Data Sufficiency

If p and n are positive integers p >n , what is the remainder when p^2-n^2 is divided by 15

The remainder when p+q is divided by 5 is 1
The remainder when p-q is divided by 3 is 1

IMO answer is E.

is the q) p^2 - q^2 's remainder when divided by 15?

imo E...

For statement1,The remainder when p+q is divided by 5 is 1p=5 q=1---remainder is 9

p=4 q=2---remainder is 12

p=7 q=4----remainder is 3--------Insufficient

For stmt 2,
The remainder when p-q is divided by 3 is 1

p=5 q=1 -----remainder is 12

p=7 q=1-----remainder is 3--insufficient


By combining both,again we have two different remainders.So insufficient..

....

statement 1:

It states that when p+q is divided by 5 the remainder is 1

so lets assume the no to be 5n+1 ( here n=0,1,2,3...etc)

p+q=5n+1

Insufficient

statement 2:

It states that when p-q is divided by 3 the remainder is 1

so lets assume the no to be 3n+1 ( here n=0,1,2,3...etc)

p-q = 3n+1

Insufficient

Now,lets combine both the statements and see whether we can deduce a solution

for n=1
p+q=6
p-q=4
2p=10
p=5 and q=1

(p^2-n^2)/15=24/15..........remainder=9

for n=2
p+q=11
p-q=7
2p=18
p=9 and q=2

(p^2-n^2)/15=77/15.........remainder=2

IT is observed that the remainder varies in both the cases..

Hence E is the ans...

well, picking no may not be the best option as in real GMAT you may have to find the .004% of 1/0.125th growth of fat level in Jay Leno's potbelly.
So better to use

p-q = 5x +1

p+q = 3Y+1 etc.
hope that helps.

imo E

gmat009 wrote:If p and n are positive integers p >n , what is the remainder when p^2-n^2 is divided by 15

The remainder when p+q is divided by 5 is 1
The remainder when p-q is divided by 3 is 1

Quick question, wouldn't this be obviously E since both of the statements are not mentioning n at all?

gmat2010 wrote:

gmat009 wrote:If p and n are positive integers p >n , what is the remainder when p^2-n^2 is divided by 15

The remainder when p+q is divided by 5 is 1
The remainder when p-q is divided by 3 is 1

Quick question, wouldn't this be obviously E since both of the statements are not mentioning n at all?

It hink it is a typo
IMHO it should be

If p and n are positive integers p >n , what is the remainder when p^2-n^2 is divided by 15

The remainder when p+n is divided by 5 is 1
The remainder when p-n is divided by 3 is 1

I understand how the equations were derived, but how does knowing that p+q= 5z + 1 sufficient to know that statement 1 (or 2) is insufficient?

Don't you still need to pick numbers and contradict the Y-N question?

Thanks!

anb,

Refer here https://www.beatthegmat.com/remainders-t22704.html#95683

The same problem has been discussed and I have picked numbers.

Thanks!