Positive odd integer

[hitmewithgmat]

If P is a positive odd integer, what ist he remianderw hen p is divided by 4?
1)when p is divided by8, the remainder is 5.
2)p is the sum of the squares of two positive integers.

OA after discussion.

[cramya]

I would go wiht D

1)when p is divided by8, the remainder is 5.

p = 8q+5

8q always divisible by 4. remainder:0
5/4 always give a remainder 1

so p always gives a remainder 1

(OR) Pick numbers

p=8q+5 = 5 when q(quotient) is 0 remainder 1
p=13 when q=1 remainder 1
p=21 when q=2 remainder 1

Recognizing a pattern so remainder always 1

SUFF

2)p is the sum of the squares of two positive integers.

One positive integer is odd and the other even


1^2+2^2 divided by 4 remainder 1
2^2+3^2 divided by 4 remainder 1
3^2+4^2 divided by 4 remainder 1

Recognizing a pattern so remainder always 1 or better theoritically an odd^2 divided by 4 leavses a remainder 1

An even square divided by 4 leaves a remainder 0

So combined remainder of the the sum is the remiander left by odd^2 division by 4

SUFF

[hitmewithgmat]

OA is D

[hardik.jadeja]

@cramya: I think answer should be A.

Take a look at the second clue. It says p is the sum of the squares of two positive integers. If does not say that p is the sum of the squares of two consecutive positive integers.

Now see this example. lets say p is 74 (5^2+7^2=74). If you divide 74 by 4 then the reminder is 2.

But when you take p as a sum of the squares of two consecutive positive integers then reminder is 1.

So we can't be sure what is the value of w when we only use information given in the second clue. So 2 is insufficient.

We must consider numbers other than consecutive integers to validate second clue. That was the trick here I guess. Hence I feel answer should be A.

[x2suresh]

@cramya: I think answer should be A.

Take a look at the second clue. It says p is the sum of the squares of two positive integers. If does not say that p is the sum of the squares of two consecutive positive integers.

Now see this example. lets say p is 74 (5^2+7^2=74). If you divide 74 by 4 then the reminder is 2.

But when you take p as a sum of the squares of two consecutive positive integers then reminder is 1.

So we can't be sure what is the value of w when we only use information given in the second clue. So 2 is insufficient.

We must consider numbers other than consecutive integers to validate second clue. That was the trick here I guess. Hence I feel answer should be A.

It should be D.

You missed the below point in the quesiton stem
"If P is a positive odd integer"

[hardik.jadeja]

yep, u r right.. I missed it.. Its 3:30AM.. I guess I should go to sleep...

[arjunn7]

Ans should be A..

Statement 2 doesnt say any where they are consecutive no.s which we are squaring..

lets 2 & 4.. u get 4+16 = 20
n dividing 20/4, remainder will be 0..

[hardik.jadeja]

u r doing the same mistake as i did..

take a look at quesiton stem.. "P is a positive odd integer"

if you take 2 odd intergers or 2 even integers and then square them to get the value of p, then p will be a possitive even number.. which we dont want..

Now take 1 positive odd integer and 1 even positive integer.. square them and add them.. you will get a positive odd value, which if u divide by 4 will produce 1 as reminder.

So ans D is correct.