g(x) is defined as the sum of all the divisors of a natural number n. If g(x) is

Sail E0 Webinar

Question

G(x) is defined as the sum of all the divisors of a natural number n.
If g(x) is less than 2n then it is placed in category A.
If g(x) is greater than 2n it is placed in category B.
Of the following numbers, which pair consists of numbers one of which can be placed in A and another in B?

Options:

A . 32,64

B . 6,64

C . 7,28

D . 14,84

Answer: Option D
:
D
g

(32) = 1 + 2 + 4 + 8 + 16 + 32 = 63 < 2 \times 32

(Category A)
g

(64) = 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127 < 2 \times 64

(Category A)
g

(6) = 1 + 2 + 3 + 6 = 12 = 2 \times 6

(neither A nor B)
g

(7) = 1 + 7 = 8 < 2 \times 7

(Category A)
g

(28) = 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 \times 28

(Neither A nor B)
g

(14) = 1 + 2 + 7 + 14 = 24 < 2 \times 14

(Category A)
g

(84) = 1 + 2 + 3 + 4 + 6 + 7 + 12 + 14 + 21 + 28 + 42 + 84 = 224 > 2 \times 84

(Category B)
Hence, option (d).

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. If a, b, c are three consecutive natural numbers, then the expression (a + b - c) (a + c - b) (b + c - a) is:....

Question 2. Arjun can kill a bird once in 3 shots. On the assumption that he fires 3 shots, the probability that the bird is killed ....bird is killed is x27. Find the value of x. ___

Question 3. In a school of 150 students, 50 students did not play football, 90 played cricket and 20 neither played football nor cri....neither played football nor cricketHow many students played only football?

Question 4. The sum of the first 100 odd numbers is divisible by:....

Question 5. A rectangle is divided into four rectangles, and their respective areas are shown in the figure. (Figure is not drawn to....What is the missing area 'X' of the fourth rectangle?25205x

Question 6. In how many ways can 80 be written as the difference of squares of two natural numbers?....

Question 7. There are some boxes labelled 1, 2, 3, 4... and so on up to 2n, where n>6 such that, for k = 1, 2, 3, 4, .... 2....the N boxes in Case 1 and Case 2 is:

Question 8. Find the minimum value of the function f(x) = |x-1| + |x-2| + |x-3| + ... + |x-20|....

Question 9. How many positive even integers less than 50 can be written as a sum of three consecutive positive integers?....

Question 10. Find the sum of all the integers N>1 such that the each prime factor of N is either 2, 3 or 7 and N is not divisible ....N is not divisible by any perfect cube greater than1. ___

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