Question

The difference between the largest 3 digit natural number x such that x = 5(mod 8) and the smallest 3 digit natural number y such that y = 2(mod 5) is

Answer 1

Answer:

Step-by-step explanation:

The difference between the divisor and remainder in each case is 1,such as 3-2=1,4-3=1 & 5-4=1. Now the LCM of divisors will be 3×4×5=60. Now it is evident that 60 and multiples of 60 are divisible by 3,4& 5 individually or with any combined forms. To satisfy the questioned condition we have to subtract 1 from the multiples of 60 upto 300 considering three digit numbers only upto 300 for the desired result. Hence the numbers are,120-1=119,180-1=179,240-1=239 & 300-1=299.

Ans: four numbers, 119,179,239 & 299.