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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 [#permalink]

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New post 20 Dec 2017, 02:46
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Re: If a is positive integer less than or equal to 100, what is the probab [#permalink]

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New post 20 Dec 2017, 03:05
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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Re: If a is positive integer less than or equal to 100, what is the probab [#permalink]

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New post 20 Dec 2017, 03:51
Bunuel wrote:
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


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
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Re: If a is positive integer less than or equal to 100, what is the probab [#permalink]

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New post 20 Dec 2017, 05:21
Bunuel wrote:
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


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
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Re: If a is positive integer less than or equal to 100, what is the probab [#permalink]

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New post 25 Dec 2017, 00:06
VeritasPrepKarishma wrote:
Bunuel wrote:
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


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


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?
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If a is positive integer less than or equal to 100, what is the probab [#permalink]

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New post 25 Dec 2017, 19:05
Bunuel wrote:
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


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
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If a is positive integer less than or equal to 100, what is the probab [#permalink]

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New post 26 Dec 2017, 04:36
Bunuel wrote:
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


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.
If a is positive integer less than or equal to 100, what is the probab   [#permalink] 26 Dec 2017, 04:36
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