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# Integer Properties

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Intern
Joined: 13 Jan 2016
Posts: 9

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02 Aug 2018, 11:59
If JKL is a 3 digit number (non zero) and have no zero at any digit place such that

JK is divisible by 9
KL is divisible by 9

Then how many numbers JKL are possible ?
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7592
GMAT 1: 760 Q51 V42
GPA: 3.82

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Updated on: 06 Aug 2018, 11:58
1
If JKL is a 3 digit number (non zero) and have no zero at any digit place such that

JK is divisible by 9
KL is divisible by 9

Then how many numbers JKL are possible ?

In order for an integer to be a multiple of 9, the sum of all digits is a multiple of 9.

If K = 1, then J = 8 and L = 8.
If K = 2, then J = 7 and L = 7.
If K = 3, then J = 6 and L = 6.
If K = 4, then J = 5 and L = 5.
If K = 5, then J = 4 and L = 4.
If K = 6, then J = 3 and L = 3.
If K = 7, then J = 2 and L = 2.
If K = 8, then J = 1 and L = 1.
If K = 9, then J = 9 and L = 9.
The case of K = 9, J = 0 and L = 0 is not the case we consider, since zero digits are there.
If K = 0, then J = 9 and L = 9, which is not a case we consider, since a zero digit is there.

Thus we have 9 cases.
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Originally posted by MathRevolution on 03 Aug 2018, 08:10.
Last edited by MathRevolution on 06 Aug 2018, 11:58, edited 1 time in total.
Intern
Joined: 13 Jan 2016
Posts: 9
Re: Integer Properties  [#permalink]

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03 Aug 2018, 10:19
You forgot one possibility of 999 so total of 9 i think
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7592
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Integer Properties  [#permalink]

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06 Aug 2018, 11:56
You forgot one possibility of 999 so total of 9 i think

Oh. You are right.
The solution is fixed.
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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Re: Integer Properties   [#permalink] 06 Aug 2018, 11:56
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# Integer Properties

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