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Re: Is the positive integer x divisible by each integer from 2 through 6 ?
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11 Sep 2021, 05:21
Is the positive integer x divisible by each integer from 2 through 6 ?
(1) x = 10m, where m is a positive integer divisible by each integer from 2 through 5
We need to check if x is divisible by 2,3,4,5,6 or not.
Its given that m is divisible by 2,3,4,5. That means x is also divisible by 2,3,4,5.
So now, we are left with the divisibility of 6. Since x is divisible by 2 and 3, we can confirm that x will be also be divisible by 6.
So Statement 1 alone is sufficient.
(2) 10x = n, where n is a positive integer divisible by each integer from 2 through 9
Its given that , n is divisible by 2,3,4,5,6,7,8,9.
10x = n
2 * 5 * x = n
Clearly we can say that x will be divisible by 3,7,9 and for rest of the numbers, we need to analyze more.
Since n is divisible by 4, then x should be divisible by 2, as there is only one factor of 2 in 10.
Also we cannot confirm that x is divisible by 5 as 5 is a factor in 10.
Example:
Its given that 10x is divisible by 5
if x= 1, 10x = 10 * 1 = 10 is divisible by 5 but x is not divisible by 5.
if x =10 , 10x = 10*10 = 100 is divisible by 5. But here x is divisible by 5.
So we cannot confirm that X is divisible by 5 in this case. Both cases are possible.
Similarly n is divisible by 8, then x should be divisible by 4, as there is only one factor of 2 in 10.
Also x is divisible by 2 and 3, then it should be divisible by 6 as well .
So here we can confirm that x is divisible by 2,3,4,6. But we are not sure if its divisible by 5 or not. Hence Insufficient.
Option A is the answer.
Thanks,
Clifin J Francis
GMAT SME