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Is the integer x divisible by 24 ?
(1) x is divisible by 8
(2) x is divisible 6
(1) x is divisible by 8
(2) x is divisible 6
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.
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.
08 Feb 2012, 02:06
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nimc2012
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.
Answer: C.
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.
