1st Q:
C

A) n = 3,5,7,9,11,13. If that's divided by 24 you'll get different answers so not sufficient
B) n = 1,2,4,7,10,13. If that's divided by 24 you'll get different answers so not sufficient

What's common in both is 7,13, etc. You'll notice that if you take n+1 and n-1 in both - (6)(8) and (12)(14) they both have a factor of 24 so there won't be any remainder. Sufficient.

2nd Q:
B

A) n = 22, 24, 26, 28, 30. If that's divided by 7 you'll get different answers so not sufficient
B) n = 31, 59, 87. If that's divided by 7 you'll get R=3 for all so sufficient.

1. what is n^2 (mod 24), we need n^2 (mod 8) and n^2 (3)

1. n = 1 (mod 2)
n = 1,3, 5, 7 (mod 8)
n^2 = 1 (mod 8)
we need n^2 (mod 3). Insuff

2. n = 1 or 2 (mod 3)
n^2 = 1 (mod 3). We need n^2(mod 8). Insuff

Combined , n^2 = 1 (mod 8). Sufficient.


2. what is n (mod 7)

1. n = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 (mod 21)
n = 1, 3, 5, 0, 2, 4, 6,1,3,5 (mod 7) Insufficient

2. n = 3 (mod 28)
n = 3 (mod 7) Sufficient. B is the answer

thanks guys... sorry I didn't understand any of that mod stuff, lol.
adam's solutions was pretty clear.

palv, are there any online websites that shows how to do the mod calculations?
thanks

What is this modulo stuff...?

palvarez wrote:1. what is n^2 (mod 24), we need n^2 (mod 8) and n^2 (3)

1. n = 1 (mod 2)
n = 1,3, 5, 7 (mod 8)
n^2 = 1 (mod 8)
we need n^2 (mod 3). Insuff

2. n = 1 or 2 (mod 3)
n^2 = 1 (mod 3). We need n^2(mod 8). Insuff

Combined , n^2 = 1 (mod 8). Sufficient.


2. what is n (mod 7)

1. n = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 (mod 21)
n = 1, 3, 5, 0, 2, 4, 6,1,3,5 (mod 7) Insufficient

2. n = 3 (mod 28)
n = 3 (mod 7) Sufficient. B is the answer