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# A number, x, is randomly selected from the integers from 42

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Kudos [?]: 1275 [0], given: 6017

A number, x, is randomly selected from the integers from 42 [#permalink]  01 Dec 2018, 10:50
Expert's post
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Question Stats:

70% (00:37) correct 29% (00:54) wrong based on 31 sessions
A number, x, is randomly selected from the integers from 42 to 92 inclusive.

 Quantity A Quantity B The probability that x is odd. The probability that x is even.

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
[Reveal] Spoiler: OA

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GRE Instructor
Joined: 10 Apr 2015
Posts: 1800
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Kudos [?]: 1686 [1] , given: 8

Re: A number, x, is randomly selected from the integers from 42 [#permalink]  01 Dec 2018, 14:19
1
KUDOS
Expert's post
Carcass wrote:
A number, x, is randomly selected from the integers from 42 to 92 inclusive.

 Quantity A Quantity B The probability that x is odd. The probability that x is even.

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given

----ASIDE---------------------
Since even and odd integers alternate, one might incorrectly assume that each probability = 1/2.
However, if there's an odd number of integers in the group (like 4, 5, 6, 7, 8), the number of even integers is one more than the number of odd integers.
----------------------------------

A nice rule says: the number of integers from x to y inclusive equals y - x + 1
So, the number of integers from 42 to 92 inclusive = 92 - 42 + 1 = 51

Since our integers start and end with an EVEN integer (42 and 92) there must be 26 EVEN integers and 25 ODD integers.

So P(x is EVEN) = 26/51
and P(x is ODD) = 25/51

We get:
QUANTITY A: 25/51
QUANTITY B: 26/51

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Joined: 22 Feb 2018
Posts: 163
Followers: 2

Kudos [?]: 109 [1] , given: 22

Re: A number, x, is randomly selected from the integers from 42 [#permalink]  27 Dec 2018, 17:22
1
KUDOS

Numbers between 42 and 92 are 42,…,92 and their quantity is 92-42+1 = 51
Odd numbers are: 43,45,…, 91, So there are (91-43) / 2 + 1 = 25 odd numbers.
Even numbers are: 42,44,…, 92, So there are (92-42) / 2 + 1 = 26 even numbers.

P(A) = 25/51
P(B) = 26/51
As number of even numbers is more than odd ones, the probability that x is even is more than the probability that x is odd.
_________________

Re: A number, x, is randomly selected from the integers from 42   [#permalink] 27 Dec 2018, 17:22
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# A number, x, is randomly selected from the integers from 42

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