Latest TCS Aptitude Question SOLUTION: If two consecutive terms are removed from a series 1,2...........n ,then the average of remaining terms is 261/4.what is the no of terms?

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If two consecutive terms are removed from a series 1,2...........n ,then the average of remaining terms is 261/4.what is the no of terms?

Asked In TCS Ritu Tomar (8 years ago)

Unsolved Read Solution (6)

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Read Solution (6) :

milan jena  (8 years ago)

Solve this problem from option.
So from option 50 is the solution.
So sum of first 50 numbers is (50*51)/2=1275
Again after remove of 2 number, the avg of 48 number is 26 1/4=105/4
so sum of 48 number is 48*(105/4)=1260
so sum of two consecutive no is 15 which are 7 and 8.

Is this solution Helpfull? Yes (16) | No (1)  

manas roy  (8 years ago)

n(n+1)/2-{K-(k-1)}=(n-2)*105/4
so from here we can say that
(n-2) is divisble by 4 as the total sum is a integer
from here we can choose the answer from multiple choice

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Sneha Singh  (8 years ago)

can anyone please explain it better

Is this solution Helpfull? Yes (2) | No (1)  

Himanshu Srivas  (8 years ago)

for consecutive terms use formula
last digit+first digit /2
so,
n+1/2 = 105/4
n=52
so,
52-2
=50

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

Shubham Tripathi  (8 years ago)

Suppose we remove the number k and k+1. Then sum of remaining numbers is:
[Math Processing Error]
Dividing this by n-2 will give us the arithmetic mean.
[Math Processing Error] ... (1)

Notice that [Math Processing Error] is in its simplest form. So, we can conclude that the numerator of (1) is 261x and the denominator is 4x for some integer x.
[Math Processing Error]
So, n=4x+2 for some integer x
Substituting in the equation and simplifying, we get:
[Math Processing Error]
So we must find positive integers x and k which satisfy this equation. Also, 4x+2>k as k and k+1 must be in 1..n
Solve this to get the answer.
One solution is n=130 and k=81

Is this solution Helpfull? Yes (1) | No (10)  

kruthika   (8 years ago)

average of n terms = n(n+1)/2*n = n+1/2 hence it should be in the form of integer or some Integer.5
when 2 consecutive terms are removed max change in avg can be -1 to +1 final avg is 65.25
hence actual avg may be 64.5 or 65 / 65.5 / 66
hence n+1 = 129 or 130 or 131 or 132
n= 128 / 129/130/131
but n-2 should be a multiple of 4 as when 2 no.s are removed denominator has 4.
only 130-2 =128 is divisible by 4
hence n= 130

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