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

 It is currently 22 Oct 2019, 09:56

### 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^2y−1)/2 has a non-zero remainder. Which of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58421
x and y are integers. (x^2y−1)/2 has a non-zero remainder. Which of  [#permalink]

### Show Tags

23 Nov 2016, 06:44
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:28) correct 42% (01:35) wrong based on 295 sessions

### HideShow timer Statistics

x and y are integers. $$\frac{(x^2y−1)}{2}$$ has a non-zero remainder. Which of the following must be true?

I. y is odd
II. x is even
III. xy is even

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

_________________
Senior Manager
Joined: 06 Jun 2016
Posts: 254
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
x and y are integers. (x^2y−1)/2 has a non-zero remainder. Which of  [#permalink]

### Show Tags

Updated on: 23 Nov 2016, 08:50
Bunuel wrote:
x and y are integers. (x^2y−1)/2 has a non-zero remainder. Which of the following must be true?

I. y is odd
II. x is even
III. xy is even

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

IMO C
[(x^2)y−1)/2] has a non-zero remainder means this expression is odd.
for this expression to be odd x^2*y has to be even
xy= even must be true
y and x can be be even or odd as long as x^2*y is even

Changing my answer as my interpretation of the equation was wrong

Originally posted by Vinayak Shenoy on 23 Nov 2016, 07:20.
Last edited by Vinayak Shenoy on 23 Nov 2016, 08:50, edited 2 times in total.
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4017
x and y are integers. (x^2y−1)/2 has a non-zero remainder. Which of  [#permalink]

### Show Tags

23 Nov 2016, 08:14
Top Contributor
1
Bunuel wrote:
x and y are integers. $$\frac{(x^2y−1)}{2}$$ has a non-zero remainder. Which of the following must be true?

I. y is odd
II. x is even
III. xy is even

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

Given: (x²y - 1) divided by 2 has a non-zero remainder.
If (x²y - 1) DID have a zero remainder, then (x²y - 1) would be divisible by 2 (aka EVEN)
Since (x²y - 1) DOES NOT have a zero remainder, then (x²y - 1) is NOT divisible by 2 (aka ODD)
So, x²y - 1 is ODD
This tells us that x²y is EVEN
x²y will be even IF x is even, y is even, or x and y are both even
The question asks, "Which of the following MUST be true?"

I. y is odd. y COULD be odd, but it doesn't have to be. (for example, if x = 1 and y = 2, x²y is still EVEN)
II. x is even. x COULD be even, but it doesn't have to be. (for example, if x = 2 and y = 2, x²y is still EVEN)
III. xy is even. Since at least one of the variables must be even, it MUST be the case that xy is even

RELATED VIDEO

_________________
Test confidently with gmatprepnow.com
Intern
Joined: 16 Nov 2016
Posts: 5
Re: x and y are integers. (x^2y−1)/2 has a non-zero remainder. Which of  [#permalink]

### Show Tags

25 Nov 2016, 09:04
GMATPrepNow wrote:
Bunuel wrote:
x and y are integers. $$\frac{(x^2y−1)}{2}$$ has a non-zero remainder. Which of the following must be true?

I. y is odd
II. x is even
III. xy is even

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

Given: (x²y - 1) divided by 2 has a non-zero remainder.
If (x²y - 1) DID have a zero remainder, then (x²y - 1) would be divisible by 2 (aka EVEN)
Since (x²y - 1) DOES NOT have a zero remainder, then (x²y - 1) is NOT divisible by 2 (aka ODD)
So, x²y - 1 is ODD
This tells us that x²y is EVEN
x²y will be even IF x is even, y is even, or x and y are both even
The question asks, "Which of the following MUST be true?"

I. y is odd. y COULD be odd, but it doesn't have to be. (for example, if x = 1 and y = 2, x²y is still EVEN)
II. x is even. x COULD be even, but it doesn't have to be. (for example, if x = 2 and y = 2, x²y is still EVEN)
III. xy is even. Since at least one of the variables must be even, it MUST be the case that xy is even

Hello,

Would it not be sufficient for x to be even? If x is even, wouldn't x^2y be even regardless of y?

