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# Which one of the following could be the difference between two numbers

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Joined: 02 Sep 2009
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Which one of the following could be the difference between two numbers  [#permalink]

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17 Jun 2017, 05:59
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5% (low)

Question Stats:

90% (01:03) correct 10% (01:15) wrong based on 112 sessions

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Which one of the following could be the difference between two numbers both of which are divisible by 2, 3 and 4?

(A) 71
(B) 72
(C) 73
(D) 74
(E) 75

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Re: Which one of the following could be the difference between two numbers  [#permalink]

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17 Jun 2017, 06:19
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Two numbers divisible by 2,3 and 4 have 2^2 and 3 always.
The smallest positive number which is divided by 2,3 and 4 is 12

The difference between 12 and any other number must be a multiple of 12,
Hence 72(Option B) is the correct choice
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Re: Which one of the following could be the difference between two numbers  [#permalink]

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17 Jun 2017, 07:44
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Bunuel wrote:
Which one of the following could be the difference between two numbers both of which are divisible by 2, 3 and 4?

(A) 71
(B) 72
(C) 73
(D) 74
(E) 75

The numbers divisible by 2, 3 and 4 will be divisible by LCM of (2, 3, 4) = Multiple of 12
The difference of two multiples of 12 should also be a multiple of 12

hence, 72

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Re: Which one of the following could be the difference between two numbers  [#permalink]

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17 Jun 2017, 07:51
Bunuel wrote:
Which one of the following could be the difference between two numbers both of which are divisible by 2, 3 and 4?

(A) 71
(B) 72
(C) 73
(D) 74
(E) 75

Least number divisible by 2, 3 and 4 is 12

Form the set of numbers - { 12 , 24 , 36 , 48......................}

Now, the difference between any 2 numbers must be a multiple of 12, check the options, only (B) is our answer
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Re: Which one of the following could be the difference between two numbers  [#permalink]

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30 Dec 2018, 20:46
This was how I guessed to the right answer.
I took a glance at the questions and recognized some patterns. I assumed that answer must be divisible by 2, 3, and 4.
First, I filtered out a group of numbers that are divisible by 3 => 72 and 75
Second, only 72 is divisible by 2 and 4. So this is the answer.
Re: Which one of the following could be the difference between two numbers   [#permalink] 30 Dec 2018, 20:46
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