ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: Solve it. 4376 + 3209 - 1784 + 97 = 3125 + ?

Solution:
4376 + 3209 - 1784 + 97 = 3125 + x
⇒ 7682 - 1784 = 3125 + x
⇒ x = 7682 - 1784 - 3125
⇒ x = 2773

Hence,
The number is 2773

Question: 7⁶ⁿ - 6⁶ⁿ, where n is an integer > 0, is not divisible by,

Solution:
7⁶ⁿ - 6⁶ⁿ
= 7⁶ - 6⁶
= (7³)² - (6³)²
= (7³ + 6³)(7³ - 6³)
= (343 - 216)(343 + 216)
= 127 × 559
= 127 × 13 × 43

Clearly, it is divisible by 127, 13, 559.

Question:
 

Solution:

Question: If (x - 1) is an odd number, what are the two other odd numbers nearest to it? 

Solution: 
(x - 1) is an odd number

The previous odd number = x - 1 - 2 = x - 3
The next odd number = x - 1 + 2 = x + 1

So, the two required odd numbers are: x - 3, x + 1

Question: Simplify the expression,


Solution:

Question: What will be the least number that when doubled will be exactly divisible by 12, 18, 21 and 30?

Solution:
12 = 2 × 2 × 3
18 = 2 × 3 × 3
21 = 3 × 7
30 = 2 × 3 × 5

L.C.M. of 12, 18, 21 and 30 = 2 × 3 × 2 × 3 × 7 × 5 = 1260

Hence, the required number = 1260/2 = 630

Question: Simplify it.


Solution:

Question: The sum of three consecutive even integers is 54. Find the least integer among them.

Solution:
Let us consider three consecutive even integers be x, x + 2 and x + 4

According to the question,
x + (x + 2) + (x + 4) = 54
⇒ 3x + 6 = 54
⇒ 3x = 48
⇒ x = 16

Hence, the least integer = 16

Question: Given that (1² + 2² + 3² + .......... + 10²) = 385, then the value of (2² + 4² + 6² + .......... + 20²) is equal to = ?

Solution:
(2² + 4² + 6² + .......... + 20²)
= (1 × 2)² + (2 × 2)² + (3 × 2)² + ............. + (2 × 10)²
= (1² × 2²) + (2² × 2²) + (3² × 2²) ............ + (2² × 10²)
= 2²(1² + 2² + 3² + .......... + 10²)
= 4 × 385 [Putting the value (1² + 2² + 3² + .......... + 10²) = 385]
= 1540

Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 147. What is that number?

Solution:
Let the number be x

According to the question,
3(2x + 9) = 147
⇒ 6x + 27 = 147
⇒ 6x = 147 - 27
⇒ 6x = 120
⇒ x = 120/6 
∴ x = 20

Hence, the number is 20.

Question: What is the value of x in the following equation,


Solution:

Question: The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can be the set of the four numbers?

Solution:
Using options,
We find that four consecutive odd numbers are 37, 39, 41 and 43

Here, 37 + 39 + 41 + 43 = 160

The sum of these 4 numbers is 160, when divided by 10 we get 16 which is a perfect square.

Hence, the required set = 37, 39, 41 and 43

Question: Find the value of,


Solution:

Question: If the sum of a number and its reciprocal be 2 then the number is = ?

Solution:
Let the number be = x
The reciprocal of the number is = 1/x

According to the question,
x + (1/x) = 2
⇒ x² + 1 = 2x
⇒ x² - 2x + 1 = 0
⇒ (x - 1)² = 0
∴ x = 1

Hence, the number = 1

Question: A man has Tk. 640 in the denominations of one-taka notes, five-taka notes and ten-taka notes. The number of notes of each denomination is equal. Simplify this with equation and what is the total number of notes that he has?
 
Solution:
Let the number of notes of each denomination be x.

Then
x + 5x + 10x = 640
⇒ 16x = 640
∴ x = 40

Hence, the total number of notes = 3x = 120