Number Properties: product of prime numbers

[Gmater-1]

For any positive integer n, [n] denotes the product of all the positive even numbers from 2 to n, what is the largest prime factor of [23]+[21]

a. 23
b. 19
c. 11
d. 7
e. 5

HOw to solve this question within 2 mins

thanks for your approaches.

Official Answer is

SPOILER: A

[narinder82]

[23] = 2x4x6x8x10x12x14x16x18x20x22
[21]= 2x4x6x8x10x12x14x16x18x20 = Say Y

[21] + [23] = Y + Yx22 = Y[1+22] = Yx23.

Ans is 23 i.e A.

[AKSTCS]

My take:-

[23]+[21]
= 2.4.6.8………22 + 2.4.6…..20

= 2.4.6.8……..20 (22 + 1)

= 2.4.6.8……..20 (23)


Now all the even nos. till 20 will have prime factors < 20
Thus, 23 will be the maximum.

Hence, answer A.