CAT Quantitative Aptitude Questions | CAT Number Systems - Remainders

The question is from CAT Remainders. We need to find out the posssible remainders when a number is divided by 'a', given the remainder when it is divided by 'b'. 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 3: A number when divided by 18 leaves a remainder 7. The same number when divided by 12 leaves a remainder n. How many values can n take?

1. 2
2. 0
3. 1
4. 3

Explanatory Answer

Method of solving this CAT Question from Number Theory - Remainders: How many possible remainders are there when A is divided by B, especially when we know that A by C leaves a specific remainder.

Number can be 7, 25, 43, 61, 79.

Remainders when divided by 12 are 7 and 1.

n can take exactly 2 values

The question is "How many values can n take?"

Hence the answer is "2".

Choice A is the correct answer.