Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
Is a number T divisible by 144?
I. T is a multiple of 216.
II. T is divisible by square of cube of 2.
Solution
Correct Answer: Option E
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.
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