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?

• A. 32,64
• B. 6,64
• C. 7,28
• D. 14,84

Answer 1

The correct option is D

14,84

g$\left(32\right)=1+2+4+8+16+32=63<2\times 32$ (Category A)
g$\left(64\right)=1+2+4+8+16+32+64=127<2\times 64$ (Category A)
g$\left(6\right)=1+2+3+6=12=2\times 6$ (neither A nor B)
g$\left(7\right)=1+7=8<2\times 7$ (Category A)
g$\left(28\right)=1+2+4+7+14+28=56=2\times 28$ (Neither A nor B)
g$\left(14\right)=1+2+7+14=24<2\times 14$ (Category A)
g$\left(84\right)=1+2+3+4+6+7+12+14+21+28+42+84=224>2\times 84$ (Category B)

Hence, option (d).