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

 It is currently 23 May 2019, 04:07

### 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

# If x is an odd integer, is y an odd integer?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55264
If x is an odd integer, is y an odd integer?  [#permalink]

### Show Tags

14 Jul 2017, 00:17
00:00

Difficulty:

45% (medium)

Question Stats:

76% (01:54) correct 24% (01:21) wrong based on 28 sessions

### HideShow timer Statistics

If x is an odd integer, is y an odd integer?

(1) The average of x and y is an integer.
(2) The average of x, y, and (y + 1) is an integer.

_________________
Director
Joined: 13 Mar 2017
Posts: 724
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If x is an odd integer, is y an odd integer?  [#permalink]

### Show Tags

14 Jul 2017, 01:02
Bunuel wrote:
If x is an odd integer, is y an odd integer?

(1) The average of x and y is an integer.
(2) The average of x, y, and (y + 1) is an integer.

Given : x is an odd integer
DS: y is an odd integer ?

Let x = 2n+1
y = 2m or 2m+1

Statement 1 : (2n+1)
Average of x and y (y even) = ((2n+1) + 2m) /2 = Not an integer
Average of x and y (y odd) = ((2n+1)+(2m+1))/2 = An integer

SUFFICIENT

Statement 2: average of x, y and y+1 ( y even) = (2n+1+2m + 2m +1)/3 = (2n +4m+2)/3 THis may be an integer or many be not.
average of x, y and y+1 ( y odd) = (2n+1+2m+1 + 2m +2)/3 = (2n +4m+4)/3 This may be an integer or many be not.
NOT SUFFICIENT

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Senior Manager
Joined: 06 Jul 2016
Posts: 363
Location: Singapore
Concentration: Strategy, Finance
Re: If x is an odd integer, is y an odd integer?  [#permalink]

### Show Tags

14 Jul 2017, 01:03
Bunuel wrote:
If x is an odd integer, is y an odd integer?

(1) The average of x and y is an integer.
(2) The average of x, y, and (y + 1) is an integer.

Average = Sum/No. of terms

1) (x+y)/2 = integer
If x = odd
y = has to be odd, otherwise the average will not be an integer.

x = 1
y = 1
Avg. = 1

x = 3
y = 3
Avg. 3

x = 3
y = 2
avg. = 2.5 (Not allowed)

Sufficient.

2) (x + y + y+1)/3 is an integer
x = 5
y = 3
y + 1 = 4
Avg. = 12/3 = 4
y = odd

x = 1
y = 2
y+1 = 3
Avg. = 6/3 = 2
Y = even

Insufficient.

_________________
Put in the work, and that dream score is yours!
Current Student
Joined: 18 Aug 2016
Posts: 618
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: If x is an odd integer, is y an odd integer?  [#permalink]

### Show Tags

14 Jul 2017, 02:49
Bunuel wrote:
If x is an odd integer, is y an odd integer?

(1) The average of x and y is an integer.
(2) The average of x, y, and (y + 1) is an integer.

given x is odd

(1) x+y is 2k (even integer)

x+y can only be even when either both x & y are odd or both are even .. in this case x is odd and hence y is also odd ..Sufficient (y can only take integer values for the average to be integer)

(2) x, y, y+1 is 3k (even or odd integer)

if k is odd then 3k is odd

y is an integer then y+y+1 has to be even which is not possible since both are consecutive and their sum would be odd
y is even then y+y+1 will be odd
y is odd then y+y+1 will be odd
but we need y+y+1 to be even

if k is even then 3k is even
y is an integer then y+y+1 has to be odd which can be irrespective of value of y to be even or odd........Not sufficient

Hence A
_________________
We must try to achieve the best within us

Thanks
Luckisnoexcuse
Re: If x is an odd integer, is y an odd integer?   [#permalink] 14 Jul 2017, 02:49
Display posts from previous: Sort by