Latest Elitmus Aptitude Question SOLUTION: The series of differences between consecutive prime numbers is represented as dp1, dp2, dp3, .... dpn .Whare dp1 is the difference between the second and the first prime number. Fi

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(#M40154783) ELITMUS Numerical Ability question Keep an EYE

The series of differences between consecutive prime numbers is represented as dp1, dp2, dp3, .... dpn .Whare dp1 is the difference between the second and the first prime number. Find the sum of series when n = 23, given that the 23rd prime number is 83 ?
A. 81
B. 82
C. 83
D. 87

Asked In Elitmus aanchal sharma (8 years ago)

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Read Solution (18) :

vihari  (8 years ago)

87 :

dp1 = p2-p1 , dp2 = p3-p2 ,... On adding ..
All gets cancelled ... except dp24 (89) and dp1(2) .

Is this solution Helpfull? Yes (28) | No (11)  

JANARTHANAN RAM  (8 years ago)

Ans: 87

dp1 = p2-p1 ,
dp2 = p3-p2
..
..
dp23=p24-p23
Sum of series=(p2-p1)+(p3-p2)+.....(p23-p22)+(p24-p23)
All terms get cancelled,except p1= 2 and p24
So Sum= -p1+p24
Sum of series=-2+89=87

Is this solution Helpfull? Yes (17) | No (4)  

Priya kumari  (8 years ago)

S1 = 1 when last prime number is 3
S2 = 3 when last prime number is 5
S3 = 5 when last prime number is 7 and so on.

So the sum of the series is 2 less than the last prime number.
So S23 = 83 - 2 = 81

Is this solution Helpfull? Yes (15) | No (5)  

priyanka  (8 years ago)

Ans is : 81
dp1= p2-p1, dp2= p3-p2.......
So, p2-p1 + p3-p2 + p4-p2 +.......... + p23-p22 = p23-p1 = 83 - 2 =81 :-)

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JUGAL KHAJURIYA  (8 years ago)

81 is right ans

Is this solution Helpfull? Yes (8) | No (3)  

Suyash Gupta  (8 years ago)

2(p1), 3(p2), 5(dp3), 7(p4), 11(p5), 13(p6), 17(p7), 19(p8), 23(p9), 29(p10), 31(p11), 37(p12), 41(p13), 43(p14), 47(p15), 53(p16), 59(p17), 61(p18), 67(p19), 71(p20), 73(p21), 79(p22), 83(p23)
dp1 = p2-p1 = 3-2 =1
dp2 = p3-p2 = 5-3=2
........................
........................
dp24 = p24-p23 = 89-83 =6
Sum= 87

Is this solution Helpfull? Yes (8) | No (6)  

abhishek kumar deepak  (8 years ago)

81 is the right ans.

Is this solution Helpfull? Yes (7) | No (2)  

Akash Kumar Modanwal  (8 years ago)

consecutive prime no's-
2,3,5,7..........83 and their differences 1,2,2,4,2,4....... so add all differences you will get 81 as a answer
so 81 is write answer

Is this solution Helpfull? Yes (7) | No (2)  

Suyash Gupta  (8 years ago)

2(p1), 3(p2), 5(dp3), 7(p4), 11(p5), 13(p6), 17(p7), 19(p8), 23(p9), 29(p10), 31(p11), 37(p12), 41(p13), 43(p14), 47(p15), 53(p16), 59(p17), 61(p18), 67(p19), 71(p20), 73(p21), 79(p22), 83(p23)
dp1 = p2-p1 = 3-2 =1
dp2 = p3-p2 = 5-3=2
........................
........................
dp23 = p24-p23 = 89-83 =6
Sum= 87

Is this solution Helpfull? Yes (6) | No (4)  

Piyush jain  (8 years ago)

81 is right answer.

Is this solution Helpfull? Yes (4) | No (2)  

Shreyans Awasthi  (8 years ago)

the answer will be B. 82
Explanation -prime numbers are always odd numbers.
And difference between odd numbers is always even.
Thus the sum of the differences will also be even.

Is this solution Helpfull? Yes (2) | No (5)  

Vikash kumar  (7 years ago)

a is the correct answer

Is this solution Helpfull? Yes (2) | No   

arpit srivastava  (7 years ago)

We can solve this by writing down all the prime number from 2 to 83 and then finding the differences between them and add them all. This is a tedious task.

Let me introduce you with a shortcut way:
If n was 1.
The series would have been just dp1, which is the difference between the second and the first prime numbers, 3 and 2.
So, dp1 = 3 - 2 = 1

If n was 2.
The series would have been just dp1 + dp2
dp2 = difference between 3rd and 2nd odd numbers, 5 and 3 = 5 - 3 = 2
So sum of the series when n is 2 = dp1 + dp2 = 1 + 2 = 3

If n was 3.
The The series would have been just dp1 + dp2 + dp3
dp3 = difference between 4th and 3rd odd numbers, 7 and 5 = 7 - 5 = 2
So sum of the series when n is 3 = dp1 + dp2 + dp3= 1 + 2 + 2= 5

Did you notice something ??
S1 = 1 when last prime number is 3
S2 = 3 when last prime number is 5
S3 = 5 when last prime number is 7 and so on.

So the sum of the series is 2 less than the last prime number.
So S23 = 83 - 2 = 81

Is this solution Helpfull? Yes (1) | No (1)  

siddharth chaudhary  (5 years ago)

solution of sayush gupta is correct as seen also becuase dp23 means p24-p23 I dont know why everyone is showing the answer given on testPot which is wrong.

Is this solution Helpfull? Yes (1) | No   

Aakansha louvanshi  (8 years ago)

@Abhishek... how???

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bharati roy  (8 years ago)

by manual calculation, calculating the sum of the differences all those prime numbers is 87.

Is this solution Helpfull? Yes | No (5)  

gmswacc  (7 years ago)

https://en.wikipedia.org/wiki/List_of_perfect_numbers

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sugandh  (6 years ago)

Explanation :
Let 'p' denotes prime number.
Given, p23 = 83.
According to the question,
dp1= p2-p1, dp2 = p3-p2 .......
So, p2-p1 + p3-p2 + p4-p2 +.......... + p23-p22 = p23-p1 = 83 - 2 = 81.

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