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15 Nov 2019, 00:42
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
53% (01:55) correct
47%
(02:09)
wrong
based on 102
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x and y are positive integers. Is x+y divisible by 24 ?
1) xy+1 is divisible by 24.
2) Both x and y are odd integers.
1) xy+1 is divisible by 24.
2) Both x and y are odd integers.
15 Nov 2019, 19:53
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Statement 1-
xy+1=24k
xy= 24k-1= 8l+7
Also, 8l+7 is odd; hence, x and y are both odd.
There can be 2 cases
1. x=8a+1 and y=8b+7 or vice-versa
x+y = 8(a+b+1)
2. x= 8c+3 and y=8d+5 or vice-versa
x+y= 8(c+d+1)
x+y must be divisible by 8
xy= 24k-1=3j+2
x=3m+2 and y=3n+1 or vice-versa
x+y=3(m+n+1)
x+y must be divisible by 3
Sufficient
Statement 2-
x=1 and y=3
x+y=4 (not divisible by 24)
x=11 and y=13
x+y=24(divisible by 24)
Insufficient
xy+1=24k
xy= 24k-1= 8l+7
Also, 8l+7 is odd; hence, x and y are both odd.
There can be 2 cases
1. x=8a+1 and y=8b+7 or vice-versa
x+y = 8(a+b+1)
2. x= 8c+3 and y=8d+5 or vice-versa
x+y= 8(c+d+1)
x+y must be divisible by 8
xy= 24k-1=3j+2
x=3m+2 and y=3n+1 or vice-versa
x+y=3(m+n+1)
x+y must be divisible by 3
Sufficient
Statement 2-
x=1 and y=3
x+y=4 (not divisible by 24)
x=11 and y=13
x+y=24(divisible by 24)
Insufficient
nick1816
nick1816
From 1
Let xy+1=24n
xy=24n-1
xy=23,47,71,95,119.....
x+y=1+23,1+47,5+19, 1+119
hence x+y will always be a multiple of 24
Sufficient
From 2
x=11 and y=13
yes
x=15 and y=17
No
Not sufficient
A:)
