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If a 3-digit integer is selected at random from the integers 100 throu

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If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

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New post 26 Nov 2015, 04:47
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A
B
C
D
E

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Question Stats:

81% (01:32) correct 19% (01:51) wrong based on 90 sessions

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If a 3-digit integer is selected at random from the integers 100 through 199, inclusive, what is the probability that the first digit and the last digit of the integer are each equal to one more than the middle digit?

(A) 2/225
(B) 1/111
(C) 1/110
(D) 1/100
(E) 1/50

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Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

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New post 26 Nov 2015, 05:37
Hundreds digit has to be 1 . So units digit needs to 1 as well
And both Hundreds and Units digit needs to be 1 more than ten's digit
The number is 101
Total numbers between 100 and 199 = (199-100)+1 = 100

Probability = 1/100

Answer D
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Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

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New post 26 Nov 2015, 12:32
Answer-D
Total number of digits=199-100=99+1=100= Number of outcomes
Numbers which fulfill given criteria= only 1 number=101
Probability= Favourable Outcome/Total number of outcomes= 1/100
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Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

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New post 28 Nov 2015, 19:52
Hi All,

The answer choices to this question provide some significant hints as to the possible outcomes that 'fit' the restrictions mentioned in the prompt.

We're told to consider the integers from 100 to 199, inclusive. That is a group of 100 numbers, so any probability question that is based on that range will have a denominator that is either 100 or reduced from 100. Only Answers D and E fit that pattern. With those answers, we know that there is either one number that fits the restrictions (1/100) or two numbers (2/100 = 1/50).

It's actually not too hard to find the integer that fits the description (since we know that the first digit has to be 1): 101. Since there's no other option, we have the answer.

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Re: If a 3-digit integer is selected at random from the  [#permalink]

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New post 31 Mar 2018, 08:45
Hi ALL,

The question uses the phrase "the first digit and the last digit of the integer are EACH EQUAL to "ONE MORE" than the middle digit." This means that the first and third digits are the SAME digit and that each is ONE MORE than the second digit.

Given the range that we have to work with (101 - 199), the ONLY number that fits this description is "101."

Since there are 100 total numbers in that range, the probability is 1/100

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Re: If a 3-digit integer is selected at random from the &nbs [#permalink] 31 Mar 2018, 08:45
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