# What is the smallest number which when increased by 5 is completely divisible by 8 and 11 and 24?

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What is the smallest number which when increased by 5 is com [#permalink]

23 Oct 2010, 03:19

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15% (low)

Question Stats:

81% (01:19) correct
19% (01:25) wrong
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What is the smallest number which when increased by 5 is completely divisible by 8, 11 and 24?A. 264B. 259C. 269D. 270

E. 282

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Re: number properties puzzle 3 [#permalink]

23 Oct 2010, 03:37

LCM(8,11,24)=24x11=264So the least divisible number is 264, and the number we are looking for is 259.Answer is (b) _________________

Re: number properties puzzle 3 [#permalink]

12 Nov 2013, 13:06

feruz77 wrote:

What is the smallest number which when increased by 5 is completely divisible by 8, 11 and 24?a) 264b) 259c) 269d) 270

e) 282

Actually let's start with the smallest cause that's what the question is askingSo let's begin with B259+5 = 264.Now divisible by 3? Digits add to multiple of 3 so yesDivisible by 8? Last two are divisible by 4 and result is divisible by 2 so yesDivisible by 11? 2+4-6=0 is a multiple of 11 so yes againOur best friend today is BHope it helpsCheers!

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Re: What is the smallest number which when increased by 5 is com [#permalink]

21 May 2015, 19:23

Hi All,This question includes a number of great Number Property shortcuts that you can take advantage of:1) The question asks for the SMALLEST number that, when increased by 5 is divisible by 8, 11 and 24. Since the answers are numbers, we can TEST THE ANSWERS.2) Any number that is divisible by 24 is ALSO divisible by 8, so we really just need to consider the 11 and the 24.3) To be divisible by 24, the end number MUST be EVEN. Since we're adding 5 to get to that end number, the starting number MUST be ODD.The last shortcut allows us to eliminate Answers A, D and E. Between Answers B and C, TESTING B first will prove that, when increased by 5, the end sum is divisible by both 11 and 24.

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Re: What is the smallest number which when increased by 5 is com [#permalink]

23 Apr 2022, 01:37

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Re: What is the smallest number which when increased by 5 is com [#permalink]