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

It is currently 18 Jun 2019, 00:30

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

x and y are two single digit positive integers. What is the sum (x+y)?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Retired Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1437
Location: India
x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

Show Tags

New post 08 Jan 2019, 23:21
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

28% (02:06) correct 72% (02:16) wrong based on 59 sessions

HideShow timer Statistics

x and y are two single digit positive integers. What is the value of sum (x+y)?

(1) The four digit number xyyx is divisible by 11.

(2) The four digit number x4y9 is divisible by 11.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7752
Re: x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

Show Tags

New post 09 Jan 2019, 10:34
1
Kem12 wrote:
Nice explanation KanishkM.
Hi, chetan2u, having a nice day I hope. Please help me out here, I noticed it is not stated here that both x and y are distinct integers, would it be safe to assume that they are distinct or would an official question state this. Thanks.

Posted from my mobile device


Hi Kem12,

If it is not mentioned they are distinct, then they will not necessarily be distinct.
Here too, both can be the SAME, and that is why answer will be E..

x and y are two single digit positive integers. What is the value of sum (x+y)?

(1) The four digit number xyyx is divisible by 11.
Divisibility by 11 means the difference between the sum of numbers at odd places and the sum of digits at even places is divisible by 11.
even places = x+y
Odd places = x+y
Difference = x+y-(x+y)=0
So all values of x and y are possible.
Insufficient

(2) The four digit number x4y9 is divisible by 11.
even places = x+y
Odd places = 9+4
Difference = 13-(x+y) is divisible by 11..
So x+y can be 13, as 13-13=0 OR x+y=2 as 13-2=11.
Insufficient

Combined..
x+y can be 2 or 13..
Insufficient

E

Note.. there is no reason you to take x and y as distinct.
_________________
General Discussion
VP
VP
avatar
G
Joined: 09 Mar 2018
Posts: 1004
Location: India
x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

Show Tags

New post Updated on: 09 Jan 2019, 10:46
1
amanvermagmat wrote:
x and y are two single digit positive integers. What is the value of sum (x+y)?

(1) The four digit number xyyx is divisible by 11.

(2) The four digit number x4y9 is divisible by 11.


Since its a value question, we need to get a definite value

Statement 1
x & y are two single digit positive integers, The four digit number xyyx is divisible by 11

1221 / 11, here sum will be 6
2332 / 11, here sum will be 10
3443 / 11, here sum will be 14

Insufficient

Statement 2
The four digit number x4y9 is divisible by 11
For this to be divisible by 11, value satisfying will be 4499 , x+y = 13

Another logic
There is a rule which states for a number to be divisible by 11,Take the alternating sum of the digits in the number, read from left to right.
eg: 31415 = 3-1+4-1+5 = 10, 10 is not / by 11
31416 = 3-1+4-1+6 = 11, 11 is / by 11

x-4+y-9 / 11 = Integer
x+y -13 = 11 * I
x+y = 11 I + 13

This says that x+y =13

IMO Answer is B
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Originally posted by KanishkM on 09 Jan 2019, 00:04.
Last edited by KanishkM on 09 Jan 2019, 10:46, edited 1 time in total.
Manager
Manager
avatar
B
Joined: 18 Apr 2018
Posts: 94
x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

Show Tags

New post 09 Jan 2019, 09:29
1
Nice explanation KanishkM.
Hi, chetan2u, having a nice day I hope. Please help me out here, I noticed it is not stated here that both x and y are distinct integers, would it be safe to assume that they are distinct or would an official question state this. Thanks.

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 15 Dec 2018
Posts: 30
CAT Tests
Re: x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

Show Tags

New post 09 Jan 2019, 09:57
IMO B

Statement A has multiple options - 1221, 1111, 2112.

Not sufficient

Statement B only had one unique possibility 4499

Posted from my mobile device
VP
VP
avatar
G
Joined: 09 Mar 2018
Posts: 1004
Location: India
Re: x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

Show Tags

New post 09 Jan 2019, 10:06
1
Kem12 wrote:
Nice explanation KanishkM.
Hi, chetan2u, having a nice day I hope. Please help me out here, I noticed it is not stated here that both x and y are distinct integers, would it be safe to assume that they are distinct or would an official question state this. Thanks.

Posted from my mobile device


Thank You Kem12.

A very interesting question, would just add 2 cents on that.

You are correct at pointing that we should not assume anything, especially in Data sufficiency questions.

I would say, It depends on case 2 case scenario. Here to make the statements true, such unstated assumptions were made.
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Manager
Manager
avatar
B
Joined: 18 Apr 2018
Posts: 94
Re: x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

Show Tags

New post 09 Jan 2019, 10:14
1
KanishkM, very Clear. thanks

Posted from my mobile device
VP
VP
avatar
G
Joined: 09 Mar 2018
Posts: 1004
Location: India
Re: x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

Show Tags

New post 09 Jan 2019, 10:52
Kem12 wrote:
KanishkM, very Clear. thanks

Posted from my mobile device


Thought of letting you know, Didn't realize for statement B there could have been another value 1419.

Making the answer as E.
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Manager
Manager
avatar
B
Joined: 18 Apr 2018
Posts: 94
Re: x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

Show Tags

New post 10 Jan 2019, 01:18
1
I know that was why I asked the question. Thanks for correcting OA.

Posted from my mobile device
GMAT Club Bot
Re: x and y are two single digit positive integers. What is the sum (x+y)?   [#permalink] 10 Jan 2019, 01:18
Display posts from previous: Sort by

x and y are two single digit positive integers. What is the sum (x+y)?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne