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15 Jul 2026, 09:58
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The numbers are 2,3,5,7,11,13,17,19,23,29,31
The total number of ways 4 numbers can be selected is 11C4 = 330.
For range = 12,
We can choose (5,17), (7,19) , (11,23), (17, 29), (19,31).
When we chose the 1st 3 pairs mentioned above.. there are 3 numbers in between which can be selected in 3C2 ways.
For the remaining two pairs, there are 2 numbers in between which can be selected in 2C2 ways.
So, the total Favourable outcomes are = (3 * 3C2) + (2 * 2C2) = 11
Therefore,
P=11/330 = 1/30
Option B is correct
The total number of ways 4 numbers can be selected is 11C4 = 330.
For range = 12,
We can choose (5,17), (7,19) , (11,23), (17, 29), (19,31).
When we chose the 1st 3 pairs mentioned above.. there are 3 numbers in between which can be selected in 3C2 ways.
For the remaining two pairs, there are 2 numbers in between which can be selected in 2C2 ways.
So, the total Favourable outcomes are = (3 * 3C2) + (2 * 2C2) = 11
Therefore,
P=11/330 = 1/30
Option B is correct
Theeldertwin
Joined: 28 Dec 2025
Last visit: 06 Sep 2026
Posts: 163
Given Kudos: 88
Concentration: Strategy
Schools: HEC Sept '27 INSEAD Aug '27 NUS '27
GMAT Focus 1: 655 Q84 V84 DI79 
15 Jul 2026, 10:03
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First 11 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
Sets of numbers which have range of 12: (5, 17) , (7, 19), (11, 23), (17, 29), (19, 31) and the reverse of each of them as well. That gives us 10 favourable outcomes.
Total outcomes= 11P2 or (11C2 × 2!) = ((11×10)/2)×2 = 110
So Probablity = 10/110 = 1/11
Sets of numbers which have range of 12: (5, 17) , (7, 19), (11, 23), (17, 29), (19, 31) and the reverse of each of them as well. That gives us 10 favourable outcomes.
Total outcomes= 11P2 or (11C2 × 2!) = ((11×10)/2)×2 = 110
So Probablity = 10/110 = 1/11
15 Jul 2026, 10:11
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I found out, only 5 pairs have a difference of 12, now fav/unfavorable would be 11/4!7!=330 unfav. Now numerator would be how many selections inside the range of 12, which is 3+3+3+1+1 which would be 11/330 and 1/30 which is B is our answer.
15 Jul 2026, 10:18
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11 prime numbers: 2,3,5,7,11,13,17,19,23,29,31.
pairs which work:
5,17 - 7,11,13 = 3c2 =3
7,19 = 3
11,23 =3
17,29 = 19,23 = 2c2 = 1
19,31= 1
total favorable outcomes = 3+3+3+1+1 = 11
total outcomes = 11c4 = 330
answer = 11/330 = 1/30
pairs which work:
5,17 - 7,11,13 = 3c2 =3
7,19 = 3
11,23 =3
17,29 = 19,23 = 2c2 = 1
19,31= 1
total favorable outcomes = 3+3+3+1+1 = 11
total outcomes = 11c4 = 330
answer = 11/330 = 1/30
