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

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

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New post 08 Jan 2019, 22:21
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B
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E

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Question Stats:

26% (01:49) correct 74% (01:54) wrong based on 46 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.
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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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New post 09 Jan 2019, 09:34
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.

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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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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

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New post Updated on: 09 Jan 2019, 09:46
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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

IMO Answer is B
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Originally posted by KanishkM on 08 Jan 2019, 23:04.
Last edited by KanishkM on 09 Jan 2019, 09:46, edited 1 time in total.
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x and y are two single digit positive integers. What is the sum (x+y)?  [#permalink]

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New post 09 Jan 2019, 08:29
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.

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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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New post 09 Jan 2019, 08:57
IMO B

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

Not sufficient

Statement B only had one unique possibility 4499

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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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New post 09 Jan 2019, 09:06
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.

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

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

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

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

Making the answer as E.
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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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New post 10 Jan 2019, 00:18
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I know that was why I asked the question. Thanks for correcting OA.

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Re: x and y are two single digit positive integers. What is the sum (x+y)? &nbs [#permalink] 10 Jan 2019, 00:18
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