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if a three-digit number is selected at random

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Intern
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Joined: 15 Dec 2015
Posts: 34

Kudos [?]: 17 [0], given: 0

if a three-digit number is selected at random [#permalink]

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New post 23 Dec 2015, 15:11
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Difficulty:

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Question Stats:

82% (00:51) correct 18% (01:16) wrong based on 51 sessions

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if a three-digit number is selected at random from the integers 100 to 999, inclusive, what is the probability that the first digit and the last digit of the integer will both be exactly two less than the middle digit?

(A) 1:900

(B) 7:900

(C) 1:1,000

(D) 1:100

(E) 7:100
[Reveal] Spoiler: OA

Kudos [?]: 17 [0], given: 0

Current Student
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B
Joined: 20 Mar 2014
Posts: 2676

Kudos [?]: 1767 [0], given: 794

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
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Re: if a three-digit number is selected at random [#permalink]

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New post 23 Dec 2015, 15:13
sara86 wrote:
if a three-digit number is selected at random from the integers 100 to 999, inclusive, what is the probability that the first digit and the last digit of the integer will both be exactly two less than the middle digit?

(A) 1:900

(B) 7:900

(C) 1:1,000

(D) 1:100

(E) 7:100


You are asked about all 3 digit numbers that conform to the follow type: ABA , where A= B-2.

There are 900 numbers between 100 and 999 (inclusive).

Numbers of the form ABA are: 131, 242,353,464,575,686,797 = total 7

Thus the probability asked = 7/900

B is the correct answer.

Hope this helps.

Kudos [?]: 1767 [0], given: 794

Manager
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Joined: 18 Jun 2017
Posts: 60

Kudos [?]: 2 [0], given: 166

Re: if a three-digit number is selected at random [#permalink]

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New post 09 Aug 2017, 00:45
Total number of digits 999-100 +1 =900
Combinations can be 1-3,2-4,3-5,4-6,5-7,6-8,7-9. Beyond this 8 & 9 cannot be considered as the difference of 2 will result in two digit numbers.
So the probability can be 7/900.
Option B.

Kudos [?]: 2 [0], given: 166

Re: if a three-digit number is selected at random   [#permalink] 09 Aug 2017, 00:45
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