Bank Math Master

Question: Find the greatest number which divides 120, 165 and 210 exactly leaving remainders 5, 4 and 3 respectively

Solution: 
১১৫ = ৫ × ২৩  
১৬১ = ৭ × ২৩
২০৭ = ৯ × ২৩ 

১১৫, ১৬১, ২০৭ এর গ সা গু = ২৩ 

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

Solution: 
n - 1 is an odd number 
previous odd number = n - 1 - 2 = n - 3
next odd number = n - 1 + 2 = n + 1

Question: Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The largest number is:

Solution: 
let, the numbers are x, 2x, 3x
HCF is x 
x = 12 

largest number = 12 × 3 
= 36 

Question: Which of the fractions given below is the largest?

Solution:
Each fraction is equivalent to a decimal
4/3 = 1.33
5/4 = 1.25
6/5 = 1.2
7/6 = 1.167 

Hence, 4/3 is the largest fraction.

Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

Solution: 
ধরি, একক স্থানীয় অঙ্ক x, দশক স্থানীয় অঙ্ক y

প্রশ্নমতে, 
10y + x - (10x + y) = 36 
⇒ 10y + x - 10x - y = 36 
⇒ 9y - 9x = 36 
⇒ 9(y - x) = 36 
⇒ y - x = 4

Question: The fraction equivalent to (2/5)% is- 

Solution: 
(2/5)%
= (2/5) × (1/100)
= 1/250

Question: What is the sum of all two-digit numbers that gives a remainder of 3 when they are divided by 7?

Solution: 
general formula for that number = 7n + 3  

n = 1, then the number is = 7 + 3 = 10 
n = 2, then the number is =14 + 3 = 17
.
.
.
n= 13,  then the number is = 94

sum  = 10 + 17 + ... + 94 
= 13 (10 + 94)/2 
= 676 

Question:

Solution: 

Question: Find a positive number which increased by 17 is equal to 60 times the reciprocal of the number.

Solution: 
let the number be x 

(x + 17) = 60 (1/x)
⇒ x² + 17x - 60 = 0 
⇒ x² + 20x - 3x - 60 = 0 
⇒ x (x + 20) - 3 (x + 20) = 0
⇒ (x + 20) (x - 3) = 0 
∴ x = - 20 , 3 

as the number is positive, answer is 3

Question: If 1² + 2² + 3² + .....+ 10² = 385, then 2² + 4² + 6² + .... + 20² =?

Solution: 
 2² + 4² + 6² + .... + 20²
= 2² (1 + 2² + 3² +....+10²)
= 4 × 385
= 1540

Question:  Find the number of the divisors of 360

Solution: 
360
= 3² × 2³ × 5

the number of the divisors of 360 is = (2 + 1) × (3 + 1) × (1 + 1)
= 3 × 4 × 2
= 24

Question: The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

Solution: 
let the two numbers be x, y 

xy = 120 
x² + y² = 289 

We know
(x + y)² = x² + y² + 2xy
⇒ (x + y)² = 289 + 2 × 120 
⇒ (x + y)² = 289 + 240
⇒ (x + y)² = 529
⇒ (x + y)² = 23²
∴ x + y = 23

Question: An apple costs 7 taka each. An orange costs 5 taka each. Rasel spends 38 taka on these fruits. The number apple purchased is- 

Solution: 
ধরি, x টি আপেল ও y টি কমলা কিনেছে। 

প্রশ্নমতে, 
7x + 5y = 38 
⇒ 5y = (38 - 7x)
∴ y = (38 - 7x)/5

x = 2, y= (38 - 14)/5 = 24/5; যা পূর্ণসংখ্যা নয়। 
x = 3, y= (38 - 21)/5 = 17/5; যা পূর্ণসংখ্যা নয়। 
x = 4, y= (38 - 28)/5 = 10/5 = 2; যা পূর্ণসংখ্যা। 

Question:

Solution: 

Question: If n is an integer between 20 and 80, then any of the following could be n + 7 except-

Solution: 
maximum value of n + 7 = 80 + 7 = 87 
88 > 87 
So, the correct answer is A 

Question: Six consecutive whole numbers are given. The sum of the first three numbers is 27. What is the sum of the last three numbers?

Solution: 
let the numbers be x - 2, x - 1, x, x + 1, x + 2, x + 3 

x - 2 + x - 1 + x = 27 
⇒ 3x - 3 = 27
⇒ 3x = 27 + 3 = 30 
⇒ x = 30/3
∴ x = 10 

the sum of the last three numbers is = x + 1 + x + 2 + x + 3
= 10 + 1 + 10 + 2 + 10 + 3
= 36 

Question: If m, n, o, p and q are integers, then m(n + o)(p - q) must be even when which of the following is even- 

Solution: 
m জোড় সংখ্যা হলে গুণফল জোড় সংখ্যা হবে। কারণ জোড় সংখ্যার সাথে জোড় বা বিজোড় গুণ করলে সবসময় জোড় সংখ্যাই পাওয়া যায়।

Question: How many pairs of natural numbers is there the difference of whose squares are 45?

Solution: 
ধরি, 45 কে x ও y এর বর্গের বিয়োগফল আকারে প্রকাশ করা যায়।
45 = x² - y² = (x - y) (x + y)

45
= 1 × 45
= 5 × 9
= 3 × 15

♦ x + y = 45, x - y = 1 হলে,
x + y + x - y = 45 + 1
⇒ 2x = 46
⇒ x = 23∴ y = 45 - 23 = 22

♦ x + y = 9, x - y = 5 হলে,
x + y + x - y = 5 + 9
⇒ 2x = 14
⇒ x = 7∴ y = 9 - 7 = 2

♦ x + y = 15, x - y = 3 হলে,
x + y + x - y = 15 + 3
⇒ 2x = 18
⇒ x = 9

∴ y = 15 - 9 = 6

অতএব, 45 কে দুটি স্বাভাবিক সংখ্যার বর্গের বিয়োগফল আকারে প্রকাশ করা যায় এমন 3 টি ক্রমজোড় হল (x, y) = (23, 22), (7, 2), (9, 6)

Question: 5/9 of a number equals twenty-five percent of the second number. Second number equals 1/4 of third number. The value of third number is 2960. What is 30% of first number? 

Solution: 
second number = 1/4 of third number = 2960/4 
 = 740 

(5/9)first number = 25% of second number 
first number = (1/4) × 740 × (9/5)
= 333

30% of first number = (3/10) × 333
= 99.9 

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: Given that √24 is approximately equal to 4.898, √(8/3) is nearly equal to- 

Solution: 
√(8/3)
=√{(8 × 3)/(3 × 3)}
= √24/3
= 4.898/3
= 1.633

Question: A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:

Solution: 
let, the digits are x, y, z 

x + y + z = 10 
y = x + z

y + y = 10 
⇒ y = 5

x + z = 5

(100z + 10y + x) - (100x + 10y + z) = 99
⇒ 99z - 99x = 99
⇒ z - x = 1

x + z + z - x = 5 + 1
⇒ 2z = 6
∴ z = 3

x = 5 - 3 = 2

The number is = 253