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Intern  Joined: 12 May 2012
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If the number x3458623y is divisible by 88, what is the  [#permalink]

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If the number x3458623y is divisible by 88, what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5

Originally posted by sarb on 08 Jun 2012, 09:21.
Last edited by Bunuel on 22 Jul 2014, 05:01, edited 2 times in total.
Edited the question and added the OA.
Math Expert V
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Posts: 58410
Re: If the number x3458623y is divisible by 88, what is the  [#permalink]

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11
sarb wrote:
If the number x3458623y is divisible by 88, what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5

Since x34,586,23y is divisible by 88=8*11 then it's divisible by both 8 and 11.

Now, in order a number to be divisible by 8 its last three digits must be divisible by 8, so 23y must be divisible by 8. That's only possibly if y=2 --> 232/8=29. So, our number is x34,586,232.

Next, in order a number to be divisible by 11 the difference between the sum of the odd numbered digits (1st, 3rd, 5th...) and the sum of the even numbered digits (2nd, 4th...) must be divisible by 11. So, (x+4+8+2+2)-(3+5+6+3)=x-1 must be divisible by 11, which means that x can only be 1.

For more on divisibility check Number Theory chapter of Meth Book: math-number-theory-88376.html

Hope it helps.
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Re: If the number x3458623y is divisible by 88, what is the  [#permalink]

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Re: If the number x3458623y is divisible by 88, what is the  [#permalink]

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2
sarb wrote:
If the number x3458623y is divisible by 88, what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5

x3458623y is divisible by 88 so, it should be divisible by 8 and 11

x+14+y -17 = n * 11
x+y-3 = n*11
n cant be 2, as in that case RHS will become 22, and on LHS the max we can get is 9+9-3 = 15

so n=0 or 1

now it should be divisible by 8 also, so 23y should be divisible by 8
240 is perfectly divisible by 8, so the no less then that will be 232

thus, y=2

now, x+2-3 =n*11
x-1=n*11

now n=1 is also not possible as lhs max can only be 9-1 =8

thus, n=0
hence, x=1

Ans: A
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Re: If the number x3458623y is divisible by 88, what is the  [#permalink]

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sarb wrote:
If the number x3458623y is divisible by 88, what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5

to be divisible by 11:

3+5+6+3=2+y+8+4+x
3=x+y

x y
3 0 - not correct (not divisible by 4)
0 3 - not correct (not divisible by 2)
2 1 - not correct (not divisible by 2)
1 2 - correct (divisible by 4) - (...232) - is divisible by 4
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Re: If the number x3458623y is divisible by 88, what is the  [#permalink]

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cumulonimbus wrote:
sarb wrote:
If the number x3458623y is divisible by 88, what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5

to be divisible by 11:

3+5+6+3=2+y+8+4+x
3=x+y

x y
3 0 - not correct (not divisible by 4)
0 3 - not correct (not divisible by 2)
2 1 - not correct (not divisible by 2)
1 2 - correct (divisible by 4) - (...232) - is divisible by 4

Did in the same way, however considered last three digits 23y for divisibility check with 8
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Re: If the number x3458623y is divisible by 88, what is the  [#permalink]

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_________________ Re: If the number x3458623y is divisible by 88, what is the   [#permalink] 27 Mar 2019, 16:36
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