If n is an integer, how many values of n will give an integral value of(16nz+7n+

Sail E0 Webinar

Question

If n is an integer, how many values of n will give an integral value of

\frac{(16 n^{z} + 7 n + 6)}{n} ?

(CAT 1997)

Options:

A . 2

B . 3

C . 4

D . None of these

Answer: Option C
:
C
Ans: (c)

\frac{(16 n^{z} + 7 n + 6)}{n} = 16 n + 7 + \frac{6}{n};

Since n is an integer, hence for the entire expression to become an integer,

(\frac{6}{n})

should be an integer. And

(\frac{6}{n})

can be integer for

n = 1, 2, 3, 6.

Hence n has 4 values.

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. L Let D be a recurring decimal of the form D=0. a1a2a1a2a1a2............; where digits a1 and a2lie between 0 and 9....necessarily produces an integer, when multiplied by D? (CAT 2000)

Question 2. Let S be a set of positive integers such that every element n of S satisfies the conditions I. 1000≤n≤....many elements of S are divisible by 3? (CAT 2005)

Question 3. If x=(163+173+183+193), then x divided by 70 leaves a reminder of? (CAT 2005)....

Question 4. When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by 1....increase by 18 when their digits are reversed? (CAT 2006)

Question 5. If R=(3065−2965)(3064−2964) , then (CAT 2005)....

Question 6. Lety =12+13+12+13+....... What is the value of y?....

Question 7. Let a1=p and b1=q where p and q are positive quantities. Define an=pbn−1 and bn=qbn−1, for even n>1 and....the smallest odd n such that an+bn<0.01? (CAT 2007)

Question 8. Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product ....up by 540. What is the new product? (CAT 2001)

Question 9. Let n!=1×2×3×...........×n for integer n>1. If p=1!+(2+2!)+(3+3!)+...........+(10+10!), then p+2 ....when divided by 11! leaves a remainder of (CAT 2005)

Question 10. Three pieces of cakes of weights 412 lbs, 634 lbs and 715 lbs respectively are to be divided into parts of equal weights....maximum number of guests that could be entertained? (CAT 2001)

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0