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Divisibility

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Divisibility

by vinayreguri » Sun Jun 12, 2011 5:26 am
The number 287X30Y4 is divisible by both 4 & 11. IF X+Y is a positive multiple of 6, find the values if X &Y

A. 0,0
B. 0,6
C. 2,4
D. 6,0
E. 6,6

OA : E
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by Frankenstein » Sun Jun 12, 2011 5:30 am
Hi,
287X30Y4
For it to be divisible by 4, y4 should be divisible by 4. So, y can be 0,2,4,6,8
For the number to be divisible by 11, (2+7+3+y)-(8+x+0+4) should be divisible by 11.
i.e. y-x should be divisible by 11.As y and x are single digits, y-x can only be 0(divisible) by 11
So, x=y=0,2,4,6,8. As x+y is multiple of 6, each of x and y should be 6.

Hence, E
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by Anurag@Gurome » Sun Jun 12, 2011 5:40 am
vinayreguri wrote:The number 287X30Y4 is divisible by both 4 & 11. IF X+Y is a positive multiple of 6, find the values if X &Y


For the number to be divisible by 4, the last two digits must be divisible by 4. Hence, Y4 should be divisible by 4. So, possible values of Y are : 0, 2, 4, 6, and 8

For the number to be divisible by 11, the difference between the sum of the odd numbered digits and the sum of the even numbered digits must divisible by 11. Hence, (2 + 7 + 3 + Y) - (8 + X + 0 + 4) = (Y - X) must be divisible by 11. Now, X and Y are digits. Hence, their difference will be divisible by 11 only if they are equal.

Hence, possible values of X and Y are : 0, 2, 4, 6, and 8.

As (X + Y) is a positive multiple of 6, only possible value of X and Y is 6.

The correct answer is E.
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by cans » Tue Jun 14, 2011 3:57 am
287X30Y4
x+y is positive multiple of 6, thus A is eliminated (0 is not positive)
also 12+y - (12+x) = y-x is multiple of 11
only E satisfies.
IMO E
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by shayam » Wed Jul 13, 2011 9:45 am
Can I say , if (X+Y) is a multiple of 6 , X and Y are also multiple of 6 ?

hence 6(X+Y) = 6X + 6Y

Looking at the choices, we can figure out the outstanding choice E .
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by gmatfeel » Wed Jul 13, 2011 10:09 am
shayam wrote:Can I say , if (X+Y) is a multiple of 6 , X and Y are also multiple of 6 ?

hence 6(X+Y) = 6X + 6Y

Looking at the choices, we can figure out the outstanding choice E .
I don't think we can make the assumption that if x+y is a multiple of 6, both x and y are also multiple of 6.
Eg.
if x=5 and y=7, X+Y=12 (multiple of 6)
but xy = 35 which is not a multiple of 6
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by shayam » Wed Jul 13, 2011 11:15 am
I get that. Thanks for pointing out..
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by krishnasty » Wed Jul 13, 2011 11:18 pm
Are we leaving out (A) 0,0 because..
a. 0 is not positive?
b. 0 is not a multiple of 6 ( or nay number?)
c. both

sorry for posting my doubt like a question, but i just wanted to get my concepts right..
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by Frankenstein » Thu Jul 14, 2011 1:25 am
krishnasty wrote:Are we leaving out (A) 0,0 because..
a. 0 is not positive?
b. 0 is not a multiple of 6 ( or nay number?)
c. both

sorry for posting my doubt like a question, but i just wanted to get my concepts right..
Hi,
The number 287X30Y4 is divisible by both 4 & 11. IF X+Y is a positive multiple of 6, find the values if X &Y
Cheers!

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by krishnasty » Thu Jul 14, 2011 1:45 am
Hi Frankenstein,

i think you misunderstood my question. what i really wanna ask is
(a) - do we consider 0 as positive or neither postive nor negative
(b) - can 0 be considered as a multiple of any number ??
Frankenstein wrote:
krishnasty wrote:Are we leaving out (A) 0,0 because..
a. 0 is not positive?
b. 0 is not a multiple of 6 ( or nay number?)
c. both

sorry for posting my doubt like a question, but i just wanted to get my concepts right..
Hi,
The number 287X30Y4 is divisible by both 4 & 11. IF X+Y is a positive multiple of 6, find the values if X &Y
---------------------------------------
Appreciation in thanks please!!
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by Frankenstein » Thu Jul 14, 2011 3:26 am
krishnasty wrote:Hi Frankenstein,

i think you misunderstood my question. what i really wanna ask is
(a) - do we consider 0 as positive or neither postive nor negative
(b) - can 0 be considered as a multiple of any number ??
Hi,
0 is neither positive nor negative
0 can be considered multiple of any number.
Cheers!

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