer.

Since the question specifies could be shouldn't the answer be D, since 2 could be false in certain cases and 3 is false.


yes you are correct

answer is D

this is a COULD question not a MUST
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Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 23 Jun 2016, 08:52
Bunuel wrote:
X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?

1. (X + Y) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a positive number.

A. 2 only.
B. 3 only.
C. 1 and 3 only.
D. 2 and 3 only.
E. 1, 2 and 3.


Inference

X= Integer, EVEN, Negative

Y= Integer, ODD, Positive

Analyzing Statement 1

1. (X + Y) is an odd number.

Let X = -2 Y = 5 then X + Y = -2 + 5 = 3 It will always be odd,

2. Y^(X + Y) is an integer.

Let Y = 3 X= -2 than Y^(X + Y) = 3 ^ 1 = 1

If

Y= 3 X = -4 Than Y^(X + Y) = 3 ^ (-1) = 1 /3 there fore Could be False

3. X^Y is a positive number.

Let X = -2 Y= 3 Since Y is Odd

(-X ) ^ Y will always be a Negative No There fore Could be False


Answer 2 And 3

Correct me if am Wrong
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X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 20 Jul 2016, 14:03
Got tricked by the "could be" false.

1. Can't be False. For any pair of numbers that cointains 1 Even & 1 Odd we know that even + odd = always odd.
So number 1 is out.

2.Can be False. Let's take for example X=-2 & Y=5. 5^3 is an integer.
But let's take X=-10 & Y=3. 3^(-7) = 1/3^7. Not an integer.

3. Can be False. For example : X=-2 & Y=3. That's a negative number
Actually, any negative number in any odd power will be negative.

So, only 2&3 COULD be False.
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Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 20 Jul 2016, 21:55
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Berlin77 wrote:
Got tricked by the "could be" false.

1. Can't be False. For any pair of numbers that cointains 1 Even & 1 Odd we know that even + odd = always odd.
So number 1 is out.

2.Can be False. Let's take for example X=-2 & Y=5. 5^3 is an integer.
But let's take X=-10 & Y=3. 3^(-7) = 1/3^7. Not an integer.

3. Can be False. For example : X=-2 & Y=3. That's a negative number
Actually, any negative number in any odd power will be negative.

So, only 2&3 COULD be False.


"Could be false" is the negation of "must be true". Whatever is not "must be true", that is "could be false".

1 must be true since even + odd = always odd. Hence it is not "could be false".
2 is not "must be true". If X = -4 and Y = 3, 3^(-4 + 3) = 1/3 (not an integer). Hence it is "could be false".
3 is not "must be true". If X = -4 and Y = 3, (-4)^3 = -64 (not a positive integer). Hence it is "could be false".
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X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 21 Jul 2016, 09:22
Bunuel wrote:
X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?

1. (X + Y) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a positive number.

A. 2 only.
B. 3 only.
C. 1 and 3 only.
D. 2 and 3 only.
E. 1, 2 and 3.



1. (X + Y) is an odd number --- is always true odd (+-) even is always odd !!
2. Y^(X + Y) is an integer. --- 3^(-4+3)=3^-1 is not an integer
3. X^Y is a positive number. --- -2^3=-8 is not a positive number


therefore D
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Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 17 Apr 2017, 04:02
Option D

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

1. (X + Y) is an odd number. : ( -E + +O) = -O or +O = O : True
2. Y^(X + Y) is an integer. : (+O)^(-E + +O) = (+O)^(-O or +O) = F or O
3. X^Y is a positive number. : (-E)^(+O) = -E
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Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

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New post 22 Jul 2017, 12:11
1. (X + Y) is an odd number. Must be True
2. Y^(X + Y) is an integer. Could be False (IfX>Y in magnitude we get decimal say x=-6,y=3, similarly if reversed i.e.Y>X say x=-2,y=5 we get integer)
3. X^Y is a positive number. Must be False
Given X and Y are integers, X is even and negative, Y is odd and positive.
From this Option A seems correct which is an example of Could be rest should always be true or false.

Hence the question should be modified else it is misleading. Please advise.
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Re: X and Y are integers, X is even and negative, Y is odd and positive. W   [#permalink] 22 Jul 2017, 12:11
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