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:
10
11
12
13
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.

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.

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.

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.
(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.
(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.

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.

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.
(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.
(1)


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