Bank Math Master

Question: What is the value of 5 + 4 × 5 + 4 × 5² + 4 × 5³ + 4 ×5⁴ + 4 × 5⁵?

Solution:
5 + 4 × 5 + 4 × 5² + 4 × 5³ + 4 ×5⁴ + 4 × 5⁵
= 5 + (5 - 1) × 5 + (5 - 1) × 5² + (5 - 1) × 5³ + (5 - 1) × 5⁴ + (5 - 1) × 5⁵
= 5 + 5² - 5 + 5³ - 5² + 5⁴ - 5³ + 5⁵ - 5⁴ + 5⁶ - 5⁵
= 5⁶

Question: What will be the least number which when doubled will be exactly divisible by 18, 24, 28, and 36?

Solution:
LCM of 18, 24, 28, and 36 is = 504
So, the number will be half of 504 = 504/2 = 252

Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is-

Solution:
Let A, B, C represent their respective weights.

Then, we have:
A + B + C =(45 × 3) = 135..............(i)
A + B = (40 × 2) = 80.................(ii)
B + C=(43 × 2) = 86.................(iii)

Adding (ii) and (iii),
we get: A + 2B + C =80 + 86
A + 2B + C =166 .....(iv)

Subtracting (i) from (iv),
we get:
A + 2B + C - (A + B + C) = 166 - 135 
B = 31

∴ B's weight =31 kg.

Question: Find the value of (3log2 + 2log3)/(log36 + log2)

Solution:
3log2 + 2log3
= log2³ + log3²
= log8 + log9
= log(8×9)
= log72


log36+log2
= log(36 × 2)
= log72

(3log2 + 2log3) / (log36 + log2)
=log72 / log72
= 1

Question: The value of (0.1 × 0.1 × 0.1 + 0.02 × 0.02 × 0.02)/(0.2 × 0.2 × 0.2 + 0.04 × 0.04 × 0.04) is -

Solution:
(0.1 × 0.1 × 0.1 + 0.02 × 0.02 × 0.02)/(0.2 × 0.2 × 0.2 + 0.04 × 0.04 × 0.04)
= {(0.1)³ + (0.02)³}/{8(0.1 × 0.1 × 0.1) + 8(0.02 × 0.02 × 0.02)}
= {(0.1)³ + (0.02)³}/[8{(0.1)³ + (0.02)³}]
= 1/8
= 0.125

Question: A man has Tk. 480 in the denominations of one-taka notes, five-taka notes and ten-taka notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
 
Solution:
Let number of notes of each denomination be x.

Then
x + 5x + 10x = 480
⇒ 16x = 480
∴ x = 30.

Hence, total number of notes = 3x = 90.

Question: Which of the following fractions is the largest? 

Solution: 
3/2 = 1.5
7/4 = 1.75
5/3 = 1.66
6/5 = 1.2 
Hence the largest fraction is 7/4 

Question: What is the least number which when divided by the numbers 3, 5, 6, 8, 10, and 12 leaves no remainder?

Solution:
LCM of 3, 5, 6, 8, 10, and 12 = 120

Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

Solution:
Let.
C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.

ATQ,
(2x + 2) + 2x + x = 27
⇒ 5x = 25
∴ x = 5.

Hence, B's age = 2x = 10 years.

Question: What least number must be added to 1056, so that the sum is completely divisible by 23?

Solution:
1056 কে 23  দ্বারা ভাগ করলে 21 অবশিষ্ট থাকে।

এখানে
23 - 21 = 2
2, 1056 এর সাথে যোগ করলে যোগফল 23 দ্বারা বিভাজ্য ।
 

Question: A grocer has a sale of Tk. 6435, Tk. 6927, Tk. 6855, Tk. 7230 and Tk. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Tk. 6500?

Solution:
Total sale for 5 months = Tk. (6435 + 6927 + 6855 + 7230 + 6562)
= Tk. 34009.

Required sale = Tk. [ (6500 x 6) - 34009 ]
= Tk. (39000 - 34009)
= Tk. 4991.

Question: What is the least perfect square that is a multiple of 7, 11 and 12?

Solution:
Let us assume the least perfect square be X
⇒ 7 = 7 × 1
⇒ 11 = 11 × 1
⇒ 12 = 2 × 2 × 3 

The LCM of (7, 11, 12) = 2× 2 × 3 × 11 × 7

⇒ The least perfect square = 2² × 3² × 11² × 7² = 213444
∴ The required result will be 213444.

Question: What is the greatest number that divides 84, 144 or 18 without any remainder?

Solution:
HCF of the given numbers will be the greatest number which can divide 48, 84 and 144
18 = 2 × 3 × 3
84 = 2 × 2 × 3 × 7
144 = 2 × 2 × 2 × 2 × 3 × 3
∴ HCF = 2 × 3 = 6
Hence 6 is the greatest number which divides 18, 84 and 144 without leaving any remainder

Question: 0.777777 ÷ 0.011 =?

Solution:
0.777777 ÷ 0.011 = 70.707

Question: What should come in place of both x in the equation x /√128 = √162/x.

Solution:
 x /√128 = √162/x
⇒ x² = √(128 × 162)
⇒ x² = √(64 × 2 × 18 × 9)
⇒ x² = √(8² × 6² × 3²)
⇒ x² = 8 × 6 × 3
⇒ x² = 144
∴ x = 12

Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

Solution:
Let,
The son's present age is x years.
Then, the man's present age is = (x + 24)
∴ (x + 24) + 2 = 2(x+ 2)
⇒ x + 26 = 2x + 4
⇒ x = 22

Question: If a and b are odd numbers. Which number is even?

Solution:
Let
a = 1
b = 3

ab = 1 × 3 = 3, which is odd.

a + 2b + 2 = 1 + 2 × 3 + 2 = 1 + 6 + 2 = 9, which is odd.

a + b + 1 = 1 + 3 + 1 = 5, which is odd.

2a + 4b = 2 × 1 + 4 × 3 = 2 + 12 = 14, which is even.