remainder question

[Gurpinder]

10) If p is positive integer, what is remainder when p is divided by 4?
a. When P is divided by 8 remainder is 5
b. P is the sum of the squares of two consecutive positive integers.


[spoiler]oa: (d)[/spoiler]

how is 2 sufficient?

[debmalya_dutta]

10) If p is positive integer, what is remainder when p is divided by 4?
a. When P is divided by 8 remainder is 5
b. P is the sum of the squares of two consecutive positive integers.


[spoiler]oa: (d)[/spoiler]

how is 2 sufficient?

Look at it this way .. it is mentioned that you have squares of 2 consecutive integers. so , one of them surely is even and the other is surely odd ..
Square of even integer is always divisible by 4... Now to the odd integer... Square of any odd integer divided by 4 leaves a remainder of 1.... Hence incase of statement 2, the remainder will be 1

[Gurpinder]

10) If p is positive integer, what is remainder when p is divided by 4?
a. When P is divided by 8 remainder is 5
b. P is the sum of the squares of two consecutive positive integers.


[spoiler]oa: (d)[/spoiler]

how is 2 sufficient?

Look at it this way .. it is mentioned that you have squares of 2 consecutive integers. so , one of them surely is even and the other is surely odd ..
Square of even integer is always divisible by 4... Now to the odd integer... Square of any odd integer divided by 4 leaves a remainder of 1.... Hence incase of statement 2, the remainder will be 1

Thx Deb!

[mgm]

I know it sounds dumb but how is 1 sufficient ? Can you provide a rule per se , you can pick numbers and derive but it is a little time consuming.

[Gurpinder]

I know it sounds dumb but how is 1 sufficient ? Can you provide a rule per se , you can pick numbers and derive but it is a little time consuming.

since 8 is a multiple of 4, the remainder of p/4 will also be 5.

[neel_mutum]

QUESTION:
10) If p is positive integer, what is remainder when p is divided by 4?
a. When P is divided by 8 remainder is 5
b. P is the sum of the squares of two consecutive positive integers.

What is the actual answer?

Statement1 says:
P%8 = 5 , where % = gives remainder. Which means smallest number P can take is 5. i.e 5%8 equals 5.

P = 8*x + 5 where x is a positive integer or least zero
when divided by 4 : spliting the terms to add the reminders:
8*x/4 => (4*2*x)/4 ------>reminder 0
5/4---> reminder "1"

It is based on the simple divisibility of numbers in the form:
(a*x+y) divided by a, reminder is y
e.g 102 divided by 10. (100+2)/10 ---> to find reminders( add reminder of(100/10) + reminder of(2/10))--> 0 + 2
this reminder rule can be extended to find reminder of expression involving powers: (a*x+y)^n/a reminder is also y.

Hence, any P/8 which gives reaminder 5 would give remainder "1" when divided by 4.

And Statement2 is true as stated in above post

I feel the the answer is "D".