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19 May 2020, 06:29
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
34% (02:55) correct
66%
(02:23)
wrong
based on 116
sessions
History
Date
Time
Result
Not Attempted Yet
What is the sum of all numbers less than 200 that are either prime or have more than 3 factors?
A. 19,900
B. 19,535
C. 19,533
D. 19,523
E. 19,522
Are You Up For the Challenge: 700 Level Questions
A. 19,900
B. 19,535
C. 19,533
D. 19,523
E. 19,522
Are You Up For the Challenge: 700 Level Questions
19 May 2020, 07:04
Kudos
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Bunuel
Hi
Please check the video explanation here
Answer: Option E
19 May 2020, 07:24
Kudos
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Bunuel
Solution
- • Positive number having exactly one factor = 1
• Positive numbers having exactly 2 factors = prime numbers
• Positive numbers having exactly 3 factors = square of prime numbers (i.e. \(p^2\) where p is a prime number)
• Apart from the above mentioned numbers, all other numbers will have more than 3 factors.
• Therefore, the sum of all numbers less than 200 that are either prime or have more than 3 factors = (sum of all integers from 1 to 199) – (sum of the square of prime numbers which are less than 15) – 1 [ since \(15^2 = 225\), and number under consideration are less than 200]
- o Thus, required the sum \(= \frac{199*(199 +1)}{2} – (2^2 +3^2 + 5^2 +7^2 + 11^2 + 13^2) – 1 = 199*100 – (4+9+25+49+121+169) - 1 = 19,522\)
