Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 58)
58.
On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is:
Answer: Option
Explanation:
Clearly, (2272 - 875) = 1397, is exactly divisible by N.
Now, 1397 = 11 x 127
The required 3-digit number is 127, the sum of whose digits is 10.
Discussion:
34 comments Page 2 of 4.
Koushal patil said:
5 years ago
Both leaving same remainder(let Remainder is R) hence,
2272-R and 875-R Both are completely divisible by number.
Their difference will also divisible by the number,
(2272-R)-(875-R) = 1397.
Factors of 1397 = 11*127.
Asked for 3 Digit number.
Hence sum of digits is 1+2+7 = 10.
2272-R and 875-R Both are completely divisible by number.
Their difference will also divisible by the number,
(2272-R)-(875-R) = 1397.
Factors of 1397 = 11*127.
Asked for 3 Digit number.
Hence sum of digits is 1+2+7 = 10.
Kuldeep Gupta said:
9 years ago
If a Two numbers are divisible by same number & gives the same remainder that means they belong to same table.
And their difference will also be divisible by same number.
e.g.
Let 4 & 10 be the numbers.
let N be 2.
So (10 - 4) = 6 is also divisible by N = 2.
And their difference will also be divisible by same number.
e.g.
Let 4 & 10 be the numbers.
let N be 2.
So (10 - 4) = 6 is also divisible by N = 2.
Sravan said:
1 decade ago
Consider that if two nos if divided by a same divisor gets same reminders. Then the difference between the nos will be exactly divisible by the divisor.
For example:
5/2 remainder is 1.
9/2 remainder is 1.
9-5 = 4, which is exactly divisible by 2.
For example:
5/2 remainder is 1.
9/2 remainder is 1.
9-5 = 4, which is exactly divisible by 2.
Mathu said:
4 years ago
@All.
Here is the solution.
2272-R=0(mod N).
875-R=0(mod N).
2272-875=0(mod N).
1397=0(mod N).
So, any factor of 1397 can be the answer for N which 127 will be correct according to the question given (3digit numbers).
1+2+7=10.
Here is the solution.
2272-R=0(mod N).
875-R=0(mod N).
2272-875=0(mod N).
1397=0(mod N).
So, any factor of 1397 can be the answer for N which 127 will be correct according to the question given (3digit numbers).
1+2+7=10.
(5)
Deepak said:
5 years ago
a=np+r
2272 = np + r ----------> (1)
b=nq+r
875=nq+r --------------> (2).
Subtracting (1)-(2).
2272-875 = n(p-q),
1397 = n(p-q),
1397 is only divisible by 11,
1397 = 11*127.
Hence n=127,
p-q = 11,
1+2+7=10.
2272 = np + r ----------> (1)
b=nq+r
875=nq+r --------------> (2).
Subtracting (1)-(2).
2272-875 = n(p-q),
1397 = n(p-q),
1397 is only divisible by 11,
1397 = 11*127.
Hence n=127,
p-q = 11,
1+2+7=10.
(6)
Ved said:
8 years ago
Once we get to 1397 & we know it is completely divided by N then we can use the options provided to find out the value of N.
Because 1397 must be completely divisible by one of them.
Because 1397 must be completely divisible by one of them.
Alaluddin akanda said:
7 years ago
Let;
a=pn+r.....(1)
b=qn+r......(2)
(1)-(2)
a-b==n(p-q)
or a-b=nd
So, a-b also exactly divisible by n.
a=pn+r.....(1)
b=qn+r......(2)
(1)-(2)
a-b==n(p-q)
or a-b=nd
So, a-b also exactly divisible by n.
SOURJYA MONDAL said:
2 years ago
2272 - 875 = 1397 which is divisible by 11.
i.e. , 1397 = 11 X 127.
so, 1+2+7 = 10.
i.e. , 1397 = 11 X 127.
so, 1+2+7 = 10.
(4)
Lava said:
8 years ago
I can't understand the steps. Can anyone please explain with an easy method?
Jagdish Chandra Pandey said:
4 years ago
2272-875 = 1397 difference,
1397/11 = 127 divisible by 11,
1+2+7 = 10.
1397/11 = 127 divisible by 11,
1+2+7 = 10.
(1)
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