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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, 01:06
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, 02:31
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, 02:59
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, 03:03



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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, 03:29
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, 20:45
sir why can't we take 5=2+3and 31=2+29



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Re: How many positive integers less than 30 are either a multiple of 2, an
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27 Oct 2018, 07:34
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, 28 Sum 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 + 5, 3 + 7, etc Evaluate to get: 5, 7, 9, 11, . . . 27, 29 At this point, our list of numbers includes 2 as well as all integers from 4 to 29 All 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, 29 So, 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 &nbs
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