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

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Math Expert
Joined: 02 Sep 2009
Posts: 60594
If an integer greater than 100 and less than 1,000 is to be selected  [#permalink]

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03 Dec 2019, 02:28
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Difficulty:

55% (hard)

Question Stats:

74% (02:18) correct 26% (02:11) wrong based on 72 sessions

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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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03 Dec 2019, 02:33
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. $$\frac{128}{899}$$

Are You Up For the Challenge: 700 Level Questions
Senior Manager
Joined: 13 Feb 2018
Posts: 494
GMAT 1: 640 Q48 V28
Re: If an integer greater than 100 and less than 1,000 is to be selected  [#permalink]

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04 Dec 2019, 00:32
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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Joined: 24 Nov 2016
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If an integer greater than 100 and less than 1,000 is to be selected  [#permalink]

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04 Dec 2019, 08:30
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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Re: If an integer greater than 100 and less than 1,000 is to be selected  [#permalink]

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09 Dec 2019, 18:52
1
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. $$\frac{128}{899}$$

Are You Up For the Challenge: 700 Level Questions

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.

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Re: If an integer greater than 100 and less than 1,000 is to be selected   [#permalink] 09 Dec 2019, 18:52
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