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}= a^{2} -2ab + b^{2}*

= (1500 – 2)

^{2 }

= 1500

^{2}– 2x1500x2 + 2

^{2}

= 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 = 318^{2} + 282^{2}

*Using the formula, (a + b) ^{2} + (a – b)^{2} = 2(a^{2} + b^{2})*

= (300+18)

^{2}+ (300 – 18)

^{2}

= 2(300

^{2}+ 18

^{2})

= 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 = (325^{3} – 236^{3}) / (325^{2} + 325 x 236 + 236^{2})

*Using the formula, (a ^{3} – b^{3}) = (a – b)(a^{2} + ab + b^{2})*, we get

(a – b)(a

^{2}+ ab + b

^{2})/(a

^{2}+ ab + b

^{2}) = a-b

a-b = 325-236 = 89