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

Question

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.

chetan2u · Accepted Answer

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.

KanishkM · Answer

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

Kem12 · Answer

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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CAtluri · Answer

IMO B

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

Not sufficient

Statement B only had one unique possibility 4499

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KanishkM · Answer

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.

Kem12 · Answer

KanishkM , very Clear. thanks

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KanishkM · Answer

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

Making the answer as E.

Kem12 · Answer

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

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

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GMAT Data Sufficiency (DS) Questions

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

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