GPrep DS3

Question

please solve it for me.

bigtreezl · Answer

im getting A for this one

given p-4n=r

1) p-8n=5
p must be 13, 21, 29 etc
 so p-4n=1
suff

2) p is the sum of the squares of 2 +ive ints
 36+16= 52 52/4 remainder=0
 9+16= 25 25/4 remainder=1
insuff

Oops forgot P had to be odd! Ans D

Dabral, great vids man!! keep it up!

dabral · Answer

Please see my video solution. https://www.gmatquantum.com/shared-posts ... eory8.html The original question is not included in the video because of copyright issues. Dabral

GMAT TIGER · Answer

Statement 1 is straight. So no dispute about it.

Statement 2 is important. Since p is an odd integer and also a sum of the squares of 2 integers. So:

p = x^2 + y^2 where one is even and the other is odd. 
Lets suppose x is even and y is odd. x^2 is always divided by 4. So remaining is y^2.

y^2 = (a+1)^2 where a is an even integer and s a multiple of 2.
y^2 = a^2 +2a + 1
y^2 = (2k)^2 +2(2k) + 1 where a = 2k
y^2 = 4k^2 +4k + 1
So reminder is 1.
Suff...

Alternatively: Only for y^2

If y = 1, y ^2 = 1, reminder is 1.
If y = 3, y ^2 = 9, reminder is 1.
If y = 5, y ^2 = 25, reminder is 1.
.
.
If y = 11, y ^2 = 121, reminder is 1.

Any odd value of gives reminder 1 when p is divided by 4.

burnttwinky · Answer

Thanks for the video solutions. They are very helpful.

burnttwinky · Answer

The theory solution to this problem makes sense, but I dont know if I can think of it that quickly for the exam. I probably would end up just testing 3 numbers for both 1 and 2.

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