If a and b are non-negative integers and a/b is an integer, is b divis

FROM STEM , a could be zero or +ve integer , b is +ve integer ( could be =1) , is b/a = integer

from 1

a = 12 , b could be 12 or 1 ... insuff

from 2

b is a multiple of 12 , but a could = zero... insuff

both

b= 12 a = 12 ... thus b/a is integer ....SUFF

C

If a/b is an integer doesn't it mean b is a factor of a (or a is a multiple of b)? If that's the case, how can b be divisible by a (how can b become multiple of a)? Could you please let me know if there is anything wrong in my understanding?

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.


We can assume 2 variables and 1 equation. Thus C could be the answer most likely.

Condition 1) \(a = 12\)
This condition alone is not sufficient, since there is no information about \(b\).

Condition 2) \(b = 12k\) for some integer \(k\)
This condition alone is not sufficient, since there is no information about \(a\).

Condition 1) & 2)

Since \(b = 12k\) for some integer \(k\), \(b/a = 12k/12 = k\), which is an integer.
Thus \(b\) is divisible by \(a\).

Both conditions together are sufficient.

Therefore, C is the answer as expected.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________