ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: The difference between the greatest and least prime numbers which are less than 80 is- 

Solution: 
Greatest prime number = 79
Least prime number = 2
So, their difference = 79 - 2 = 77

Question: What is the least common multiple (LCM) of 18 and 24? 

Solution: 
18 = 2 × 3 × 3 
24 = 2³ × 3 

the least common multiple (LCM) of 18 and 24 = 2³ × 3 × 3 
= 72

Question: The sum of first 40 natural numbers is -

Solution: 
We know that,
The sum of the first n natural numbers is n(n+1)​/2

Sum of first 40 natural numbers is = 40(40 + 1)/2
= 820

Question: What smallest number should be added to 4456 so that the sum is completely divisible by 6?

Solution: 
4456 divided by 6 leaves a remainder of 4. Therefore, we need to add 2 to 4456 to make the sum divisible by 6.

4456 + 2 = 4458, and when divided by 6, this results in a remainder of 0.

Question: The smallest 3-digit prime number is:

Solution: 
১ এর চেয়ে বড় যে সকল সংখ্যাকে শুধু ১ এবং ঐ সংখ্যা ছাড়া আর কোনো সংখ্যা দ্বারা ভাগ করা যায় না, তাদেরকে মৌলিক সংখ্যা বলে। 
অর্থাৎ মৌলিক সংখ্যার উৎপাদক হবে দুইটি: ১ এবং শুধুমাত্র সেই সংখ্যাটি।
তিন অঙ্ক বিশিষ্ট সবচেয়ে ছোট মৌলিক সংখ্যা = ১০১। 

Question: What is the GCD of 18 and 30?

Solution: 
18 = 2 × 3 × 3 
30 = 2 × 3 × 5

the GCD of 18 and 30 is =  2 × 3 = 6

Question: On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder?

Solution: 
If a number divided by 56 leaves a remainder of 29, we can express it as:
Number = 56 × Quotient + 29

Now, to find the remainder when this number is divided by 8, let's try to simplify the expression.
Number = 56 × Quotient + 29

We know that 56 is divisible by 8, so let's express 56 in terms of 8:
56 = 8 × 7

Therefore, we can rewrite the expression for the number:
Number = 8 × 7 × Quotient + 29
Number = 8 × (7 × Quotient) + 29

Now, when we divide this expression by 8, we'll focus on the remainder:

8 × (7 × Quotient) leaves no remainder when divided by 8 because it's a multiple of 8.

So, the remainder when 29 is divided by 8 is 5.

Question: How many numbers between 1000 and 5000 are exactly divisible by 225?

Solution: 
225 × 5 = 1125
.
.
.
225 × 22 = 4950

numbers between 1000 and 5000 are exactly divisible by 225 = 22 - 5 + 1
= 18  

Question: 7 is added to a certain number; the sum is multiplied by 5, the product is divided by 9 and 3 is subtracted from the quotient. The remainder left is 12. The number is:

Solution:
Let the original number be x

Now
{5(x + 7)/9} - 3 = 12
⇒ {5(x + 7) - 27}/9 = 12
⇒ 5(x + 7) - 27 = 108
⇒ 5x + 35 - 27 = 108
⇒ 5x + 8 = 108
⇒ 5x = 100
∴ x = 20

Question: A prime number N, in the range of 10 to 40, remains unchanged when its digits are reversed. The square  of such a number is: 

Solution: 
মৌলিক সংখ্যা ১১ এর একক ও দশক স্থানীয় অঙ্ক একই। 

১১^২ 
= ১২১ 

Question: The difference between three times and seven times of a number comes to 36. What is the number?

Solution: 
let, the number be x 

ATQ, 
7x - 3x = 36 
⇒ 4x = 36
⇒ x =36/4 = 9

Question: The L.C.M of three different numbers is 120. Which of the following can't be their H.C.F? 

Solution: 
যেহেতু গ.সা.গু , ল.সা.গু র একটি উৎপাদক , তাই তিনটি সংখ্যার ল.সা.গু ১২০ হলে তাদের গ সা গু ৩৫ হবে না। 
কারণ, ১২০, ৩৫ দ্বারা নিঃশেষে বিভাজ্য নয়।  

Question: If n is an integer between 10 and 70, then any of the following could be n + 7 except-

Solution: 
maximum value of n + 7 = 69 + 7 = 76 
78 > 76
So, the correct answer is A

Question: The product of two numbers is 72 and the sum of their squares is 145. The sum of the numbers is:

Solution: 
let the two numbers be x, y 

xy = 72 
x² + y² = 145
⇒ (x + y)² - 2 × 72 = 145
⇒ (x + y)² = 289
∴ x + y = 17

Question:  Find the number of the divisors of 72

Solution: 
72
= 3² × 2³ 

the number of the divisors of 72 is = (2 + 1) × (3 + 1)
= 3 × 4 
= 12

Question: Three numbers are in ratio 1 : 2 : 3 and HCF is 17. The largest number is:

Solution: 
let, the numbers are x, 2x, 3x
HCF is x 
x = 17 

largest number = 17 × 3 
= 51