collection of tough problems from G PREP - 33

[abhasjha]

If p is a positive odd integer, what is the remainder when p is divided by 4?

1. When p is divided by 8, the remainder is 5.
2. p is the sum of the squares of two positive integers

[shashank.ism]

If p is a positive odd integer, what is the remainder when p is divided by 4?

1. When p is divided by 8, the remainder is 5.
2. p is the sum of the squares of two positive integers

Ans is A

[harsh.champ]

If p is a positive odd integer, what is the remainder when p is divided by 4?

1. When p is divided by 8, the remainder is 5.
2. p is the sum of the squares of two positive integers

This is a repeat ques.-plz check before posting.

[shashank.ism]

If p is a positive odd integer, what is the remainder when p is divided by 4?

1. When p is divided by 8, the remainder is 5.
2. p is the sum of the squares of two positive integers

Ans is A

If no. odd no. is divided by 4 , remainder can be either 1 or 3.

S1: when P is divided by 8, the remainder is 5. so P-5 is divisible by 4 and dividing 5 by 4 , we get remainder = 1...sufficient
S2: so the on no. must be odd and one must be even to give an odd number p
so even^2 is surely divisible by 4 and odd^2 when divisble by 4 gives remainder 1

so overall remainder = 1. ----sufficient

So Ans is

D

[ajith]

If p is a positive odd integer, what is the remainder when p is divided by 4?

1. When p is divided by 8, the remainder is 5.
2. p is the sum of the squares of two positive integers

1. Sufficient; Any no that leaves a remainder of 5 with 8 will leave a remainder of 1 when divided by 4
2. Insufficient

Hence A