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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.
  • a)
    Choose this option if the Question can be answered by one of the Statements alone but not by the other.  
  • b)
    Choose this option if the Question can be answered by either Statement alone.
  • c)
    Choose this option if the Question can be answered by using both Statements together, but cannot be answered by using either Statement alone.  
  • d)
    Choose this option if the Question cannot be answered even by using both Statements together.
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
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.
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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.a)Choose this option if the Question can be answered by one of the Statements alone but not by the other. b)Choose this option if the Question can be answered by either Statement alone.c)Choose this option if the Question can be answered by using both Statements together, but cannot be answered by using either Statement alone. d)Choose this option if the Question cannot be answered even by using both Statements together.e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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