If a is positive integer less than or equal to 100, what is the probab

Question

If a is positive integer less than or equal to 100, what is the probability that a(a – 1) is a multiple of 5?

A. 1/5
B. 39/100
C. 2/5
D. 1/2
E. 29/50

Sumo23 · Answer

Hi Bunuel... I am not 100% sure since solved orally while on the move...

Is the answer 2/5... cos 40 out of 100 integers would be divisible by 5... thanks

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Turkish · Answer

There are two numbers that can be multiple of 5. a multiple of 5 and a multiple of 5 + 1 since a(a – 1)

So there are 40 numbers; 20 multiple of 5 and 20 from (a – 1).

40/100=2/5

KarishmaB · Answer

You want (a - 1)*a to be a multiple of 5. a can take values from 1 to 100.

Note that a can be 1 since (a - 1) = 0 which gives us 0 (a multiple of 5)

Next, a can be 5 or 6. It can be 10. So there are 4 acceptable values of a in the first 10.

The same pattern will be repeated for every 10 numbers till 100.

So total acceptable values of a = 4 * 10 = 40

Required probability = 40/100 = 2/5

rocko911 · Answer

Is this a right way?

either a or a-1 will be a multiple of 5

So for a to be multiple of 5 = 20/100
 for (a-1) to be multiple of 5 = 20/100

1/5+1/5 = 2/5

Is this correct way?

gracie · Answer

for a^2-a to be a multiple of 5,
a must have a units digit of 0,1,5 or 6
4 units digits/10 possible units digits=2/5
C

exc4libur · Answer

Positive integers are > 0: {1,2,3,57,99...}

From 1 to 100 there are:  Number.Terms=Last.term-First.term+1=100-1+1=100  total outcomes.

If x is a multiple of 5 then x(x+1) = multiple of 5.
If x+1 is a multiple of 5 then x(x+1) = multiple of 5.

From 1 to 100 there are:  Number.Multiples=\frac{Largest.multiple-Smallest.multiple}{Multiple}+1=\frac{100-5}{5}+1=20  multiples of 5 that fit x, and  20  multiples of 5 that fit  x-1 .

Probability:  \frac{Favorable.Outcomes}{Total.Outcomes}=\frac{(20+20)}{100}=2/5 .

(C) is the answer.

Ayush3678 · Answer

I think there is a problem with the answer Question is telling the value of a is  Less than or equal to 100  then when we take value of a to find probability of given condition :
 a  must be  5  or  (5+1) to satisfy the given condition
next we have to calculate total number of favorable conditions for that count number of 5 multiples from 1 to 100 which is  20 
next there will be 20  (5+1)  condition 
total will be => 20+20 = 40 but thats where everyone are going wrong  100 can be value of a but 100+1 cannot be value of a according to the question value of a can be less than or equal to 100 not greater than 100   
since, we already added up in our favourable condition we have to subtract 1 condition of 100+1
40-1=39 
probability = favourable condition/total number of condition 
p= 39/100 
idk why option is wrong and even many peoples are doing wrong even if i am wrong please direct me i am only self studying student
Jay shree ram

If a is positive integer less than or equal to 100, what is the probab

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If a is positive integer less than or equal to 100, what is the probab

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