netcaesar wrote:
If p, x, and y are positive integers, y is odd, and p = x^2 + y^2, is x divisible by 4?
(1) When p is divided by 8, the remainder is 5.
(2) x – y = 3
I think it was just easier to use various numbers
Statement II is insufficient alone.
For Statement I, I used various numbers for Option A and noted that x is not divisible by 4
Given Statement 1: p when divided by 8 leaves a remainder of 5
p = 8q + 5
Numbers that work here for p are 5, 13, 21, 29, 37, 45, 53 etc.,
Also, p = x^2 + y^2, y is odd
So of p = 5 -> y should be 1 since when y = 3, y^2 = 9. Therefore, p = 2^2 + 1^2 --> x = 2 [Not div. by 4]
Similarly, when p = 13 --> p = 2^2 + 3^2 --> x = 2[Not div. by 4]
p = 21 -> Can't think of numbers here
p = 29 -> p = 2^2 + 5^2 -> x = 2[Not div by 4]
p = 37 -> p = 6^2 + 1^2 -> x = 6[Not div by 4]
p = 45 -> p = 6^2 + 3^2 -> x = 6[Not div by 4]
p = 53 -> p = 2^2 + 7^2 -> x = 2[Not div by 4]
Since x is not div by 4 for any of the situations above, it is safe to conclude that A is sufficient !!!
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Siddharth Ramachandran
B School Aspirant, 2021 Intake