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27 Jul 2017, 01:30
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C
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Difficulty:
85%
(hard)
Question Stats:
57% (02:31) correct
43%
(02:54)
wrong
based on 334
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A math teacher assigns a distinct prime number, starting with the lowest, for each student in her class. If she chooses two students at random, the probability the sum of their numbers is not even is less than 1/10. What is the fewest possible number of students in her class?
(A) 19
(B) 20
(C) 21
(D) 71
(E) 73
(A) 19
(B) 20
(C) 21
(D) 71
(E) 73
27 Jul 2017, 07:31
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Bunuel
Hi..
The proper method would be
let n be the number, so n-1 are ODD prime..
1) choosing any 2 out of n is nC2..
2) ways in which sum is not even..
one has to be 2 and other any from n-1.. so n-1C1..
Probability =\(\frac{n-1C1}{nC2}= \frac{(n-1)!}{(n-1-1)!1!}*\frac{(n-2)!2!}{n!}=(n-1)*\frac{2}{n(n-1)}=\frac{2}{n}\)..
so from Q \(\frac{2}{n}<\frac{1}{10}\) or n>20..
so ans is n=21
C
General Discussion
27 Jul 2017, 03:18
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The first 23 prime numbers 2,3,5,7,9,....67, 71 and 73. Selecting 2 out of 23is 23C2 means 253
And except 2 if we add any number to the other we will stand ven number only. So total outcomes are (2,3), (2,5), (2,7)......(2,73), leading to total of 20 outcomes.
So probability is 20/253 which is less than 1/10.
But if we select 19 or 20 numbers then the probability turns out to be ≥1/10 which is not acceptable as per te question stem.
So my Answer is C.
Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
And except 2 if we add any number to the other we will stand ven number only. So total outcomes are (2,3), (2,5), (2,7)......(2,73), leading to total of 20 outcomes.
So probability is 20/253 which is less than 1/10.
But if we select 19 or 20 numbers then the probability turns out to be ≥1/10 which is not acceptable as per te question stem.
So my Answer is C.
Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
