DIVISIBILITY

Question

I have this two problems and i can not understand the answer, can you please help me.

Is X divisible by 119

1) x is divisible by 17
2) x is divisible by 7

Is X divisible by 96

1)x is divisible by 6
2)x is divisible by 16

My question is that how in the first the answer is together SUFFICIENT and in the second both INSUFFICIENT?

Thank you.

farful · Answer

Let x = 48.
Then x is not divisible by 96, but is divisible by 6 and 16.

KarishmaB · Answer

In the first problem, you are given that 17 and 7 are factors of x. Both are prime numbers hence you cannot make them using any other numbers. So 17*7 = 119 must be a factor of x.

In the second question, first statement tells you that 2 and 3 are factors of X.
The second statement tell you that four 2s are factors of X. 
Together, you know that four 2s and a 3 are factors of X. That is 48 is a factor of X. But is 96? We don't know. Note that 6 and 16 have a common 2. Hence we cannot say that x must be divisible by 6*16 = 96.

utkmittal1 · Answer

Hey

One way of solving such problems is to find Least common multiple of the two numbers.
In first problem - LCM of 17 and 7 is 119. So X will definitely be divisible by 119
In second problem - LCM of 16 and 6 is 48. So X will definitely be divisible by 48. But may or may not be divisible by 96.

DIVISIBILITY

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