How many positive integers less than 5,000 are evenly divisible by neither 15 nor 21?
A. 4,514
B. 4,475
C. 4,521
D. 4,428
E. 4,349
Difficult Math Problem #79 - Number Theory
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- aim-wsc
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5000/15 = 333 quotient & 5 remainder
5000/21 = 238 quotient & 2 remainder
LCM for 15 & 21 =105
5000/105 = 47 quotient
5000-333-238+47 = 4476
ANSWER :
4475
C'mon 800guy i dont think they will ask such questions...
5000/21 = 238 quotient & 2 remainder
LCM for 15 & 21 =105
5000/105 = 47 quotient
5000-333-238+47 = 4476
ANSWER :
4475
C'mon 800guy i dont think they will ask such questions...
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here's the OA. merry christmas!
We first determine the number of integers less than 5,000 that are evenly divisible by 15. This can be found by dividing 4,999 by 15:
= 4,999/15
= 333 integers
Now we will determine the number of integers evenly divisible by 21:
= 4,999/21
= 238 integers
some numbers will be evenly divisible by BOTH 15 and 21. The least common multiple of 15 and 21 is 105. This means that every number that is evenly divisible by 105 will be divisible by BOTH 15 and 21. Now we will determine the number of integers evenly divisible by 105:
= 4,999/105
= 47 integers
Therefore the positive integers less than 5000 that are not evenly divisible by 15 or 21 are 4999-(333+238-47)=4475
We first determine the number of integers less than 5,000 that are evenly divisible by 15. This can be found by dividing 4,999 by 15:
= 4,999/15
= 333 integers
Now we will determine the number of integers evenly divisible by 21:
= 4,999/21
= 238 integers
some numbers will be evenly divisible by BOTH 15 and 21. The least common multiple of 15 and 21 is 105. This means that every number that is evenly divisible by 105 will be divisible by BOTH 15 and 21. Now we will determine the number of integers evenly divisible by 105:
= 4,999/105
= 47 integers
Therefore the positive integers less than 5000 that are not evenly divisible by 15 or 21 are 4999-(333+238-47)=4475
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you're probably right, but it always helps to prepare for the worstaim-wsc wrote:5000/15 = 333 quotient & 5 remainder
5000/21 = 238 quotient & 2 remainder
LCM for 15 & 21 =105
5000/105 = 47 quotient
5000-333-238+47 = 4476
ANSWER :
4475
C'mon 800guy i dont think they will ask such questions...