Find the least number which when divided by 5 leaves no remainder, when divided by 4 leaves a remainder of 1, but when divided by 6 or 7, leaves a remainder of 5.

Correct option is C

Given:

Find the least number which satisfies the following:

Divisible by 5 then, remainder 0

Divided by 4 then, remainder 1

Divided by 6 or 7 then, remainder 5

Solution:

We will check each option.

Option A: 400

400 ÷ 5 = 80 right

400 ÷ 4 = 100 then, Remainder 0 ( wrong)

Option B: 450

450 ÷ 5 = 90 right

450 ÷ 4 = 112 Remainder 2  wrong

Option C: 425

425 ÷ 5 = 85  right

425 ÷ 4 = 106 Remainder 1  right

425 ÷ 6 = 70 Remainder 5  right

425 ÷ 7 = 60 Remainder 5  right
All conditions satisfied

Option D: 430

430 ÷ 5 = 86 right

430 ÷ 4 = 107 Remainder 2  wrong

Thus, Option(C) is correct.