Quantitative Aptitude
Numbers based Aptitude
shikha
December 16, 2015
Rules-based on Numbers is simple, no need to learn anything new. These are all, we have already done in our school times. Recall the Mathematical Formula in Algebra

(a + b)2 = a2 + b2 + 2ab
(a - b)2 = a2 + b2 -2ab
(a2 - b2 )= (a + b) (a - b)
(a + b)3 = a3 + b3 + 3ab (a+b)
(a - b)3 = a3 – b3 -3ab (a-b)
a3 + b3 = (a+b) (a2- ab +b2)
a3- b3 = (a-b) (a2+ ab +b2)
(a+b+c)3 = a2 + b2 + c2 + 2ab +2bc + 2ca

The concept needs a better understanding and thorough reading of statements given to solve.

Let see how to figure out the number of based problems.....

Problem1: The sum of two numbers is 29 and the difference of their squares is 145. The difference between the numbers is?

Solution:

Step1: Take two numbers X and Y
Step2: The sum of two numbers is 29

X + Y = 29

Step3: The difference of their squares is 145

X2 – Y2 = 145

Step4: To evaluate both the statements apply algebraic formula and put the given values here

(a2 - b2)= (a + b) (a - b)
145 = 29 (a-b)
145/29 = (a-b)

Step5: The difference of the numbers (X - Y)= 5

Problem2: The ratio between two numbers is 3:4 and their sum is 420. The greater of the two numbers is?

Solution:

Step1: Take a numbers x
Step2: The ratio between two numbers is 3:4
Step3: Ratio means both the numbers are divisible with single common multiple. Let’s take it ‘x’ which will multiply with both the numbers as

First number = 3x
Second Number = 4x
Step4: Their sum is 420
3x + 4x = 420
7x= 420
x=60
Step5: Numbers are
3x= 3 * 60= 180
4x= 4 * 60 = 240

Step6: The second number is greater than first one

Problem3: Three fourth of one-fifth of a number is 60. The number is?

Solution:

Step1: Three fourth ¾ and one fifth 1/5
Step2: ‘Of ’ designated multiplication here
Step3: A number takes it as ‘x’

3/4 * 1/5 * x = 60
3/20 * x = 60
x = 400

Step4: The number is 400

Problem4: The difference between the squares of two consecutive numbers is 35. The number are?

Solution:

Step1: Consecutive numbers are numbers follow each other like 1, 2,3 ,4
Step2: Imagine two consecutive number x and (x + 1)
Step3: The difference between the squares of two numbers is 35. Square it first x2 , (x+1)2
Step4: The difference between two means subtract the smaller number from greater one i.e.

(x+1)2 - x2 = 35

Step5: Evaluate and it comes out x=18
Step6: First number x=18
Second number is x + 1 =19

Problem5: The sum of the two numbers is twice their difference. If the one of the number is 10, the other number is?

Solution:

Step1: Take two number X and Y
Step2:Take X= 10 ( Given one number)
Step3: The sum of the two numbers is twice their difference.

(10 + Y) =2 (10 –Y)
10 +Y = 20 -2Y
Y= 10/3

Step4: Other number is 10/3 or take in mixed fraction as 3 1/3

Problem6: The number whose fifth part is increased by 5 is equal to its fourth part diminished by 5. The number is?

Solution:

Step1: Take a number X
Step2: Fifth part of number is 1/5 of x and fourth part of number is 1/4 of x
Step3: The number whose fifth part is increased by 5 is equal to its fourth part diminished by 5

1/5 * x + 5 =1/4 * x -5

Step4: Evaluate it
x/5+ 5 = x/4 -5
10 = x/4 – x/5
Step5: The number is x = 200

Post on the Higher level difficulty in Numbers is coming soon.......