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23 Nov 2022, 02:30
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E
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Difficulty:
55%
(hard)
Question Stats:
61% (02:23) correct
39%
(01:46)
wrong
based on 90
sessions
History
Date
Time
Result
Not Attempted Yet
What is the sum of all the integers between 100 and 400 that have exactly three positive factors?
A. 60
B. 120
C. 240
D. 480
E. 940
A. 60
B. 120
C. 240
D. 480
E. 940
23 Nov 2022, 02:39
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Nos. Between 100 and 400 having three positive factors mean perfect squares of prime nos. Between 100 and 400.
11^2= 121 (factors:1,11,121)
13^2= 169 (factors:1,13,169)
17^2= 289 (factors:1,17,289)
19^2= 361 (factors:1,19,361)
121+168+289+361= 940
Answer is option E IMO
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11^2= 121 (factors:1,11,121)
13^2= 169 (factors:1,13,169)
17^2= 289 (factors:1,17,289)
19^2= 361 (factors:1,19,361)
121+168+289+361= 940
Answer is option E IMO
Posted from my mobile device
23 Nov 2022, 03:36
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A number which has exactly three positive factors will be of the form p^2 where, p is prime.
Thus 100 < p^2 < 400
'p' can be 11,13,17 & 19 only.
Now sum of 11^2+13^2+17^2+19^2=940.
Hence E is the correct choice.
Posted from my mobile device
Thus 100 < p^2 < 400
'p' can be 11,13,17 & 19 only.
Now sum of 11^2+13^2+17^2+19^2=940.
Hence E is the correct choice.
Posted from my mobile device
