Bank Math Master

Question: The greatest 3-digit number that is divided by 15 and 25 is - 

Solution:
তিন অংকের বৃহত্তম সংখ্যা = ৯৯৯
১৫ = ৩ × ৫
২৫ = ৫ × ৫
ল.সা.গু = ৫ × ৫ × ৩ = ৭৫

৯৯৯ কে ৭৫ দিয়ে ভাগ করলে ভাগশেষ থাকে ২৪

∴ সংখ্যাটি = ৯৯৯ - ২৪ = ৯৭৫

Question: A two-digit number has 6 in its ten's digit. The sum of its digits is one seventh of the number itself. What is the number? 

Solution: 
দশক স্থানীয় অঙ্ক ৬
একক স্থানীয় অঙ্ক x
সংখ্যাটি = ৬ × ১০ + x 
= ৬০ + x

প্রশ্নমতে, 
৬ + x = (৬০ + x)/৭
⇒ ৪২ + ৭x = ৬০ + x
⇒ ৭x - x = ৬০ - ৪২ 
 ⇒ ৬x = ১৮
∴ x = ৩

সংখ্যাটি ৬৩

Question: If 283P is divisible by 9, what is the value of P? 

Solution:
 একটি সংখ্যা ৯ দ্বারা বিভাজ্য হবে যদি সংখ্যাটির অঙ্কগুলোর সমষ্টি ৯ দ্বারা বিভাজ্য হয়। 

২ + ৮ + ৩ = ১৩; এর সাথে ৫ যোগ করলে ১৮ হয়, যা ৯ দ্বারা বিভাজ্য।
∴ P = ৫

প্রশ্ন:

সমাধান: 

Question: - 6m - [3n - {8m - (4n - 10m)}] simplifies to

Solution: 
- 6m - [3n - {8m - (4n - 10m)}]
= - 6m - [3n - {8m - 4n + 10m}]
= - 6m - [3n - 8m + 4n - 10m]
= -6m - 3n + 8m - 4n + 10m 
= 12m - 7n 

Question:


Solution: 

Question: The G.C.D. of 1.08, 0.36 and 0.9 is -

Solution: 
১.০৮ = ১০৮/১০০ = ২৭/২৫
০.৩৬ = ৩৬/১০০ = ৯/২৫
০.৯ = ৯/১০ 

ভগ্নাংশের গ.সা.গু = ( লব সমূহের গ.সা.গু ) / ( হর সমূহের ল.সা.গু)
= (২৭,৯, ৯ এর গ.সা.গু)/(২৫,২৫,১০ এর ল.সা.গু)
= ৯/৫০
= ০.১৮

প্রশ্ন:

সমাধান: 

Question: Two-fifth of one-fourth of three seventh of a number is 30. What is the half of the number?

Solution:
let the number be x

(2/5) × (1/4) × (3/7)x = 30
⇒ x = (30 × 5 × 4 × 7)/(2 × 3)
⇒ x = 700
∴ x/2 = 350

Question:

Solution: 

Question:

Solution: 

Question: Find the remainder when 4⁹⁶ is divided by 8.

Solution: 
4⁹⁶/8
= (4² × 4⁹⁴)/8
= (16 × 4⁹⁴)/8
= 2 × 4⁹⁴

যেহেতু 4⁹⁶, 8 দ্বারা নিঃশেষে বিভাজ্য। অতএব, ভাগশেষ শূন্য হবে। 

Question: Which of the following has the most number of divisors?

Solution: 
৯৮ = ২ × ৭ × ৭
১০১ = ১ × ১০১
১৭৬ = ২ × ২ × ২ × ২ × ১১
৩৫ = ৫ × ৭

অর্থাৎ ১৭৬ এর উৎপাদক সবচেয়ে বেশি।

Question: The sum of three numbers is 144. The ratio of the first number to the second number is 2 : 3 and between the second and third numbers, this ratio is 3 : 4, find the second number.

Solution:
Given that, 
The sum of three numbers is = 144
The ratio of first number to second number is = 2 : 3
The ratio of second number of third number is = 3 : 4

The ratio of first, second and third number = 2 : 3 : 4 
Let the numbers are 2x, 3x , 4x

According to the question
2x + 3x + 4x = 144
⇒ 9x = 144
⇒ x = 144/9
⇒ x = 16

∴ The second number is
= 3 × 16
= 48

Question: What will be the least number which 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 30 = 2 × 3 × 2 × 3 × 7 × 5 = 1260
Required number = 1260/2 = 630

Question: A number is 2/5 times of another number. If the sum of two numbers is 98, what is the difference of two numbers?

Solution:
Let, a number is x
another number is 2x/5

ATQ,
x + 2x/5 = 98
⇒ (5x + 2x)/5 = 98
⇒ 7x/5 = 98
⇒ 7x = 98 × 5
⇒ 7x = 490
∴ x = 70

So, a number is 70
another number is 2x/5 = (2 × 70)/5 = 28
∴ difference = 70 - 28
= 42

Question: Of the four numbers, the first is twice the second, the second is one - third of the third and the third is 5 times the fourth. The average of the numbers is 24.75. The lowest of these numbers is-

Solution: 
The average of the numbers is 24.75.
The sum of these numbers = (24.75 × 4)
= 99

Let the fourth number be x.
Then,
third number = 5x,
second number = 5x/3 and
first number = 10x/3
x + 5x + 5x/3 + 10x/3 = (24.75 × 4)
or, 11x = 99
or, x = 9
So, the numbers are 9, 45, 15 and 30.
∴ Lowest number = 9.

Question: If you divide 40 by half and add 5 with the resulting figure, then what is the final result?

Solution: 
40/(1/2)
= 80

adding 5 = 80 + 5 
= 85 

Question: The product of two positive numbers is m. If each number is increased by 3, the new product is how much greater than thrice the sum of the two original number? 

Solution: 
let, two positive number x, y
xy = m

After increasing 3, their product = (x + 3) (y + 3)
= xy + 3 (x + y) + 9
= m + 3 (x + y) + 9 

thrice of sum of two original number = 3 (x + y)

∴ m + 3 (x + y) + 9 - 3 (x + y)
= m + 9

Question: If (p² - q²) × (p - q)^-1 = 9, what is the value of p + q?

Solution: 
(p² - q²) × (p - q)^-1 = 9
⇒ (p² - q²)/(p - q) = 9
⇒ (p + q) (p - q)/(p - q) = 9
∴ p + q = 9