# CAT Quantitative Aptitude Questions | CAT Number Systems - Remainders

###### CAT Questions | Number Theory | Divisibilty - Large number CAT Questions

The question is from CAT Number Theory - Remainders. A large number is given and we need to find out the divisibility of 7, 11, 13, 17. A range of CAT questions can be asked based on this simple concept of Remainders. When we divide 24 pigeons into 5 groups, 4 are left out or remain. This is the remainder. When there is a question based on this idea in the exam, we have a CAT among the pigeons.

Question 12: Given a number, N = 555 + 175 – 725, then which of the following is true?

1. N is divisible by both 7 and 13
2. N is divisible by both 3 and 17
3. N is divisible by 17 but not 3
4. N is divisible by 11 but not 17

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##### Method of solving this CAT Question from Number Theory - Remainders: Try expressing the given number in terms of multiples of the divisors.

N = 555 + 175 – 725
N = (54 + 1)5 + (18 - 1)5 – 725
The above is divisible by 3

N = (51 + 4)5 + 175 – (68 + 4)5
The above is divisible by 17
N = 555 + (11 + 6)5 – (66 + 6)5
The above is divisible by 11
N cannot be expressed in favourable of 7 and 13 and hence is not divisible by 7 and 13
From the above the best answer choice is (B) – N is divisible by both 3 and 17

The question is "which of the following is true?"

##### Hence the answer is N is divisible by both 3 and 17.

Choice B is the correct answer.

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