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Re: How many positive integers less than 30 are either a multiple of 2, an
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19 Aug 2017, 02:06
Bunuel wrote: enigma123 wrote: How many positive integers less than 30 are either a multiple of 2, an odd prime number, or the sum of a positive multiple of 2 and an odd prime? (A) 29 (B) 28 (C) 27 (D) 25 (E) 23
Any idea how to solve this guys? 30 sec approach: Any odd nonprime, greater than 1, can be obtained by the sum of an odd prime and a positive even number. So this set plus the set of odd primes basically makes the set of all odd numbers greater than 1 in the range. Now, the set of all odd numbers greater than 1 together with the set of all even numbers makes the set of all numbers from 1 to 30, not inclusive, so total of 28 numbers. Answer: B. To illustrate: # of even numbers in the range is (282)/2+1=14: 2, 4, 6, ..., 28; # of odd primes in the range is 9: 3, 5, 7, 11, 13, 17, 19, 23, and 29; # of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4; Total: 14+9+5=28. You can see that we have all numbers from 1 to 30, not inclusive: 2, 3, 4, 5, 6, ...., 29. Hope it's clear. Hello BunuelIf in such series, we get a number that repeats in both sets. Then do we have to count it once or twice? For example: How many positive integers less than 20 are multiple of 2 or a multiple of 3? Multiple of 2: 2,4,6,8,10,12,14,16,18 Multiple of 3: 3,6,9,12,15,18 So do we have to count 6, 12, and 18 once or twice? Total would be 15 or 12 ? Thanks



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Re: How many positive integers less than 30 are either a multiple of 2, an
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19 Aug 2017, 03:31
Shiv2016 wrote: Bunuel wrote: enigma123 wrote: How many positive integers less than 30 are either a multiple of 2, an odd prime number, or the sum of a positive multiple of 2 and an odd prime? (A) 29 (B) 28 (C) 27 (D) 25 (E) 23
Any idea how to solve this guys? 30 sec approach: Any odd nonprime, greater than 1, can be obtained by the sum of an odd prime and a positive even number. So this set plus the set of odd primes basically makes the set of all odd numbers greater than 1 in the range. Now, the set of all odd numbers greater than 1 together with the set of all even numbers makes the set of all numbers from 1 to 30, not inclusive, so total of 28 numbers. Answer: B. To illustrate: # of even numbers in the range is (282)/2+1=14: 2, 4, 6, ..., 28; # of odd primes in the range is 9: 3, 5, 7, 11, 13, 17, 19, 23, and 29; # of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4; Total: 14+9+5=28. You can see that we have all numbers from 1 to 30, not inclusive: 2, 3, 4, 5, 6, ...., 29. Hope it's clear. Hello BunuelIf in such series, we get a number that repeats in both sets. Then do we have to count it once or twice? For example: How many positive integers less than 20 are multiple of 2 or a multiple of 3? Multiple of 2: 2,4,6,8,10,12,14,16,18 Multiple of 3: 3,6,9,12,15,18 So do we have to count 6, 12, and 18 once or twice? Total would be 15 or 12 ? Thanks How many positive integers less than 20 are multiple of 2 OR a multiple of 3?Answer: 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18. So, total of 12 numbers.
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Re: How many positive integers less than 30 are either a multiple of 2, an
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19 Aug 2017, 03:59
Thank you Bunuel for your reply. Is it because of OR? If there was AND in place of, will the answer still be 12?
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Re: How many positive integers less than 30 are either a multiple of 2, an
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19 Aug 2017, 04:03
Shiv2016 wrote: Thank you Bunuel for your reply. Is it because of OR? If there was AND in place of, will the answer still be 12? How many positive integers less than 20 are multiple of both 2 and 3?Answer: 6, 12, 18. Total of 3 numbers.
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Re: How many positive integers less than 30 are either a multiple of 2, an
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19 Aug 2017, 04:29
multiple of 2 =14 which are even , 2,4,6,8,10........28 odd primes = 3,5,7,11,13,17,19,23,29 =9 numbers odd prime and sum of multiple of 2 = 5,7,9,11,13,15,17,19,21,23,25,27,29 so total are 14+ (1) + 13 = 28 1 is used because 3 is only which is not there in 3rd list total 28.
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Re: How many positive integers less than 30 are either a multiple of 2, an
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07 Oct 2017, 21:45
sir why can't we take 5=2+3and 31=2+29



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How many positive integers less than 30 are either a multiple of 2, an
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27 Oct 2018, 08:34
enigma123 wrote: How many positive integers less than 30 are either a multiple of 2, an odd prime number, or the sum of a positive multiple of 2 and an odd prime?
A. 29 B. 28 C. 27 D. 25 E. 23 Multiples of 2: 2, 4, 6, 8, 10, . . .26, 28Sum of a positive multiple of 2 and an odd prime3 is the smallest ODD prime So, let's add multiples of 2 to 3. We get: 3 + 2, 3 + 4, 3 + 6, 3 + 8, etc Evaluate to get: 5, 7, 9, 11, . . . 27, 29At this point, our list of numbers includes 2 as well as all integers from 4 to 29All we're missing is 1 and 3 An odd prime number3 is odd, so, now our list becomes: 2, 3, 4, 5, 6, . . . 27, 28, 29So, the ONLY value that is NOT in the list is 1 (1 is NOT prime) So, there are 28 numbers that meet the given conditions. Answer: B Cheers, Brent
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Re: How many positive integers less than 30 are either a multiple of 2, an
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02 Nov 2019, 09:28
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