Remainders

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Stockmoose16: Master | Next Rank: 500 Posts; Posts: 347; Joined: Mon Aug 04, 2008 1:42 pm; Thanked: 1 times

Remainders

by Stockmoose16 » Wed Nov 12, 2008 8:54 pm

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

Anyone know how to solve this problem? I'm trying to use the remainders formula: N=QD+R

It mentions N in the question stem, then never mentions it again, so I'm confused.

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Source: Beat The GMAT — Data Sufficiency | Wed Nov 12, 2008 8:54 pm

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pm; Thanked: 237 times; Followed by:25 members; GMAT Score:730

Re: Remainders

by logitech » Wed Nov 12, 2008 9:29 pm

SM16, where is this question from bro ?

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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vishubn: Legendary Member; Posts: 574; Joined: Sun Jun 01, 2008 8:48 am; Location: Bangalore; Thanked: 28 times

by vishubn » Wed Nov 12, 2008 9:31 pm

WOWW!!
No wayss @! this king of all typos!! no way one cal solve this

Vishu

KILL !! DIE !! or BEAT my FEAR !!! de@D END!!

Quote

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pm; Thanked: 237 times; Followed by:25 members; GMAT Score:730

by logitech » Wed Nov 12, 2008 9:35 pm

vishubn wrote:WOWW!!
No wayss @! this king of all typos!! no way one cal solve this

Vishu

okay lets make our own problem then, what the hell!

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

alright lets go!

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

Quote

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pm; Thanked: 331 times; Followed by:11 members

by cramya » Wed Nov 12, 2008 9:39 pm

It mentions N in the question stem, then never mentions it again, so I'm confused

Either all n's needs to be replaced by q or vice versa.

I picked numbers and still got E)

Whats the OA?

Stmt I

p=4 q=2
Remainder for p^2-q^2/15 will be 12

p=10 q=6
Remainder for p^2-q^2/ 15 will be 4

INSUFF

Stmt II

p=8 q=4

Remainder for p^2-q^2/ 15 will be 3

p=11 q=4

Remainder for p^2-q^2 / 15 will be 0

INSUFF

Stmt I amd I together

lcm of 5 and 3 is 15 so pick 16 and 31 (1 more than the multiples of their lcm)

p=10 q=6

Remainder for p^2-q^2 / 15 will be 4

p=19 q=12

Remainder for p^2-q^2 / 15 will be 7

E)

Quote

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pm; Thanked: 237 times; Followed by:25 members; GMAT Score:730

by logitech » Wed Nov 12, 2008 9:49 pm

logitech wrote:
vishubn wrote:WOWW!!
No wayss @! this king of all typos!! no way one cal solve this

Vishu
okay lets make our own problem then, what the hell!

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

alright lets go!

p^2-n^2 = (p+n) (p-n)

So we are trying to find the remainder when it is divided by 15

1 and 2 insuf they talk either p+n or p-n

1+2)

p+n = 5x+1
p-n= 3y+1

(5x+1)*(3y+1)/3*5

(x,y) = 0,0 --> R=1
(x,y) = 1,0 --> R=6

Hence, E

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

Quote

vishubn: Legendary Member; Posts: 574; Joined: Sun Jun 01, 2008 8:48 am; Location: Bangalore; Thanked: 28 times

by vishubn » Wed Nov 12, 2008 10:34 pm

A) so adding up p+q is always one numebr greatre than multiple of 5

now p=11, q=5

and stem /15 give remainder of 1

again p=16 q=5 gives u the diffe remainder
Inssuff

B)p=12,n=3

Isufficent Again

A and C togetrjer also Insufficent

OA E

KILL !! DIE !! or BEAT my FEAR !!! de@D END!!