Bank Math Master

Question: The sum of the perfect squares between 110 and 300 is - 

Solution: 
Perfect squares between 110 and 300 =  121, 144, 169, 196, 225, 256, 289
Sum = 121 + 144 + 169 + 196 + 225 + 256 + 289 = 1400

Question: Which one of the following is an irrational number?

• √32/√16 = (√16 × √2) / √16 = √2
• π
• √1000

Here, all of them are irrational numbers.

Question: The difference between a number and its one-fourth is 60. What is the number?

Solution: 
Let the number be x 

ATQ,
x - (x/4) = 60
⇒ (4x - x)/4 = 60
⇒ 3x/4 = 60
⇒ 3x = 240
⇒ x = 80

Question: A number when divided by 195 leaves a remainder 47. If the same number is divided by 15, the remainder will be?

Solution:
Let the number be x and the quotient is q.

Then,
x = 195q + 47
= (15 × 13q) + (15 × 3) + 2
= 15 (13q + 3) + 2

So, the given number when divided by 15 gives 2 as remainder.

Question: If 'x' is an odd number and 'y' is an even number, which one of the following must be an even number?

Solution:
Suppose, x = 1 and y = 2

• xy + 1 = 1 × 2 + 1 = 3
• x² + y² = 1² + 2² = 5
• (x + y)² + 1 = (1 + 2)² + 1 = 10
• x + y = 1 + 2 = 3

Question: What is the greatest number that can be subtracted from 10,000 so that the remainder may be divisible by 32, 36, 48, and 54?

Solution:
L.C.M of 32, 36, 48, and 54 is = 864

So, required number  is = 10000 - 864 = 9136

Question: The capacity of two pots is 12 liters and 48 liters respectively. Find the capacity of a which can exactly measure the content of the two pots.

Solution: 
Required capacity = H.C.F. of 12 liters and 48 liters = 12 liters

1 liter = 1000 cc
12 liters = 12000 cc

Question: The least number of square tiles required to pave the ceiling of a room 15m 17cm long and 9m 2cm broad is-

Solution:
15m 17cm = 1517 cm
9m 2cm = 902 cm

Maximum size of the tile = HCF of 1571 cm and 902 cm = 41 cm

So, the required number of tiles = Area of ceiling / Area of each tile
= (1517 × 902) / (41 × 41)
= 814

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: If 555/0.01 = x/0.001, then what is the value of x?

Solution:
555/0.01 = x/0.001
⇒ 0.01x = 0.001 × 555
⇒ 0.01x = 0.555
⇒ x = 0.555 / 0.01
⇒ x = 55.5

• 13/15 = 0.87
• 16/17 = 0.94
• 17/21 = 0.81
• 21/25 = 0.84

√(0.0288 × 0.08)
= √0.002304
= √(0.048)²
= 0.048

Question: The number of trees in each row of a garden is equal to the total number of rows in the garden. If 59 trees have been uprooted in a storm, there are 841 trees in the garden. The number of rows of trees in the garden is -

Solution:
So, number of trees before storm = 841 + 59 = 900
So, the number of in the garden = √900 = 30

Question: The flowers in a basket double every minute and the basket gets full in 1 hr. How much time does it take to fill the basket half?

Solution:
In 60 minutes the basket will be full 1 part
So, in 59 minutes the basket will be full 1/2 part [Because, every minute it gets double]

Question: Which of the following fraction is smaller than 7/8 and greater than 4/9?

Solution:
7/8 = 0.875
4/9 = 0.444

Option (ক) 17/41 = 0.415
Option (খ) 5/13 = 0.385
Option (গ) 9/10 = 0.900
Option (ঘ) 13/21 = 0.690

Here, 0.444 < 0.690 < 0.875

So, Option (ঘ) 13/21 = 0.690 is smaller than 7/8 and greater than 4/9.

Question: What is the root cube of √4096?

Solution:
Here,
√4096 = 64

Now,
the root cube of 64 is = ³√64 = (4³)^1/3 = 4

0.01 × (0.01)² × (10)⁶
= 0.01 × 0.0001 × 1000000
= (1/100) × (1/10000) × 1000000
= 1

Question: Find the least number which when divided by 4, 5, 6, and 7 leaves remainder 2 in each case.

Solution:
LCM of 4, 5, 6, and 7 = 420
So, the number is = 420 + 2 = 422

Question: Which greatest number will divide 1304 and 1869 leaving remainders 8 and 9 respectively?

Solution:
The required number is = HCF of (1304 - 8) and (1869 - 9)
=  HCF of 1296 and 1860
= 12

Question: A train started with 540 passengers. At the first stop 1/9 of them got down and 24 got up. On its second stop 1/8 of the existing passengers got down and 9 got up. With how many passengers did it reach the third stop?

Solution:
Number of passengers after first stop = {540 - (1/9 of 540) + 24} = 504
Number of passengers after second stop = {504 - (1/8 of 504) + 9} = 450

Question: A total of 300 coins of 25 paise and 50 paise make the sum of Tk 120. The number of 50 paise coins is- 

Solution: 
Let the number of 50 paise coins be = x
So, the number of 25 paise coins is = 300 - x

ATQ,
50x + {25 × (300 - x)} = 120 × 100
⇒ 50x + 7500 - 25x  = 12000
⇒ 25x = 4500
⇒ x = 180