Bank Math Master

Question: If x and y are odd numbers, which number is even?

Solution:
Let x = 1 and y = 3 (both are odd numbers)

a) x × y = (1 × 3) = 3 ............. Odd

b) x + y + 1 = (1 + 3 + 1) = 5 ......... Odd

c) 3x + 4 = (3 × 1 + 4) = 3 + 4 = 7 ......... Odd 

d) 2x + 2y = (2 × 1 + 2 × 3) = 2 + 6 = 8 .......... Even 

Question: What is the least number which when doubled is exactly divisible by 8, 14, 18, and 24?

Solution:
Let the number be x.
Double the number is 2x.

8 = 2 × 2 × 2
14 = 2 × 7
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3

∴ LCM = 2 × 2 × 2 × 3 × 3 ×7
= 504

∴ x = 504/2 = 252

Question: Which of the following is the smallest?

Solution:
ক) 1/2 = 0.5
খ) 3/8 = 0.375
গ) 11/25 = 0.44
ঘ) 5/12 = 0.4167

∴ The smallest value is 3/8.

Question: - 5x - [4y - {9x - (3y - 7x)}] simplifies to 

Solution:
- 5x - [4y - {9x - (3y - 7x)}]
= - 5x - [4y - {9x - 3y + 7x}]
= - 5x - [4y - 9x + 3y - 7x]
=  - 5x - [7y - 16x]
= - 5x - 7y + 16x
= 11x - 7y

Question: What is the value of the expression?
(√3 + √12)² = ?

Solution:
(√3 + √12)²
= {√3 + √(3 × 4)}²
= (√3 + 2√3)²
= (3√3)²
= 3² × (√3)²
= 9 × 3
= 27

Question: The ratio of two numbers is 5:7 and their H.C.F is 6. What is their L.C.M?

Solution:
Let the numbers be 5x and 7x.
∴ HCF = x = 6

We know,
HCF × LCM = Product of two numbers
⇒ 6 × LCM = (5x) × (7x)
⇒ 6 × LCM = (5 × 6) × (7 × 6)
⇒ LCM = (30 × 42)/6
⇒ LCM = 1260/6
∴ LCM = 210

Question: Which of the following fraction is smaller than 3/4 and
greater than 1/2?

Solution:
3/4 = 0.75
1/2 = 0.5

ক) 2/5 = 0.4
খ) 5/8 = 0.625
গ) 3/7 = 0.428
ঘ) 4/9 = 0.444

∴ 5/8 is the required fraction.

Question: If , then x = ?

Solution:

Question: If one fifth of one sixth of a number is 10, then what is 2/5 of the number?

Solution:
ধরি, সংখ্যাটি = x

প্রশ্নমতে,
(1/5) × (1/6) × (x) = 10
⇒ (1/30)x = 10
⇒ x = 10 × 30
∴ x = 300

∴ সংখ্যাটি = 300

এখন,
সংখ্যাটির 2/5 অংশ = (2/5) × 300
= 600/5
= 120

Question: Find the least number that leaves a remainder of 5 when divided by 6, 9, 15, and 20.

Solution:
We have to find the least number,
therefore, we find out the LCM of 6, 9, 15, and 20.

6 = 3 × 2
9 = 3 × 3
15 = 3 × 5
20 = 2 × 2 × 5

∴ LCM = 2 × 2 × 3 × 3 × 5
= 180

This is the least number which is exactly divisible by 6, 9, 15, and 20.
So, required number leaves remainder of 5 is = 180 + 5 = 185

Question: A water tank contains 24 liters of water. Rahim uses 1/4 of the total water. Then Karim uses 1/2 of the remaining water. How many liters of water are left in the tank?

Solution:
Total water = 24 liters
Water used by Rahim = (1/4) × 24 = 6 liters

∴ Remaining water = 24 - 6 = 18 liters

Water used by Karim = (1/2) × 18 = 9 liters

∴ Water left in the tank = 18 - 9 = 9 liters

Question: A two-digit number has 5 in its ten's digit. The sum of its digits is one-sixth of the number itself. What is the number?

Solution:
ধরি,
একক স্থানীয় অঙ্ক = x
দশক স্থানীয় অঙ্ক = 5

∴ সংখ্যাটি = 50 + x

প্রশ্নমতে,
5 + x = (50 + x)/6
⇒ 6(5 + x) = 50 + x
⇒ 30 + 6x = 50 + x
⇒ 6x - x = 50 - 30 
⇒ 5x = 20
∴ x = 4

∴ সংখ্যাটি = 50 + 4 = 54

Question: Find

Solution:

Question: Which of the following numbers is a prime number?

Solution:
A prime number is a number that can only be divided by itself and 1 without remainders.

ক) 213 is divisible by 3.
খ) 191 has no divisors other than 1 and itself → prime
গ) 275 is divisible by 5.
ঘ) 333 is divisible by 3.

∴ 191 is the required prime number as it is not divisible by any prime number.

Question: What is the H.C.F. of the following fractions?
6/10, 9/15, 12/20.

Solution:
আমরা জানি,
ভগ্নাংশের গসাগু = লবের গসাগু/হরের লসাগু

এখানে,
লব = 6, 9, 12
6 = 2 × 3
9 = 3 × 3
12 = 2 × 2 × 3

∴ গসাগু (HCF) = 3

হর = 10, 15, 20
10 = 2 × 5
15 = 3 × 5
20 = 2 × 2 × 5

∴ লসাগু (LCM) = 2 × 2 × 3 × 5
= 60

ভগ্নাংশের গসাগু = লবের গসাগু/হরের লসাগু
= 3/60
=1/20

Quesiton: Find

Solution:

Question: Find

Solution:

Question: Find the greatest number which on dividing 1567 and 1979, leaves remainders 3 and 7 respectively.

Solution:
1567 - 3 = 1564
1979 - 7 = 1972

বৃহত্তম সংখ্যাটি হবে 1564 এবং 1972 এর গসাগু।

ইউক্লিডীয় পদ্ধতিতে গসাগু বের করি,

∴ গসাগু = 68

∴ নির্ণেয় বৃহত্তম সংখ্যা = 68