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08 Jan 2019, 23:21
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
32% (02:17) correct
68%
(02:02)
wrong
based on 73
sessions
History
Date
Time
Result
Not Attempted Yet
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.
(1) The four digit number xyyx is divisible by 11.
(2) The four digit number x4y9 is divisible by 11.
09 Jan 2019, 10:34
Kudos
Bookmarks
Kem12
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
KanishkM
Joined: 09 Mar 2018
Last visit: 18 Dec 2021
Posts: 755
Given Kudos: 123
Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
amanvermagmat
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
