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# Is the integer x divisible by 24?

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Is the integer x divisible by 24? [#permalink]

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07 Feb 2012, 20:38
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Is the integer x divisible by 24 ?

(1) x is divisible by 8
(2) x is divisible 6
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Oct 2012, 03:44, edited 2 times in total.
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Re: Number Properties - Question [#permalink]

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07 Feb 2012, 22:20
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Is X divisible by 24?
Question can become does x have prime factors of 2*2*2*3 (prime factors of 24)
1. x is divisible by 8 = 2*2*2 (The number of prime factors in 8) Not enough info
2. x is divisible by 6 = 2*3 (The number of prime factors in 6) Not enough info

1+2) = First set (2*2*2) second set (2*3). There is a repeat of common factor of 2 in the second set, so ignore 2.
First set + second set = (2*2*2*3) = Prime factors of 24.

Another way you can think about it is just find the LCF of 8 and 6. The answer of 24 is the same.

Logically speaking you need to know if the number is a multiple of 24 (I know sounds redundant).
1. Something that is divisible by 8 CAN be a multiple of 24 (24,48,72) or it CAN'T (8,16,32)
2. Exact same thing

We need to find a number that can be divided by both 8&6, so naturally we find the LCF, since it is the smallest number that can divide into the both of them and any other number that can by divided by the both of them are multiples of the LCF. So if LCF = 24 we know that regardless of what X is it is a multiple of 24.

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Is the integer x divisible by 24? [#permalink]

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08 Feb 2012, 02:06
nimc2012 wrote:

a few questions form number properties that are bothering me alot

1) Is the integer x divisible by 24 ?
a) x is divisible by 8
b) x is divisible 6

Is the integer x divisible by 24 ?

(1) x is divisible by 8 --> x can be: ..., 0, 8, 16, 24, 32, ... So it may or may not be divisible by 24. Not sufficient.
(2) x is divisible 6 --> x can be: ..., 6, 12, 16, 24, 30, ... So it may or may not be divisible by 24. Not sufficient.

(1)+(2) x is a divisible by both 8 and 6 which means that it's divisible by the least common multiple of 8 and 6, which is 24. Sufficient.

Generally, if a positive integer n is a multiple of positive integer a and positive integer b, then n is a multiple of LCM(a,b).

Hope it helps.
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Is the integer x divisible by 24? [#permalink]

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16 Oct 2012, 21:42
Is the integer x divisible by 24?
(1) x is divisible by 8.
(2) x is divisible by 6.

The solution is easy. However, I have some conceptual doubts related to this problem.
To solve the problem we have to find the LCM, which is 24 in this question. Therefore, x is divisible by 24.

But what about the number 0. According to the MGMAT guide, 0 is a multiple of every integer. Let's see: "any integer * 0 = 0 "
In this sense, and based on that definition, the LCM wouldn't be 24 but it would be 0. Because 0 is a multiple of 8 and 6 and also is less than 24.
Why is 0 not considered the LCM of any set of integers?, Should we calculate the LCM or only analyze whether 0 is divisible by 24?

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Re: Is the integer x divisible by 24? [#permalink]

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16 Oct 2012, 22:07
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danzig wrote:
Is the integer x divisible by 24?
(1) x is divisible by 8.
(2) x is divisible by 6.

The solution is easy. However, I have some conceptual doubts related to this problem.
To solve the problem we have to find the LCM, which is 24 in this question. Therefore, x is divisible by 24.

But what about the number 0. According to the MGMAT guide, 0 is a multiple of every integer. Let's see: "any integer * 0 = 0 "
In this sense, and based on that definition, the LCM wouldn't be 24 but it would be 0. Because 0 is a multiple of 8 and 6 and also is less than 24.
Why is 0 not considered the LCM of any set of integers?, Should we calculate the LCM or only analyze whether 0 is divisible by 24?

When you say LCM is Lowest Common Multiple, you are including only positive multiples. LCM is at least as great as the greater of the numbers.
Also, 0 is divisible by every number.
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Re: Is the integer x divisible by 24? [#permalink]

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08 Jun 2015, 07:01
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Re: Is the integer x divisible by 24? [#permalink]

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09 Jun 2015, 18:49
Hi All,

Variations of this DS question have been appearing on the GMAT for years. It's a great test of your 'thoroughness' and it often catches Test Takers who are moving too quickly and not thinking about all of the possible values of X....

We're told that X is an INTEGER. We're asked if X is divisible by 24. This is a YES/NO question.

Fact 1: X is divisible by 8

X COULD be 0, 8, 16, 24, 32, 40, 48, etc.

IF...X = 8, then the answer to the question is NO.
IF...X = 24, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: X is divisible 6

X COULD be 0, 6, 12, 18, 24, 30, 36, 42, 48, etc.

IF...X = 6, then the answer to the question is NO.
IF...X = 24, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know...
X is a multiple of 8
X is a multiple of 6

X COULD be 0, 24, 48, 72, etc. In ALL cases, X is divisible by 24, so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.

[Reveal] Spoiler:
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Re: Is the integer x divisible by 24? [#permalink]

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17 Aug 2017, 09:29
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Re: Is the integer x divisible by 24? [#permalink]

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18 Aug 2017, 14:39
Is the integer x divisible by 24 ?

(1) x is divisible by 8

x is divisible by 8 ==> Possible numbers: 0, 8, 16, 24, 32, 40

As the answer can be either "YES" or "NO", this information is not sufficient.

Hence, (1) ===== is NOT SUFFICIENT

(2) x is divisible 6

x is divisible by 6 ==> Possible numbers: 0, 6, 12, 18, 24, 30

As the answer can be either "YES" or "NO", this information is not sufficient.

Hence, (2) ===== is NOT SUFFICIENT

Combining (1) & (2)

x is divisible by 8 and 6 ==? Possible numbers: 0, 24, 48

All the above numbers are divisible by 24 and hence this information is sufficient.

Hence, (1) & (2) ===== is SUFFICIENT

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Re: Is the integer x divisible by 24?   [#permalink] 18 Aug 2017, 14:39
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