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# if a three-digit number is selected at random

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Intern
Joined: 15 Dec 2015
Posts: 34
if a three-digit number is selected at random  [#permalink]

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23 Dec 2015, 15:11
1
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:43) correct 19% (01:51) wrong based on 63 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
CEO
Joined: 20 Mar 2014
Posts: 2626
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: if a three-digit number is selected at random  [#permalink]

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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

Hope this helps.
Manager
Joined: 18 Jun 2017
Posts: 59
Re: if a three-digit number is selected at random  [#permalink]

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