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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  x and y are two single digit positive integers. What is the sum (x+y)?

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

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Difficulty:   95% (hard)

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

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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.
Math Expert V
Joined: 02 Aug 2009
Posts: 7752
Re: x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

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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.
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General Discussion
VP  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]

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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

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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  B
Joined: 18 Apr 2018
Posts: 94
x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

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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  B
Joined: 15 Dec 2018
Posts: 30
Re: x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

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IMO B

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

Not sufficient

Statement B only had one unique possibility 4499

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VP  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]

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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.
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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  B
Joined: 18 Apr 2018
Posts: 94
Re: x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

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KanishkM, very Clear. thanks

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VP  G
Joined: 09 Mar 2018
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Re: x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

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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.

_________________
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  B
Joined: 18 Apr 2018
Posts: 94
Re: x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

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I know that was why I asked the question. Thanks for correcting OA.

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