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If the sum of 5 consecutive integers is x, which of the [#permalink]
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Updated on: 08 Mar 2013, 16:30
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If the sum of 5 consecutive integers is x, which of the following must be true?I. x is an even number II. x is an odd number III. x is a multiple of 5 (A) I only (B) II only (C) III only (D) I and III (E) II and III
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Originally posted by megafan on 08 Mar 2013, 16:02.
Last edited by Bunuel on 08 Mar 2013, 16:30, edited 1 time in total.
Edited the tags: not a 700level question at all.



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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]
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08 Mar 2013, 21:10
I. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true. II. Same as above. This need not be always true. III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4) = 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases. Therefore C is the answer.
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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]
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08 Mar 2013, 23:19
OA: C there can be two cases 1. first no is oddthen sun of 5 consecutive no is odd 2. first no is eventhen sun of 5 consecutive no is even so we can't conclude 1 and second statement. Sum of five consecutive no is always divisible by 5 hence option C



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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]
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09 Mar 2013, 01:52
megafan wrote: If the sum of 5 consecutive integers is x, which of the following must be true?
I. x is an even number II. x is an odd number III. x is a multiple of 5
(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III You can solve this question simply considering different sets of 5 consecutive integers. I. x is an even number > if the set is {1, 0, 1, 2, 3}, then the sum is 5=odd. Thus this statement is not always true. Eliminate A and D. II. x is an odd number > if the set is {2, 1, 0, 1, 2}, then the sum is 0=even. Thus this statement is not always true. Eliminate B and E. Only option C remains. Answer: C.
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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]
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22 Apr 2013, 22:52
Sum of every odd number of consecutive integers is always divisible by the odd number Eg: sum of 5 odd number of integers= 1+2+3+4+5 = 15/5=3 The same does not hold true for even number of consecutive integers Thus IMO C Statements 1 and 2 are not true, since we dont know what exactly is the value of x
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If the sum of 5 consecutive integers is x, which of the [#permalink]
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03 Jan 2015, 13:26
Assume the simplest series , I assumed following a) 1,2,3,4,5 Sum=15 , Odd b) 2,3,4,5,6 Sum=20, Even c) 3,4,5,6,7 sum= 25, Odd Took less than a minute to find such series will be multiple of 5. Now see why ? In another way this series can be rewritten as (a2),(a1),a,(a+1),(a+2) , where a is an integer Sum = 5a ...... Easy isnt it ? whatever may the value of 'a' be the sum of the given series will be a multiple of '5'
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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]
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03 Feb 2017, 12:44
megafan wrote: If the sum of 5 consecutive integers is x, which of the following must be true?
I. x is an even number II. x is an odd number III. x is a multiple of 5
(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III We can let our integers be the following: n, n + 1, n + 2, n + 3, n + 4 Summing them, we have: n + n + 1 + n + 2 + n + 3 + n + 4 = 5n + 10 Since the sum is 5n + 10, we see that if n were an odd number, then 5n + 10 would be odd; however, if n were even, 5n + 10 would be even. Thus, I or II do not have to be true. However, regardless of the value of n, we see that 5n + 10 is divisible by 5: (5n + 10)/5 = 5n/5 + 10/5 = n + 2 Thus, III must be true. Answer: C
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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]
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03 Apr 2017, 07:04
The 5 nos. are: a,(a+1),(a+2),(a+3),(a+4) Add them, we get: 5a+10= 5(a+2) If a is even, the expression would be even. (5*even)  If a is odd, the expression would be odd. (5*odd) But whatever the final answer would be, it would be a multiple of 5 because 5 is a factor here.
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Re: If the sum of 5 consecutive integers is x, which of the
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