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

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Math Expert
Joined: 02 Sep 2009
Posts: 43360
If a is positive integer less than or equal to 100, what is the probab [#permalink]

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20 Dec 2017, 01:46
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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
[Reveal] Spoiler: OA

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Intern
Joined: 18 Jan 2017
Posts: 33
Re: If a is positive integer less than or equal to 100, what is the probab [#permalink]

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20 Dec 2017, 02:05
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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Manager
Joined: 13 Jun 2012
Posts: 185
Location: United States
WE: Supply Chain Management (Computer Hardware)
Re: If a is positive integer less than or equal to 100, what is the probab [#permalink]

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20 Dec 2017, 02:51
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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7873
Location: Pune, India
Re: If a is positive integer less than or equal to 100, what is the probab [#permalink]

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20 Dec 2017, 04:21
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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Joined: 11 Feb 2017
Posts: 184
Re: If a is positive integer less than or equal to 100, what is the probab [#permalink]

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24 Dec 2017, 23:06
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?
Director
Joined: 07 Dec 2014
Posts: 885
If a is positive integer less than or equal to 100, what is the probab [#permalink]

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25 Dec 2017, 18:05
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
C
Manager
Joined: 24 Nov 2016
Posts: 151
If a is positive integer less than or equal to 100, what is the probab [#permalink]

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26 Dec 2017, 03:36
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: $$\frac{Favorable.Outcomes}{Total.Outcomes}=\frac{(20+20)}{100}=2/5$$.

If a is positive integer less than or equal to 100, what is the probab   [#permalink] 26 Dec 2017, 03:36
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