DIVISIBILITY AND REMAINDERS

N IS A POSITIVE NUMBER AND R IS THE REMAINDER WHEN 4+7N IS DIVIDED BY 3. WHAT IS THE VALUE OF R?

1) N+1 IS DIVISIBLE BY 3
2)N > 20

1) is sufficient: Since N+1 is divisible by 3, N can be 2, 5, 8, 11 .... Let's try each one of them
N=2, then 4+7N = 4+14 = 18 >> 18 div 3 = remainder = 0
Similarly you get 0, if you try N = 5,8,11,14...

2) not sufficient since N>20 means, N can be 21,22,23,24...etc which does not give the same remainder.

Hope it heps.

THANK YOU. I GUESS PLUGGING IN NUMBERS IS NOT A BAD STRATEGY AFTER ALL

4+7N=3*c+R where c is an integer.(1)
1+N+3+6N=3*c+R
1+N=-3-6N+3*c+R
1+N=3*(c-2N)+R-3
by 1 we know that N+1=3*d where d is an integer
then we know that R-3=0 then R=3.
subsituting in (1)
yields 4+7*N=3*(c+1)
put c+1=e
4+7*N=3d
reminder is 0
then 1 is sufficient
2 is not

hpgmat wrote:N IS A POSITIVE NUMBER AND R IS THE REMAINDER WHEN 4+7N IS DIVIDED BY 3. WHAT IS THE VALUE OF R?

1) N+1 IS DIVISIBLE BY 3
2)N > 20

Forget about verbal reasoning when you come to this kind of problems. Set up algebraically, using modulus, etc.

4+7n = r (3)

1 + n = r (3)

1. n +1 = 0 (mod 3)
n = 2 (mod 3)
r = n+1 (mod 3) = 3 (mod 3) = 0 Sufficient.

2. n > 20, we need to know n (mod 3). Useless.

A is sufficient.

palvarez wrote:

hpgmat wrote:N IS A POSITIVE NUMBER AND R IS THE REMAINDER WHEN 4+7N IS DIVIDED BY 3. WHAT IS THE VALUE OF R?

1) N+1 IS DIVISIBLE BY 3
2)N > 20

Forget about verbal reasoning when you come to this kind of problems. Set up algebraically, using modulus, etc.

4+7n = r (3)

1 + n = r (3)

1. n +1 = 0 (mod 3)
n = 2 (mod 3)
r = n+1 (mod 3) = 3 (mod 3) = 0 Sufficient.

2. n > 20, we need to know n (mod 3). Useless.

A is sufficient.

I believe r in your equations represent the quotient ( vs R for reminder). Any how, in your first equation (4+7n = r (3))youve made an assumption that R is equal to zero. . ... how did you make that assumption? we dont know the value of R

hpgmat wrote:

palvarez wrote:

hpgmat wrote:N IS A POSITIVE NUMBER AND R IS THE REMAINDER WHEN 4+7N IS DIVIDED BY 3. WHAT IS THE VALUE OF R?

1) N+1 IS DIVISIBLE BY 3
2)N > 20

Forget about verbal reasoning when you come to this kind of problems. Set up algebraically, using modulus, etc.

4+7n = r (3)

1 + n = r (3)

1. n +1 = 0 (mod 3)
n = 2 (mod 3)
r = n+1 (mod 3) = 3 (mod 3) = 0 Sufficient.

2. n > 20, we need to know n (mod 3). Useless.

A is sufficient.

I believe r in your equations represent the quotient ( vs R for reminder). Any how, in your first equation (4+7n = r (3))youve made an assumption that R is equal to zero. . ... how did you make that assumption?

I din't use the garbage of quotients. Just dont use quotients at all when you are dealing with remainders.

r is a remainder. Just used small letters.

"when 4 + 7n is divided by 3, remainder is r"

Translate that line, algebraically wrt modulus, etc.

4 +7n = r (modulo 3)

1 + n = r (modulo 3), because 4 (modulo 3) =1, 7n(modulo 3) = 7(modulo 3)*n(moduo 3) = 1 (modulo 3) * n (modulo 3) = n (modulo 3)

Another simple solution can be:

1) N+1 is divisible by 3

i.e. 7N+7 would also be divisible by 3
or, 7N+7 - 3 would also be divisible by 3
or 7N+4 is also divisible by 3
This is what we need to find out: the remainder when 4+7N is divided by 3 : its zero.

Hence SUFFICIENT.

2) N>20. No other information given. Not possible to tell the remainder. Hence INSUFFICIENT.

So the answer is A

My Approach:

R = (7n + 4) % 3 (% is a C-programming syntax for remainder

stmt 1: n+1 divisible by 3
=> n+1 = 3k
=> n = 3k -1

Substitute n in eqn for R

R = (7(3k - 1) + 4) % 3
= (21k - 3) % 3
= 3(7k -1) % 3
= 0

Hence stmt 1 is SUFFICIENT.

stmt 2: n > 20

Multiple values possible for R.

Hence stmt 2 is NOT SUFFICIENT.

Hence Ans is A.

lets keep this simple...lets not get excited
....what is modulo

aks.anupam wrote:Another simple solution can be:

1) N+1 is divisible by 3

i.e. 7N+7 would also be divisible by 3
or, 7N+7 - 3 would also be divisible by 3
or 7N+4 is also divisible by 3
This is what we need to find out: the remainder when 4+7N is divided by 3 : its zero.

Hence SUFFICIENT.

2) N>20. No other information given. Not possible to tell the remainder. Hence INSUFFICIENT.

So the answer is A

Just one doubt: N is given as a positive number but not an integer. How can we assume it to be an integer?