Is positive integer x divisible by 48?

Hi,

Let the prime factors of x be \(P^a * Q^b * ....so on\)
To check if it is divisible by 48, it must have atleast the prime factors of 48 in same or more number. i.e. x must have at least 4 2s and one 3.

1) if x is divisible by 8, it will have at least 3 2s as its prime number but this condition does not give us any information about one more 2 and a 3. Hence, not sufficient.

2) if x is divisible by 6, it will have atleast one 2 and one 3 as its prime factor. We are still short of 3 2s to prove its divisibility by 48. Hence not sufficient.

Combining 1 & 2 we get that it will have at least 3 2s and one 3. still not enough information to prove.

Hence, E is the correct choice.

we are asked to find out whether x is divisible or not. To be divisible by 48 x has to be the multiple of 48.

statement 1: x is divisible by 8. So, x could be 8, 16, 24 etc. if x is divisible by 8 it doesn't necessarily mean that x will be divisible by 48. Consider x=8, 16. Thus statement 1 is not sufficient.

statement 2: x is divisible by 6. This one is the same as statement 1. x is divisible by 6 doesn't mean that x will be divisible by 48. Insufficient.

combining both statement : we all know is that x is LCM of both 6 and 8 which is 24. x is multiple of 24. So x could be 24, 48 etc. Still we don't have sufficient data to answer this question. If we take 24 as a value of x it is not divisible by 48 but if x is 48 , x is divisible by 48.

Thus the best answer is E.

Is positive integer x divisible by 48?

(1) x is divisible by 8.
Ans: 8, 16, 24, 32, 40, 48, 56,....
Not sufficient

(2) x is divisible by 6.
Ans: 6, 12, 18, 24, 30, 36, 42, 48, 54,....
Not sufficient

Both....
A: 8, 16, 24, 32, 40, 48, 56,....
B: 6, 12, 18, 24, 30, 36, 42, 48, 54,....

24 is not divisable by 48
Not sufficient

Ans: E

Target question: Is positive integer x divisible by 48?

When I scan the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……

Statements 1 and 2 combined
Statement 1 tells us that x is divisible by 8.
Statement 2 tells us that x is divisible by 6
There are many values of x that satisfy BOTH statements. Here are two:
Case a: x = 48. In this case, the answer to the target question is YES, x is divisible by 48
Case b: x = 24. In this case, the answer to the target question is NO, x is not divisible by 48

Answer: E

Cheers,
Brent

Stem says is x divisible by \(2^4.3\)

Combining (1)+(2)
LCM of 8 and 6 = \(2^3.3\)
If the LCM had one more 2, then the answer would have been YES.
Right now we do not know, it may or may not be.

Answer: E

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