In a class of students, the first student has 2 toffees, second has 4 toffees, third has 6 toffees and so on. If the number of students in the class is 25, then the total number of toffees are divisible by .

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 2)

Answer 1

Given:

In a class of students, the first student has 2 toffees, the second has 4 toffees, the third has 6 toffees, and so on.

Concept used:

1. Number of terms of an AP = (L - A)/D + 1

2. Sum of N terms of an AP = (L + A)/2 × N

3. N^th term = A + (N - 1) × D

(Where L = Last Term, A = First Term and D = Common Difference)

Calculation:

The number of toffees according to the number of students is in an Arithmetic Progression where

2 = First Term

(4 - 2) = (6 - 4) = ... = 2 = Common Difference

So, the number of toffees 25th student will get = 2 + (25 - 1) × 2 = 50

Now, the total number of toffees

⇒ (2 + 50)/2 × 25

⇒ 26 × 25

⇒ 2 × 5² × 13

∴ The total number of toffees is divisible by 5 and 13.