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# If a 3-digit integer is selected at random from the

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VP
Joined: 09 Jul 2007
Posts: 1065
Location: London
If a 3-digit integer is selected at random from the  [#permalink]

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Updated on: 15 Oct 2018, 05:40
1
3
00:00

Difficulty:

25% (medium)

Question Stats:

82% (00:48) correct 18% (01:08) wrong based on 213 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) $$\frac{2}{225}$$
(B) $$\frac{1}{111}$$
(C) $$\frac{1}{110}$$
(D) $$\frac{1}{100}$$
(E) $$\frac{1}{50}$$

Originally posted by Ravshonbek on 11 Nov 2007, 15:29.
Last edited by pushpitkc on 15 Oct 2018, 05:40, edited 2 times in total.
VP
Joined: 09 Jul 2007
Posts: 1065
Location: London
Re: If a 3-digit integer is selected at random from the  [#permalink]

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11 Nov 2007, 16:15
eyunni wrote:
(C).1/100.

(101)

wah, i got where i made mistake.

199-100+1=200
and got
1/200

rather than 100

thxz!
Senior Manager
Joined: 26 Jul 2007
Posts: 496
Schools: Stern, McCombs, Marshall, Wharton
Re: If a 3-digit integer is selected at random from the  [#permalink]

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12 Nov 2007, 13:17
I'm confused

I've got 10 possible numbers
100 1+0 is 1 greater than 0
111 1+1 is 1 greater than 1
122 1+2 is 1 greater than 2
133 ....etc
144
155
166
177
188
199

That gives 10/100. What am I missing???
VP
Joined: 09 Jul 2007
Posts: 1065
Location: London
Re: If a 3-digit integer is selected at random from the  [#permalink]

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12 Nov 2007, 13:22
gixxer1000 wrote:
I'm confused

I've got 10 possible numbers
100 1+0 is 1 greater than 0
111 1+1 is 1 greater than 1
122 1+2 is 1 greater than 2
133 ....etc
144
155
166
177
188
199

That gives 10/100. What am I missing???

Here we go...

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
?

only possible number is 101

1/100
Senior Manager
Joined: 26 Jul 2007
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Schools: Stern, McCombs, Marshall, Wharton
Re: If a 3-digit integer is selected at random from the  [#permalink]

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12 Nov 2007, 13:31
I see now, I thought it meant to add the first and last digit.
Manager
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Posts: 180
Re: If a 3-digit integer is selected at random from the  [#permalink]

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28 Sep 2009, 10:35
The only number between 100 and 199 that satisfies this condition is 101.

Probability = 1/100
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Re: If a 3-digit integer is selected at random from the  [#permalink]

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10 Jan 2012, 09:53
+1 D

The number is 101. So, the probability is 1/100.
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Re: If a 3-digit integer is selected at random from the  [#permalink]

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10 Jan 2012, 21:32
Ans is 1/100

only 1 number satisfies the above mentioned condition i.e. 101.
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Re: If a 3-digit integer is selected at random from the  [#permalink]

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10 Jan 2012, 23:36
1
the required number is 101 (one number)
total of numbers=199-100+1=100
1/100
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Re: If a 3-digit integer is selected at random from the  [#permalink]

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31 Mar 2018, 09:45
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, 09:45
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