n is an integer from 1 to 50, what is the probability that n(n+1) is n

Question

n is an integer from 1 to 50, what is the probability that n(n+1) is not divisible by 4?

A. 12/25
B. 13/25
C. 14/25
D. 15/25
E. 16/25

chetan2u · Accepted Answer

For n(n+1) to be multiple of 4, either n or n+1 should be multiple of 4, as ONLY one of n or n+1 will be even and other will be ODD..

Till 50 , multiple of 4 are 50/4=12.25 so 12 multiples are there..
These 12 can be both n and n+1, so total 2*12=24..

Since n can take values from 1 to 50..
So n(n+1) will take 50 values..

Therefore ways when none of n and n+1 will be multiple of 4 is 50-24=26..
Prob of picking these =26/50=13/25

B

BillyZ · Answer

Multiples of x in the range =  + 1

n = 4, 8, 12, 16, ..., 48

Multiples of x in the range =  + 1 = 12

(n+1)  to be a multiples of 4, n must be 3, 7, 11, 15, ...., 47

n(n+1)  to be a multiple of 3, n can take 12 + 12 = 24 value

P = (favourable outcome) / (total number of outcomes)

P = 24 / 50

Probability that n(n+1) is not divisible by 4 = 1 - (24/50) = 13/25

Bunuel · Answer

Similar questions mimght help: if-integer-c-is-randomly-selected-from-20-to-99-inclusive-121561.html if-an-integer-n-is-to-be-chosen-at-random-from-the-integers-126654.html an-integer-n-between-1-and-99-inclusive-is-to-be-chosen-at-160998.html if-1-n-99-what-is-the-probability-that-n-n-1-is-perfec-106168.html if-integer-c-is-randomly-selected-from-20-to-99-inclusive-121561.html Hope it helps.

ScottTargetTestPrep · Answer

We can use the following equation:

1 = P(n(n+1) is divisible by 4) + P(n(n+1) is NOT divisible by 4)

Thus:

P(n(n+1) is NOT divisible by 4) = 1 - P(n(n+1) is divisible by 4)

Let’s determine the probability that n(n+1) is divisible by 4. If n(n+1) is divisible by 4, then either n is divisible by 4 or n +1 is divisible by 4. Calculating the number of values of n divisible by 4 is the same as calculating the number of multiples of 4 between 1 and 50 inclusive. To calculate this, we can use this formula:
 
(largest multiple of 4 - smallest multiple of 4)/4 + 1
 
(48 - 4)/4 + 1
 
44/4 + 1 = 11 + 1 = 12
 
Thus, there are 12 multiples of 4 between 1 and 50 inclusive. That is, n can be any one of these 12 multiples of 4 so that n(n + 1) will be divisible by 4.

Similarly, if (n + 1) is a multiple of 4, n(n + 1) also will be divisible by 4. Since we know that there are 12 values of n that are multiples of 4, there must be another 12 values of n such that (n + 1) is a multiple of 4. Let’s expand on this idea:
 
When n = 3, n + 1 = 4, and thus n(n+1) is a multiple of 4.

When n = 23, n + 1 = 24, and thus n(n+1) is a multiple of 4.
 
When n = 47, n + 1 = 48, and thus n(n+1) is a multiple of 4.
 
We can see that there are 12 values of n that are multiples of 4, and 12 more values of n for (n + 1) to be a multiple of 4. Since there are 50 total integers from 1 to 50, inclusive, the probability of selecting a value of n so that n(n+1) is a multiple of 4 is:
 
24/50 = 12/25

Thus, the probability that n(n+1) IS NOT a multiple of 4 is 1 - 12/25 = 13/25.

Answer: B

Fdambro294 · Answer

(N) (N + 1) will be divisible by 4 if the integer N that is picked is either of the form:

N = 4k

or

N = 4k - 1

Find how many multiples of 4 there are from 1 to 50

Then double that amount because for each corresponding multiple there will be one value that is (-1) below that multiple

Ex: (3 and 4) ——- (7 and 8) ........ (47 and 48)

Count = (48 - 4)/4 + (1)

Count = 12

12 * 2 = 24 integers N such that (N) (N + 1) will be divisible by 4

Thus:

50 integers - (24 multiples of 4) =

26 Numbers that will NOT make (N) (N + 1) divisible by 4

Probability = 26/50 = 13/25

13/25

Posted from my mobile device

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n is an integer from 1 to 50, what is the probability that n(n+1) is n

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n is an integer from 1 to 50, what is the probability that n(n+1) is n

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