Wednesday, 7 June 2017

Number System III – Number System Questions on Two Consecutive Numbers for IBPS PO Exam

In this post, we will solve Number System Questions based on Two Consecutive Numbers for IBPS PO Exam
Number System Questions
Number System Questions are the most frequently asked questions in  IBPS PO Exam. Number System Questions are the basic foundational questions which check your ability to perform mathematical operations or calculations. Scoring marks in Number System Questions based on two consecutive numbers in an easy task if you know the tricks to solve them. In this post, we will solve Number System Questions based on two consecutive numbers using the smart method which will help you save time in IBPS PO Exam.
Number System Questions
Model 2: Number System Questions on Two Consecutive Numbers
This module comprises of questions that are asked on the concept of two consecutive numbers. Consecutive numbers are classified into three different categories,

Consecutive Natural Number:
Number System Questions
Examples: 1, 2, 3, 4, 5….
                  83, 84, 85, 86 ……

Consecutive Even Numbers: 
Number System Questions
Examples: 2, 4, 6, 8,10…………..

Consecutive Odd Number: 
Number System Questions
Examples: 1, 3, 5, 7………

Example 1: Number System Questions on Two Consecutive Numbers

Question: The sum of 4 consecutive even numbers is 44. What is the sum of the original squares of these numbers?

Regular Method
Solution:
Step 1:
To solve this number system question we need to first find the consecutive numbers
Let us assume the 4 consecutive numbers to be as  x, (x + 2), (x + 3) and (x + 4)
As mentioned in the question, the sum of all consecutive numbers is 44
x + (x + 2) + (x + 3) + (x + 4) = 44
4x + 12 = 44
x = 8

Step 2: Now that we know the value of x, we can easily determine the consecutive numbers by substituting the value of x.
x = 8
x + 2 = 10
x + 4 = 12
x + 6 = 14

Step 3:  The last step is to find the squares of the numbers so that we can find the sum of its squares.
8² = 64
10² = 100
12²= 144
14² = 196
Add the squares to find their sum. 
64 + 100 + 144 + 196 = 504
Therefore, the sum of the original squares of the consecutive numbers is 504.
Number System Questions
Example 2: Number System Questions on Two Consecutive Numbers

Question: The product of the two successive numbers is 4692. Which is the smaller number among these two?
1) 69    2)62    3) 68    4) 67     5) None of these

SMART METHOD
Solution:
Step 1: Let us assume the smaller number to be x and the larger number to be as x + 1.
As given in the question (x)(x + 1) = 4692

Step 2: We can solve this number system question by taking the options into consideration.

Option 1: If 69 is the smaller number then 70 is suppose to be the larger number.

When we multiply the unit digit of these numbers, we get 0 as the product. Therefore this option cannot be taken into consideration as its units place is not 2.

Option 2: If 62 is the smaller number then 63 is suppose to be the larger number.

When we multiply the unit digits of these numbers, we get 6 as the product. Therefore this option cannot be taken into consideration as its units place is not 2.

Option 3: If 68 is the smaller number then 69 is suppose to be the larger number.

When we multiply the unit digits of these numbers, we get 2 as the product. Therefore this option can be taken into consideration as its units place is 2.

Option 4: If 67 is the smaller number then 68 is suppose to be the larger number.

When we multiply the unit digits of these numbers, we get 6 as the product. Therefore this option cannot be taken into consideration as its units place is not 2.

You can mark the option 3 if you have less time. But if you need to verify the answer then follow the next step or else you can carry on with solving other number system question. 

Step 3:
68 x 69 = 4692
Therefore, the correct answer is option 3: 68.

Example 3: Number System Questions on Two Consecutive Numbers

Question: The sum of 5 consecutive even numbers is 200.What is the sum of the next set of consecutive even numbers?

Regular Method
Solution:
Step 1: As we need to find the sum of 5 consecutive even numbers, we assume them to be
 x + (x + 2) + (x + 4) + (x + 6) + (x + 8)
In the question it is given that the sum of 5 consecutive numbers is 200
x + (x + 2) + (x + 4) + (x + 6) + (x + 8)
5x + 20 = 200
5x = 180                                                                                                     
x = 36

Step 2: As we know the value of x, we substitute its value to find the 5 consecutive numbers.
x = 36
x + 2 = 38
x + 4 =40
x + 6 =42
x + 8 =44

Step 3: The sum of the next consecutive numbers; 46, 48, 50, 52, 54 = 250

Therefore, the sum of the next 5 consecutive numbers is 250.

Smart method:
Solution:
To solve this question through the smart method, we need to know that any 5 consecutive numbers will have a difference of 10 in between them.
So when we add their differences we get the sum which will be 50 more than original sum.
Number System Questions
Therefore, to find the sum of the next 5 consecutive numbers we need to add 50 to 200. So, the sum of the next 5 consecutive number is 50. 
Number System Questions
We need to know that, this trick can only be used when we need to find the sum of 5 consecutive numbers. We can not take 40 or 30 when need to find the sum for 4 or 3 consecutive numbers because the difference between consecutive number will not remain the same, it varies. 
For example, let's find the sum of 4 consecutive numbers. 
Number System Questions

Number System Questions on Two Consecutive Numbers for Practice! 

Question 1: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is?
1) 9    2) 11    3)13    4)15     5) None of these.


Question 2: There are four prime numbers written in ascending order. The product of the first three is 385 and that of the last three is 1001. The last number is?
1)11    2)12     3)13      4)15    5) None of these

- unanswered
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Number System Questions
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