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If an integer greater than 100 and less than 1,000 is to be

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If an integer greater than 100 and less than 1,000 is to be [#permalink] New post 29 Nov 2019, 03:22
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If an integer greater than 100 and less than 1,000 is to be selected at random, what is the probability that the integer selected will be a multiple of 7?

A. \(\frac{142}{999}\)

B. \(\frac{142}{900}\)

C. \(\frac{142}{899}\)

D. \(\frac{128}{900}\)

E. \(\frac{128}{899}\)


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[Reveal] Spoiler: OA

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Re: If an integer greater than 100 and less than 1,000 is to be [#permalink] New post 29 Nov 2019, 06:53
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Carcass wrote:
If an integer greater than 100 and less than 1,000 is to be selected at random, what is the probability that the integer selected will be a multiple of 7?

A. \(\frac{142}{999}\)

B. \(\frac{142}{900}\)

C. \(\frac{142}{899}\)

D. \(\frac{128}{900}\)

E. \(\frac{128}{899}\)


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We should start by asking "How many integers are greater than 100 and less than 1000?"
And other words, "How many integers are there from 101 to 999 inclusive?"

A nice rule says: the number of integers from x to y inclusive equals y - x + 1
So, the number of integers from 101 to 999 inclusive = 999 - 101 + 1 = 899

So, we are randomly selecting one number from 899 integers
This tells us that the denominator of the probability must be 899
So we can eliminate answer choices A, B and D

We are left with answer choice C (142/899) and answer choice E (128/899)

Since the numerators are quite spread apart we can use some estimation.
There are 899 images to choose from and approximately 1/7 of those integers are multiples of 7
1/7 of 899 ≈ 128.4

So, the correct answer must be E

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Brent
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Re: If an integer greater than 100 and less than 1,000 is to be [#permalink] New post 29 Nov 2019, 11:19
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Let's first count the total possible scenarios or events.
If an integer greater than 100 and less than 1,000 ==> means there is total (999-101+1)=899 numbers including 101 & 999.

Now 7*15=105 ; which is the immediate number after 101 which is divisible by 7
And 7*142=994 ; which is the last number before 999 which is divisible by 7

So (142-15+1)=128 numbers including 105 and 994 are divisible by 7.


so Probability = no of successful events/Total possible events= 128/899 ==> hence answer is (E).
Re: If an integer greater than 100 and less than 1,000 is to be   [#permalink] 29 Nov 2019, 11:19
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