Question

The product of two positive numbers is p. If each of the numbers is increased by 2, the new product is how much greater than twice the sum of the two original numbers ?

A) p times B) 2p times C) (p + 4) times D) (2p + 3) times

Answer 1

Answer:   C) (p + 4) times

Explanation:

Let the two numbers be a and b.

Given: product of the numbers is: p = ab

If each of the numbers is increased by 2, then the new product:

(a+2)(b+2) = ab + 2a + 2b + 4

= ab + 2(a+b) + 4

= p + 2(a+b) + 4

Hence, the new product is (p+4) times greater than twice the sum of the two original numbers.

Final answer is Opt. C) (p + 4) times.

Answer 2

$\huge\bold{Question :-}$

The product of two positive numbers is p. If each of the numbers is increased by 2, the new product is how much greater than twice the sum of the two original numbers ?

A) p times

B) 2p times

C) (p + 4) times

D) (2p + 3) times

Given :

Product of the numbers is: p = ab

$\huge\bold{Answer :-}$

Let the two numbers be a and b.

If each of the numbers is increased by 2, then the new product:

(a+2)(b+2) = ab + 2a + 2b + 4

= ab + 2(a+b) + 4

= p + 2(a+b) + 4

Hence, the new product is (p+4) times greater than twice the sum of the two original numbers.

Final answer :

C) (p + 4) times.