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# If a number N is chosen at random from the set of two-digit integers

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Joined: 02 Sep 2009
Posts: 50613
If a number N is chosen at random from the set of two-digit integers  [#permalink]

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22 Jul 2018, 22:13
00:00

Difficulty:

65% (hard)

Question Stats:

45% (01:42) correct 55% (01:46) wrong based on 74 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  [#permalink]

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Updated on: 22 Jul 2018, 22:40
Bunuel wrote:
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

Prime number: 2,3,5,7
number of 2 digit integers whose digit are both prime: 4A2=12 number
number in set divisible by 3: 27,72, 57,75; 4 number
Probability that N is divisible by 7: 4/12=1/3
assuming 2 number is different=>wrong answer
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Originally posted by LeoGT on 22 Jul 2018, 22:28.
Last edited by LeoGT on 22 Jul 2018, 22:40, edited 1 time in total.
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Re: If a number N is chosen at random from the set of two-digit integers  [#permalink]

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22 Jul 2018, 22:28
3
Bunuel wrote:
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

The 4 digits which are prime numbers are 2,3,5, or 7. N can have 16(4*4) possibilities.

For any number with 2 digits, the sum of the 2 digits must be divisible by 3.

There are 2 possibilities for the 2-digit number to be divisible by 3
1. When digits differ - (2,7) and (5,7) - 4 such numbers | 2. Same digit - (3,3) - 1 such number

Therefore, the probability that N is divisible by 3 is $$\frac{5}{16}$$(Option D)
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Re: If a number N is chosen at random from the set of two-digit integers  [#permalink]

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23 Jul 2018, 00:17
N=_ _
there are 4 prime numbers less than 10: 2,3,5,7
therefore the total events equal 4*4=16
to be divisible by 3, sum of the digits of the number must be divisible by 3.
2+7=9
3+3=6
5+7=12
7+2=9
7+5=12

p=5/16
option D
Re: If a number N is chosen at random from the set of two-digit integers &nbs [#permalink] 23 Jul 2018, 00:17
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# If a number N is chosen at random from the set of two-digit integers

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