Bank Exams challenge: Can you solve these 5 number problems

Dear Reader, number problems are usually very easy to solve and score in bank exams. Below you will find 5 number problems. Try to solve them on your own. For your reference, solutions are provided after each questions.

Question 1:
Simplify 8 x (666 x 555) / [(666 + 555)² – (666-555)²] =?
a) 3 b) 4 c) 2 d) 1

Answer: c) 2

Solution:
The given expression is in the form,
8ab / [(a+b)² – (a-b)² ]
Using the formula, (a+b)² – (a-b)² = 4ab
So, the expression becomes, 8ab / 4ab = 2

Question 2:
Simplify 1498 x 1498 =?
a) 2244004 b) 2244550 c) 2244440 d) 2250000

Answer: a) 2244004

Solution:
Given expression = (1498)²
Using the formula, (a-b)²= a² -2ab + b²
= (1500 – 2)²
= 1500² – 2x1500x2 + 2²
= 2250000 + 4 – 6000 = 2244004

Question 3:
The sum of the 2 numbers is 15 and their product is 33. What is the sum of the reciprocals of these numbers.
a) 6/11 b) 5/11 c) 3/11 d) 7/11

Answer:b) 5/11

Solution:
Let the two numbers be x and y
Sum of two numbers x+y=15
Product of two numbers, xy = 33
Sum of the reciprocals of x and y = (1/x) + (1/y)
= (x+y)/xy
By substituting the value, we get
15/33 = 5/11

Question 4:
Simplify 318 x 318 + 282 x 282 =?
a) 180648 b) 180543 c) 170648 d) 1800065

Answer: a) 180648

Solution:
Given expression = 318² + 282²
Using the formula, (a + b)² + (a – b)² = 2(a² + b²)
= (300+18)² + (300 – 18)²
= 2(300² + 18²)
= 2×90324
= 180648

Question 5:
Simplify (325x325x325 -236x236x236) / (325 x 325 + 325 x 236 + 236 x 236)
a) 98 b) 89 c)90 d) 88

Solution:
Given expression = (325³ – 236³) / (325² + 325 x 236 + 236²)
Using the formula, (a³ – b³) = (a – b)(a² + ab + b²), we get
(a – b)(a² + ab + b²)/(a² + ab + b²) = a-b
a-b = 325-236 = 89