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Algebra Level 2 Test 2

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Question 1
What will be the sum of first 50 odd natural numbers?
A
1250
B
2500
C
2601
D
2306
Question 1 Explanation: 
Since the sum of first odd natural numbers = {(last term +1)/2}2
So in general we can say that the sum of first natural odd numbers would be = n2
So in this case the series will become = 1+3+5+7…..99
So therefore the sum of series = n2
n = 50
so the sum would be the square of 50 = 2500
Question 2
If 1+2+3+4+….. +40 = 820 Then what will be the value of 21 +22+23+24……….+60
A
1620
B
1630
C
1840
D
2306
Question 2 Explanation: 
We will solve this series with logic
We can write the above as:
21 +22+23+24……….+60 = (20 +1) + (20+2) + (20 +3) ………… (20 + 40)
If you see 20 is present in all terms
i.e. 20 came 40 times in the series
so the series can be written as 20 x 40  +(1+2+3……….. 40)
and in the question we are given by 1+2+3+4+….. +40 = 820
so the sum of the series is = 800 + 820 = 1620
Question 3
In a book, containing 20 pages, one sheet is missing. Sum of the page numbers of the remaining pages is 195. The numbers written on both the sides of the sheet must be
A
6, 2
B
6, 3
C
7, 8
D
8, 9
Question 3 Explanation: 
Since the pages of a book are consecutive numbers,
we can first find the sum of all pages of the book
The sum of pages of the book = {n(n+1)} / 2 = (21 x 20 )/2 = 210
And in the question we are given by the sum of pages excluding the missing page = 195
So the difference between both the values = 210 – 195 = 15
Now check the options, the option with sum of 15 is the right option i.e. option number (c)
Question 4
The product of two positive numbers is 2500. If one is four times the other then the sum of these two numbers would be
A
120
B
130
C
124
D
125
Question 4 Explanation: 
Since product of two positive numbers is 2500
Therefore let us consider the number be = p
Then the second number will be = 4p
Now p x 4p = 2500
P2 = 2500/4 = 625
P2 = 625
p = 25
so if the number is 25 then the other number will be = 100
and the sum of these two number would be = 125
Question 5
If the difference between the squares of two consecutive numbers is 47 , then what would be the smallest number
A
20
B
21
C
23
D
25
Question 5 Explanation: 
If there are consecutive numbers then they will be in the form of (p), (p+1)
Let first number = p
Then the second number would be = (p+1)
We are given that the difference = 47
Here we use a property
The difference of two consecutive squares = sum of those numbers
So p + (p+1) = 47
On solving
P = 23
So the numbers are 23 ,24
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