AP ICET 2017 Shift 2 Paper

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Note:
In questions numbered 1 to 20, a question is followed by data in the form of two statements labelled as I and II. You must decide whether the data given in the statements are sufficient to answer the questions. Using the data make an appropriate choice from (1) to (4) as per the following guidelines:

Question : 16 of 200

Marks: +1, -0

Is the integer n divisible by 120?
I.

{n}={k}({k}^{2}-1)({k}^{2}-4)

for some integer k
II. n is divisible by 4 and 30

if the statement I alone is sufficient to answer the question.
if the statement II alone is sufficient to answer the question.
if both the statements I and II are sufficient to answer the question but neither statement alone is not sufficient.
if both the statements I and II together are not sufficient to answer the question and additional data is required.

Validate

Solution:

n=k(k^2-1)(k^2-4)

For

k=

n=3(3^2-1)(3^2-4)=3×8×5=120

which is divisible by 120
For

k=4

n=4(4^2-1)(4^2-4)=4×15×12=120×6

which is divisible by 12.
This is true for other integral values of k too.
Hence, I alone is sufficient.

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