Explanation

• 997 is a prime number, while 996, 998, and 999 are not.
  • 996 is divisible by 2, 3, 6, 12, ..., and is therefore not prime.
  • 998 is divisible by 2, 7, 14, ..., and is therefore not prime.
  • 999 is divisible by 3, 9, 27, ..., and is therefore not prime.

• So, the greatest 3-digit prime is 997.

Explanation

The prime numbers from 1 to 100 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Explanation

9600=27∗3∗52 So the total number of divisors= 8∗2∗3=48

Explanation

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Explanation

Here we need sum of 2,4,6,……..,98(between 1 and 100)

Now here First term = 2 difference= 2, n = 50

So now sum of these terms = n/2(2a+(n-1)d)

= 49/2(2*2+(50–1)2)

= 49/2(4+(49)*2)

= 49/2(4+98)

= 49/2(102)

= 49*51

=2550

Explanation

The mid point of (2,7) and (4,1) is (3,4).

Explanation

Explanation

Step 1: Calculate the square root of 9

√9 = 3

Step 2: Multiply 3 by the square root of 9

3 × 3 = 9

Explanation

 Natural numbers start from 1 (1, 2, 3, ...), so the 150th natural number is simply 150.

Explanation

Using the concept of work and rate, we can analyze the given information:

A+B = 1/18 (work done per day)

A+C = 1/12

B+C = 1/9

By adding the first two equations, we get:

(A+B) + (A+C) = 1/18 + 1/12

2A + (B+C) = 1/6

2A + 1/9 = 1/6

2A = 1/6 - 1/9

2A = 1/18

A = 1/36 (work done by A per day)

Now, we can find B's work per day:

B = 1/18 - 1/36 = 1/24

So, B alone can do the work in 24 days.