GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 26 Apr 2019, 08:56

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54696
X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

22 Jun 2016, 03:04
00:00

Difficulty:

65% (hard)

Question Stats:

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

### HideShow timer Statistics

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.

_________________
Senior Manager
Joined: 23 Apr 2015
Posts: 300
Location: United States
WE: Engineering (Consulting)
Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

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.

(Share a kudo's, if you like the explanation.)
Current Student
Joined: 18 Oct 2014
Posts: 836
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

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.

_________________
I welcome critical analysis of my post!! That will help me reach 700+
Senior Manager
Joined: 18 Jan 2010
Posts: 251
Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

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.

Darden & Kenan Flagler Thread Master
Joined: 28 Oct 2015
Posts: 141
X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

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.
Senior Manager
Joined: 02 Mar 2012
Posts: 293
Schools: Schulich '16
Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

22 Jun 2016, 07:35
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.

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

Senior Manager
Joined: 02 Mar 2012
Posts: 293
Schools: Schulich '16
Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

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

this is a COULD question not a MUST
Intern
Joined: 05 Jan 2015
Posts: 11
Schools: Mays '17
GMAT 1: 620 Q47 V28
GPA: 2.9
Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

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

Correct me if am Wrong
Manager
Joined: 26 Mar 2016
Posts: 71
Location: Greece
GMAT 1: 710 Q51 V34
GPA: 2.9
X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

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.
_________________
+1 Kudos if you like the post
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9151
Location: Pune, India
Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

20 Jul 2016, 21:55
1
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".
_________________
Karishma
Veritas Prep GMAT Instructor

Director
Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management
X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

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
Manager
Joined: 18 Oct 2016
Posts: 139
Location: India
WE: Engineering (Energy and Utilities)
Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

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
_________________
Press Kudos if you liked the post!

Manager
Joined: 18 Jun 2017
Posts: 59
Re: X and Y are integers, X is even and negative, Y is odd and positive. W  [#permalink]

### Show Tags

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.

Re: X and Y are integers, X is even and negative, Y is odd and positive. W   [#permalink] 22 Jul 2017, 12:11
Display posts from previous: Sort by