if a is a positive integer, is there any integer n where (1<n<a) such that a/n is an integer?
Considering
Statement 1 alone1) a is a multiple of a prime numberFor example, lets consider the prime number to be 5.
If a is a multiple of prime number 5, a could be 5 or 10 or 15 or ...
which shows that a could be the prime number itself or any of the other multiples.
If a is the prime number itself, then n takes the vale of any integer between 1 and 5
In this case, a/n is not an integer.
However, if a is not the prime number itself, but takes other values 10 or 15 or ...
n can the vale of 5 and
in this case a/n will be an integer (eg. a=15 and n=5, a/n = 3)
As both the above cases are opposing and do not give a unique answer,
statement 1 by itself is not sufficient.Considering
Statement 2 alone2) a is a product of 2 integers.If a (eg. 6) is a product of two integers (eg. 2 and 3), a is not a prime number.
Additionally, the two factors (eg. 2 and 3) of a will lie between 1 and a.
Thus, n can take up the values of these two factors (eg. 2 and 3) of a (eg. 6)
Therefore, a/n will be an integer.As statement 2 is sufficient by itself,
the Answer is Option B _________________
Your critical analysis of this post is appreciated and would help me reach 700+