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13 Nov 2022, 00:26
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (01:41) correct
29%
(01:11)
wrong
based on 7
sessions
History
Date
Time
Result
Not Attempted Yet
0 < P*Q < 100, P and Q are both prime numbers,and P < Q, how many combinations of P and Q are there?
A. 11
B. 15
C. 21
D. 28
E. 30
A. 11
B. 15
C. 21
D. 28
E. 30
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13 Nov 2022, 00:47
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Afroditee
if P = 2
2*{3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47} = 14 cases
if P = 3
3*{5, 7, 11, 13, 17, 19, 23, 29, 31} = 9 cases
if P = 5
5*{7, 11, 13, 17, 19} = 5 cases
if P = 7
7*{11, 13} = 2 cases
Total Cases = 14+9+5+2 = 30
Answer: Option E
13 Nov 2022, 00:49
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Let's start listing all the primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 ....
We have to choose 2 primes and their product has to be < 100
Smallest prime is 2. That means, the other prime has to be less than 50 (else product will become greater than 100)
Now, let's choose a P and get corresponding Qs such that (P < Q and P*Q < 100)
P=2
Q can be - (3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47) - 14 cases
P=3
Q can be - (5, 7, 11, 13, 17, 19, 23, 29, 31) - 9 cases
P=5
Q can be - (7, 11, 13, 17, 19) - 5 cases
P=7
Q can be - (11, 13) - 2 cases
Total 14 + 9 + 5 + 2 = 30 cases
So, 30 combinations (E)
We have to choose 2 primes and their product has to be < 100
Smallest prime is 2. That means, the other prime has to be less than 50 (else product will become greater than 100)
Now, let's choose a P and get corresponding Qs such that (P < Q and P*Q < 100)
P=2
Q can be - (3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47) - 14 cases
P=3
Q can be - (5, 7, 11, 13, 17, 19, 23, 29, 31) - 9 cases
P=5
Q can be - (7, 11, 13, 17, 19) - 5 cases
P=7
Q can be - (11, 13) - 2 cases
Total 14 + 9 + 5 + 2 = 30 cases
So, 30 combinations (E)
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