# CAT Quant Practice Problems

Question: If n = 1+ x where x is the product of four consecutive positive integers, then which of the following is/are true?

A. n is odd

B. n is prime

C. n is a perfect square

1. A and C only
2. A and B only
3. A only
4. None of these

Correct Option:1

Let the four consecutive number be $( a - 2 ) , ( a - 1 ) ,$ a,
$( a + 1 )$ .
Multiplying these, we get
$\left( a ^ { 4 } - 2 a ^ { 3 } - a ^ { 2 } + 2 a \right) ,$ which will always be even.
By the problem we add 1 .

Thus the expression becomes $\left( a ^ { 4 } - 2 a ^ { 3 } - a ^ { 2 } + 2 a + 1 \right)$
which is odd.
This is also the perfect square of $\left( a ^ { 2 } - a - 1 \right)$
You can also take any four consecutive numbers and check for the validity.