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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
A box contains every positive 4-digit integer whose digits add to 34.
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01 Aug 2022, 06:23
01 Aug 2022, 06:23
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A box contains every positive 4-digit integer whose digits add to 34. If a number is randomly selected from the box, what is the probability the number is divisible by 4?
(A) 1/16
(B) 1/12
(C) 1/10
(D) 1/8
(E) 1/6
(A) 1/16
(B) 1/12
(C) 1/10
(D) 1/8
(E) 1/6
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: A box contains every positive 4-digit integer whose digits add to 34.
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08 Aug 2022, 06:23
08 Aug 2022, 06:23
2
GreenlightTestPrep wrote:
A box contains every positive 4-digit integer whose digits add to 34. If a number is randomly selected from the box, what is the probability the number is divisible by 4?
(A) 1/16
(B) 1/12
(C) 1/10
(D) 1/8
(E) 1/6
(A) 1/16
(B) 1/12
(C) 1/10
(D) 1/8
(E) 1/6
If the sum of the digits is 34, then there are only 2 possible cases:
Case i: The 4 digits are 9, 9, 9, and 7, in which case there are 4 possible numbers: 7999, 9799, 9979 and 9997
Case ii: The 4 digits are 9, 9, 8, and 8, in which case there are 6 possible numbers: 8899, 8989, 8998, 9988, 9898, 9889
To the total number of 4-digit numbers in the box = 4 + 6 = 10
Aside: we could also you the MISSISSIPPI rule to determine the number of ways to arrange 9, 9, 8, and 8, but I wanted to see which numbers are divisible by 4.
Test for divisibility by 4: A number is divisible by 4 if and only it the 2-digit number created by the last 2 digits is divisible by 4.
So, since 88 is divisible by 4, we know that 9988 is divisible by 4.
Since 9988 is the only number divisible by 4, P(selected integer is divisible by 4) = 1/10
Answer: C
Re: A box contains every positive 4-digit integer whose digits add to 34.
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27 Jul 2024, 13:45
27 Jul 2024, 13:45
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