Each new driving offense results in increasing penalty points per offe

Question

Each new driving offense results in increasing penalty points per offense on a driver's "rap sheet". A driver gets one point for the first offense, and the incremental increase in penalty points for each new offense is 2 points.

If the maximum number of offense points before the revocation of the license is 100, what is the maximum number of offenses a driver can make and continue to drive legally?

1 + (1+2) + (1+2+2) + .....(1+2(n-1)) <=100
n + 2n(n-1)/2 <=100
n + n^2 - n <=100
n^2 <=100
n = 10

The maximum number of offenses a driver can make and continue to drive legally = 10

IMO C

A. 8

B. 9

C. 10

D. 11

E. 12

happypuppy · Accepted Answer

For the 1st offence, the penalty point = 1
For 2nd -> 1+2 = 3
For 3rd -> 3+2 = 5
and so on.
Series becomes: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19....

That is basically consecutive odd numbers.

And the LIFE saving fact:  The sum of odd numbers from 1 to infinity is N^2, where N is the number of numbers.

1 -> 1^2 = 1
1+3 -> 2^2 = 4
1+3+5 -> 3^2 = 9
...

Since the upper cap here is 100, so the closest number is 10, i.e. 10^2 = 100
Hence (C)

Anurocks1233 · Answer

so we can test numbers on this, let's start with 10 middle number - 
first number 1 
Nth number - (n-1)+1 = which is 19 as n=10

AM = 1+19/2 =10

so sum = AM*N = 10*10
100
so C is the answer

Jxmes · Answer

surely the answer to this question is 9?

the question asks "what is the maximum number of offenses a driver can make  and continue to drive legally ?". once he makes the 10th offense, he cannot continue driving legally. Unless license is revoked once you cross the threshold of 100 and not at 100, in which case the answer is indeed 10. If we use a baseball analogy, it's 3 strikes and you're out. Batter has a max number of 3 strikes before he is out. At least this is how I was thinking about it.

varunkasat2801 · Answer

@
Bunuel Please confirm if it is 9 or 10, I agree to @Jxmes's point

Bunuel · Answer

I see your point; however, one might interpret "the maximum number of offense points  before  the revocation of the license is 100" as meaning the revocation happens  after  reaching 100 points. Therefore, with 100 points, the driver can still drive, but if they exceed this (101 points or more), the license is revoked.

Kinshook · Answer

Each new driving offense results in increasing penalty points per offense on a driver's "rap sheet". A driver gets one point for the first offense, and the incremental increase in penalty points for each new offense is 2 points.

If the maximum number of offense points before the revocation of the license is 100, what is the maximum number of offenses a driver can make and continue to drive legally?

1 + (1+2) + (1+2+2) + .....(1+2(n-1)) <=100
n + 2n(n-1)/2 <=100
n + n^2 - n <=100
n^2 <=100
n = 10

The maximum number of offenses a driver can make and continue to drive legally = 10

IMO C

gasserlo69 · Answer

So what I did to come to the conclusion 10 is the following... I might be wrong...

1, 3, 7, 13, 21, 31, 43, 57, 73, 91.

Explanation of the Sequence:
The first offense gets 1 point.
The second offense adds 2 points to make a total of 3 points.
The third offense adds 4 points, and so on. Each time, the number of points added increases by 2.
Thus, the points for each offense are:

1 point for the 1st offense.
3 points for the 2nd offense (1 + 2).
7 points for the 3rd offense (3 + 4).
13 points for the 4th offense (7 + 6), and so on.

Conclusion:
The next offense (11th) would push the total over 100 points (since 91 + 11 = 102). Therefore, 10 offenses is the maximum number before reaching or exceeding 100 points.

Let me know if this was just luck..

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Each new driving offense results in increasing penalty points per offe

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Each new driving offense results in increasing penalty points per offe

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