Given below is a question and two statements numbered I and II given b...
From statement I:
If T is multiple of 216, then T can be 216 which is not divisible by 144 or T can be 432 which is divisible by 144. So, divisibility of T with 144 cannot be uniquely established.
∴ Statement I alone is not sufficient to answer the question.
From statement II:
T is divisible by square of cube of 2.
Square of cube of 2 = (2 × 2 × 2)2 = 64
⇒ T is a multiple of 64.
So, T can be 192 which is not divisible by 144 or T can be 576 which is divisible by 144. So, divisibility of T with 144 cannot be uniquely established.
∴ Statement II alone is not sufficient to answer the question.
From statements I and II together:
T is divisible by square of cube of 2.
Square of cube of 2 = (2 × 2 × 2)2 = 64
⇒ T is a multiple of 64.
Also, T is a multiple of 216.
⇒ T will be a multiple of LCM(216, 64).
⇒ T will be a multiple of 1728.
We know, 1728 = 144 x 12.
If T is divisible by 1728, it would be divisible by all its factors.
∴ T will be divisible by 144.
∴ Using both the statements together, we can answer the given question.