Question

Multiply the consecutive even
positive integers together until the
product 2.4.6.8............... becomes
divisible by 1995. The largest even
integer used is :
(A) between 1 and 21
(B) between 21 and 31
(e) between 31 and 41
(D) bigger than 41
​

Answer 1

Given :- Multiply the consecutive even positive integers together until the product 2.4.6.8________ becomes divisible by 1995. The largest even integer used is :

(A) between 1 and 21

(B) between 21 and 31

(e) between 31 and 41

(D) bigger than 41

Answer :-

→ 2 * 4 * 6 * 8 * _________ = n * 1995

→ 2 * 4 * 6 * 8 * _________ = n * 3 * 5 * 7 * 19

so,

→ 2 * 4 * (2*3) * ____ 12 * (2 * 7) _______ 36 * (2 * 19) = n * 3 * 5 * 7 * 19 .

in this case all RHS multiple of 1995 will be cancel from LHS and we gets n .

therefore, we can conclude that, the largest even integer we must used is 38 .

hence, Option (e) between 31 and 41 is correct answer.

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