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.
DIVISIBILITY AND REMAINDERS
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Source: Beat The GMAT — Data Sufficiency |
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
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
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palvarez
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Forget about verbal reasoning when you come to this kind of problems. Set up algebraically, using modulus, etc.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
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.
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hpgmat
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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 Rpalvarez wrote:Forget about verbal reasoning when you come to this kind of problems. Set up algebraically, using modulus, etc.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
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.
Will Win
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palvarez
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I din't use the garbage of quotients. Just dont use quotients at all when you are dealing with remainders.hpgmat wrote: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?palvarez wrote:Forget about verbal reasoning when you come to this kind of problems. Set up algebraically, using modulus, etc.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
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.
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)
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aks.anupam
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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
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
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sreak1089
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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.
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
....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
