Answer this math Question?

Question

Let p be the product of 3 consecutive numbers and q be product of another 3 consecutive numbers. The show that pq is not equal to 135?

Answer 1

Product of 3 consecutive numbers is always an even number.Product of 2 even numbers is also even. So pq cannot be equal to any odd numbers.So pq is not equal to 135.

Answer 2

Let p = a*(a+1)*(a+2)

Note that if a is odd, e.g. a=1

p = 1*(1+1)*(1+2) = 6

We get even number result because of the middle term, an odd number add 1 gives you an even number.

However if a is even, e.g. a=2

p = 2*(2+1)*(2+2) = 24

We will also get an even number because of first and last terms.

Therefore, p will always be an even number as there will always be at least one even term in the expression.

Similarly,

Let q = b*(b+1)*(b+2)

we can show that q will be an even number using the same reasoning above.

Therefore if p and q are even numbers, the product of the two numbers will also be an even number.

As such, the product of pq is not equal to 135, which is an odd number.

Answer 3

The product of 3 (or 2) consecutive numbers is even, because three consecutive numbers always contains even numbers. The product of an even number and an even number is another even number, and so it can't be 135.

Answer 4

135 = 5 * 3 * 3 * 3

135 is the product of max. 4 numbers. but pq are the product of 6 numbers.

Answer 5

The product of three consecutive numbers has to be even. The product of two even numbers is even. 135 is not even, so is not the product of p and q

Answer 6

1*2*3=6
4*5*6=120
120*6=720
not = to 135