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17 Apr 2020, 12:08
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B
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:
42% (02:47) correct
58%
(02:36)
wrong
based on 119
sessions
History
Date
Time
Result
Not Attempted Yet
How many positive integers less than 100 are divisible by exactly one of the integers 2,5,7?
(A) 39
(B) 49
(C) 59
(D) 69
(E) 79
(A) 39
(B) 49
(C) 59
(D) 69
(E) 79
17 Apr 2020, 12:24
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Ravixxx
How many positive integers less than 100 are divisible by exactly one of the integers 2,5,7?
(A) 39
(B) 49
(C) 59
(D) 69
(E) 79
(A) 39
(B) 49
(C) 59
(D) 69
(E) 79
Multiple of 2 less than 100 = 49
Multiple of 5 less than 100 = 19
Multiple of 7 less than 100 = 14
Multiple of 2 and 5 less than 100 = 99/10 = 9
Multiple of 2 and 7 less than 100 = 99/14 = 7
Multiple of 5 and 7 less than 100 = 99/35 = 2
Multiples of 2 and 5 and 7 all = 1
Required numbers = 49+19+14 - 2*(9+7+2) + 3*1 = 49
ANswer: Option B
General Discussion
17 Apr 2020, 12:45
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positive integer from 1- 100 are divisible by 2= [100/2] = 50
positive integer from 1- 100 are divisible by 5= [100/5] = 20
positive integer from 1- 100 are divisible by 7= [100/7] = 14
positive integer from 1- 100 are divisible by 10= [100/10] = 10
positive integer from 1- 100 are divisible by 14= [100/14] = 7
positive integer from 1- 100 are divisible by 35= [100/35] = 2
positive integer from 1- 100 are divisible by 70= [100/70] = 1
positive integers less than 100 are divisible by exactly one of the integers 2,5,7 = 50+20+14- 2(10+7+2) +3*1 = 49
[100 got deducted as it's divisible by 2 and 5.]
positive integer from 1- 100 are divisible by 5= [100/5] = 20
positive integer from 1- 100 are divisible by 7= [100/7] = 14
positive integer from 1- 100 are divisible by 10= [100/10] = 10
positive integer from 1- 100 are divisible by 14= [100/14] = 7
positive integer from 1- 100 are divisible by 35= [100/35] = 2
positive integer from 1- 100 are divisible by 70= [100/70] = 1
positive integers less than 100 are divisible by exactly one of the integers 2,5,7 = 50+20+14- 2(10+7+2) +3*1 = 49
[100 got deducted as it's divisible by 2 and 5.]
Ravixxx
How many positive integers less than 100 are divisible by exactly one of the integers 2,5,7?
(A) 39
(B) 49
(C) 59
(D) 69
(E) 79
(A) 39
(B) 49
(C) 59
(D) 69
(E) 79