Thanks!
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4017
Re: x and y are integers. (x^2y−1)/2 has a non-zero remainder. Which of  [#permalink]

### Show Tags

25 Nov 2016, 09:21
3
Top Contributor
FransmanPL wrote:
GMATPrepNow wrote:
Bunuel wrote:
x and y are integers. $$\frac{(x^2y−1)}{2}$$ has a non-zero remainder. Which of the following must be true?

I. y is odd
II. x is even
III. xy is even

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

Given: (x²y - 1) divided by 2 has a non-zero remainder.
If (x²y - 1) DID have a zero remainder, then (x²y - 1) would be divisible by 2 (aka EVEN)
Since (x²y - 1) DOES NOT have a zero remainder, then (x²y - 1) is NOT divisible by 2 (aka ODD)
So, x²y - 1 is ODD
This tells us that x²y is EVEN
x²y will be even IF x is even, y is even, or x and y are both even
The question asks, "Which of the following MUST be true?"

I. y is odd. y COULD be odd, but it doesn't have to be. (for example, if x = 1 and y = 2, x²y is still EVEN)
II. x is even. x COULD be even, but it doesn't have to be. (for example, if x = 2 and y = 2, x²y is still EVEN)
III. xy is even. Since at least one of the variables must be even, it MUST be the case that xy is even

Hello,

Would it not be sufficient for x to be even? If x is even, wouldn't x^2y be even regardless of y?

Thanks!

Hi FransmanPL,

I believe you are misinterpreting the question.
We are asked to determine what must be true BASED ON the fact that x²y is EVEN
So, for statement 2, we should ask "Given the fact that x²y is EVEN, must it be true that x is even?" The answer is no. It need not be true that x is even.

You are treating the statements in the opposite order. So, for statement 2, you are asking, "Given the fact that x is even, must it be true that x²y is EVEN?"
This is not what the question is asking.

Does that help?

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Intern
Joined: 16 Nov 2016
Posts: 5
Re: x and y are integers. (x^2y−1)/2 has a non-zero remainder. Which of  [#permalink]

### Show Tags

25 Nov 2016, 11:40
Hi Brent,

I see what you mean, I was indeed looking at it the other way around.

Thanks for the clarification!
Intern
Joined: 11 Nov 2017
Posts: 11
Re: x and y are integers. (x^2y−1)/2 has a non-zero remainder. Which of  [#permalink]

### Show Tags

13 Dec 2017, 14:08
Bunuel wrote:
x and y are integers. $$\frac{(x^2y−1)}{2}$$ has a non-zero remainder. Which of the following must be true?

I. y is odd
II. x is even
III. xy is even

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

Easy C.
Since ((x^2)*y -1)/2 has a non-zero remainder, the remainder has to be 1.
If (n-1)/2 has a remainder of 1 then n must be divisible by 2. Hence, (x^2)*y must be divisible by 2.
For that, either x or y has to be even or both x, y can be even. Thus,xy will always be even.
_________________
Cheers.

Never gonna give up!!!!
VP
Joined: 31 Oct 2013
Posts: 1465
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
x and y are integers. (x^2y−1)/2 has a non-zero remainder. Which of  [#permalink]

### Show Tags

21 Feb 2019, 09:44
Bunuel wrote:
x and y are integers. $$\frac{(x^2y−1)}{2}$$ has a non-zero remainder. Which of the following must be true?

I. y is odd
II. x is even
III. xy is even

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

$$\frac{(x^2y−1)}{2}$$

So, $$x^2y - 1$$ must be odd as it's not divisible by 2.

even - 1 = odd.

$$x^2y$$ = even.

xy must be even.

x and y are integers. (x^2y−1)/2 has a non-zero remainder. Which of   [#permalink] 21 Feb 2019, 09:44
Display posts from previous: Sort by