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

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If an integer greater than 100 and less than 1,000 is to be selected  [#permalink]

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New post 03 Dec 2019, 01:28
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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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Re: If an integer greater than 100 and less than 1,000 is to be selected  [#permalink]

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New post 09 Dec 2019, 17:52
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Bunuel 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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The least multiple of 7 greater than 100 is 105. The greatest multiple of 7 less than 1000 is 994.

Thus, the total number of multiples of 7 greater than 100 but less than 1000 is:

(994 - 105)/7 + 1 = 128

The total number of numbers greater than 100 but less than 1000 is 999 - 101 + 1 = 899.

Thus, the probability is 128/899.

Answer: E
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Re: If an integer greater than 100 and less than 1,000 is to be selected  [#permalink]

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New post 03 Dec 2019, 01:33
total integers >100 <1000 ; 999-101+1 = 899
and multiples of 7 <100 ; 14 and <1000 ; 142
so 142-14 ; 128 ;
P = 128/899
IMO E

Bunuel 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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Re: If an integer greater than 100 and less than 1,000 is to be selected  [#permalink]

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New post 03 Dec 2019, 23:32
The number of integers greater than 100 and less than 1,000
(last integer-first integer)+1
(999-101)+1=899

The number of multiple of 7 integers greater than 100 and less than 1,000
\(\frac{{last integer-first integer}}{7 }\)+1
\(\frac{{994-105}}{7}+1=128\)

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

IMO
Ans: E
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If an integer greater than 100 and less than 1,000 is to be selected  [#permalink]

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New post 04 Dec 2019, 07:30
Bunuel 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. \(\frac{128}{899}\)


Total cases: 999-101+1=899
Favorable cases are multiples 7 from 101 to 999: (994-105)/7+1=128
Probability: 128/899

Ans (E)
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If an integer greater than 100 and less than 1,000 is to be selected   [#permalink] 04 Dec 2019, 07:30
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