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# A pass code is created by combining one-digit prime numbers. What is

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Joined: 27 Jan 2016
Posts: 130
Schools: ISB '18
GMAT 1: 700 Q50 V34
A pass code is created by combining one-digit prime numbers. What is  [#permalink]

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16 Jul 2017, 01:16
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38% (02:36) correct 63% (02:34) wrong based on 29 sessions

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A pass code is created by combining one-digit prime numbers. What is the probability that the resulting four-digit number is a multiple of 12 ?

A) 1/16
B) 21/256
C) 3/16
D) 1/12
E) 15/16
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A pass code is created by combining one-digit prime numbers. What is  [#permalink]

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16 Jul 2017, 05:41
1
There are 4 one digit prime numbers - 2,3,5,7.

The total number of 4 digit numbers possible is 4*4*4*4(since digits can be repeated)
In order to determine how many of these 4 digit numbers are divisible by 12,
we employ the following method :
For a number to be divisible by 12, it has to be divisible by both 3 and 4.

Only numbers ending with 32,52 and 72 can be divisible by 4
as the rule for divisibility of 4 is that the last 2 digits must be divisible by 4.
For the number to be divisible by 3, the sum of the digits must add to give a multiple of 3 :

We have the possible total combinations for the numbers ending :

1. _ _ 32 are 2532,5232,5532,3732,7332, and2232(6 combinations)
2. _ _ 52 are 7752,3552,5352,2352, and 3252(5 combinations)
3. _ _ 72 are 5772,7572,2772,7272, and 3372(5 combinations)

P(Numbers divisible by 12) = P(A) = 6+5+5 = 16
Also P(T) = P(Total possible combinations) = 256

The probability is $$\frac{P(A)}{P(T)}$$ = $$\frac{16}{256} = \frac{1}{16}$$ (Option A)
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A pass code is created by combining one-digit prime numbers. What is   [#permalink] 16 Jul 2017, 05:41
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