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CAT 1997 — QA Question 11

FactorsEasy
Passage / Data

Answer the next 3 questions based on the following information.

There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each. The groups A and C are combined to form group D.

If n is an integer, how many values of n will give an integral value of (16n2+7n+6)n?

Answer & solution

  • A

    2

  • B

    3

  • C

    4

  • None of these

Solution

The given expression can be written as

(16n2n)+(7nn)+(6n)=16n+7+(6n)

Since n is an integer, the expression (16n + 7) will always be an integer. Hence, for the entire expression to be an integer, the part (6n) should also be an integer.
This can be possible only if n is a factor of 6, viz. n = 1, 2, 3, 6, –1, –2, –3 and –6.

Hence, n can have eight values.

CAT 1997 QA Q11: If n is an integer, how many values of n will give an integral value of ( 16 n 2 + 7 n + 6 ) n ? — Solution | TheCATExam