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If a number N is chosen at random from the set of two-digit integers 02 Mar 2011, 19:16
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Difficulty:

75% (hard)

Question Stats:

50% (02:23) correct 50% (01:57) wrong based on 28 sessions

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If a number N is chosen at random from the set of two-digit integers whose digits are both prime numbers, what is the probability that N is divisible by 3?

A. 1/3
B. 1/4
C. 9/25
D. 5/16
E. 0

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If a number N is chosen at random from the set of two-digit integers 02 Mar 2011, 20:35
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Prime digits are: 2, 3, 5, 7

Total number of 2 digit #s with both digits prime are: 4*4 = 16

out of these numbers divisible by 3 = 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.

=> prob = 5/16.

Ans D. Took me 3:20 mins.
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If a number N is chosen at random from the set of two-digit integers 23 Apr 2011, 03:44
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If this has been done manually...there should be a better way of solving this th

dreambeliever
Prime digits are: 2, 3, 5, 7

Total number of 2 digit #s with both digits prime are: 4*4 = 16

out of these numbers divisible by 3 = 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.

=> prob = 5/16.

Ans D. Took me 3:20 mins.
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If a number N is chosen at random from the set of two-digit integers 23 Apr 2011, 04:19
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dreambeliever
Prime digits are: 2, 3, 5, 7

Total number of 2 digit #s with both digits prime are: 4*4 = 16

out of these numbers divisible by 3 = 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.

=> prob = 5/16.

Ans D. Took me 3:20 mins.
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Manually:
2,3,5,7

Start from left most;
Pick 2 for tens place; units digit should be greater than 2.
23-ignore
25-ignore
27-consider. Count=2; 27,72
**********
Pick 3 for tens place; units digit should be greater than 3.
35-ignore
37-ignore
*******
Pick 5 for tens place; units digit should be greater than 5.
57-consider. Count=2; 57,75
************
With repetition:
22-ignore
33-consider. Count=1
55-ignore
77-ignore

********
P=5/(4)^2
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If a number N is chosen at random from the set of two-digit integers 23 Apr 2011, 12:43
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Nice question. I had missed considered prime numbers can repeat and so took whole set to be 12 numbers alone.

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