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Nov 30, 2022 9:30 am
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Two different prime numbers are greater than 2 and less than 50. If the product of them is less than 100, then how many combinations of them will there be?
A. 13
B. 14
C. 15
D. 16
E. 17
A. 13
B. 14
C. 15
D. 16
E. 17
Nov 30, 2022 10:24 am
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Prime number set:
(3,5,7,11,13,17,19,23,29,31,37, 41,43,47)
P*Q<100
P=3 Q=(5,7,11,13,17,19,23,29,31)
9 combinations
P=5 Q=(7,11,13,17,19)
5 combinations
P=7 Q=(11,13)
2 combinations
Total= 9+5+2= 16 combinations.
Posted from my mobile device
(3,5,7,11,13,17,19,23,29,31,37, 41,43,47)
P*Q<100
P=3 Q=(5,7,11,13,17,19,23,29,31)
9 combinations
P=5 Q=(7,11,13,17,19)
5 combinations
P=7 Q=(11,13)
2 combinations
Total= 9+5+2= 16 combinations.
Posted from my mobile device
Nov 30, 2022 10:31 am
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Bunuel
We can write the first few prime numbers greater than 2
3, 5, 7, 11, 13, 17, 19 , 23, 29, 31
We don't need to consider primes greater than 31 (as 33 * 3 = 99)
With 3 , we can have 9 pairs - All the above numbers can be multiplied.
With 5, all primes less than 20 need to be considered. So 5 pairs.
With 7, we can have 2 pairs
There can not be any further pairs.
So total 16 combinations.
