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Which of the following cannot be the sum of two or more cons

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Which of the following cannot be the sum of two or more cons [#permalink] New post 25 Mar 2013, 09:00
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A
B
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D
E

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Question Stats:

51% (02:15) correct 49% (01:40) wrong based on 92 sessions
Which of the following cannot be the sum of two or more consecutive positive integers?

(A) 3^7
(B) 4^6
(C) 5^5
(D) 6^4
(E) 7^3

This Week's Challenge Problem from MGMAT : "Consecutive Positive Madness"

https://www.manhattangmat.com/challenge_thisweek.cfm?submitted=1

I got this wrong ... Can anybody please explain?
[Reveal] Spoiler: OA

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Last edited by Bunuel on 26 Mar 2013, 01:14, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Challenge Problem from MGMAT: Consecutive Positive Madness [#permalink] New post 25 Mar 2013, 09:32
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Every natural number not of the form 2^k for some natural number k can be written as the sum of two or more consecutive positive integers.
Hence answer is B.
I solved this question manually but later found on internet that numbers which can be expressed as 2^n, n is a natural number, cannot be represented as sum of 2 or more consecutive numbers.

Please give a kudo if you like my explanation.
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Re: Challenge Problem from MGMAT: Consecutive Positive Madness [#permalink] New post 25 Mar 2013, 20:45
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TheNona wrote:
This Week's Challenge Problem from MGMAT : "Consecutive Positive Madness"

https://www.manhattangmat.com/challenge_thisweek.cfm?submitted=1

Which of the following cannot be the sum of two or more consecutive positive integers?

(A) 3^7 (B) 4^6 (C) 5^5 (D) 6^4 (E) 7^3

I got this wrong ... Can anybody please explain?



There are lots of properties of numbers and GMAT does not expect you to know them. So a question that appears of GMAT must be solvable without knowing the properties. So think hard about what you know and what you can apply. Use pattern recognition.

Try some numbers to start off:
1+2 = 3
2+3 = 5
3+4 = 7
ok, so is there a pattern here? We are getting all odd numbers. 3, 5, 7, 9, 11 etc. Every odd number can be written as sum of two consecutive numbers. Why? Say an odd number is N. When you divide it by 2, you get half of it which has a .5. You take the integer above it and below it and they will add up to give N
e.g. N = 11.
11/2 = 5.5 so take numbers 5 and 6 and they will add to give 11. Why? because 5.5 is the arithmetic mean of 2 consecutive numbers:5 and 6.

Takeaway: Every odd number can be written as sum of two consecutive integers.

So rule out (A), (C) and (E).

Now, try to sum up three consecutive numbers.
1+2+3 = 6
2+3 +4 = 9 (ignore odd numbers so we have already dealt with them)
3+4+5 = 12
4+5+6 = 15
5+6+7 = 18
6+7+8 = 21
7+8+9 = 24

You are getting all multiples of 3. The important thing is that no multiple of 3 is getting skipped. You are getting all of them. Hence we can represent all multiples of 3 as sum of 3 numbers. Hence (D) is also out since it is a multiple of 3.
Now think why?
Sum of three consecutive integers is given by (n-1) + n + (n + 1) = 3n

Takeaway: Sum of any three consecutive numbers will be a multiple of 3.

Hence answer must be (B) i.e. 4^6
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Re: Challenge Problem from MGMAT: Consecutive Positive Madness [#permalink] New post 25 Mar 2013, 21:23
Expert's post
TheNona wrote:
This Week's Challenge Problem from MGMAT : "Consecutive Positive Madness"

https://www.manhattangmat.com/challenge_thisweek.cfm?submitted=1

Which of the following cannot be the sum of two or more consecutive positive integers?

(A) 3^7 (B) 4^6 (C) 5^5 (D) 6^4 (E) 7^3



We know that the sum of consecutive integers is :S = n/2(f+l) --> Here n is the number of terms and f and l are the first and last terms respectively. Now, we have been told that n>=2.

We can have only the following cases :

f = odd, l = odd, n = (odd-odd)+1 = odd. Thus, S = odd*even/2.

f = odd, l = even, n = (even-odd)+1 = even. S = odd.even/2. Similarly, for the other two combinations also, the sum S = odd*even/2. Now, out of the given options, all the options can be in this pattern except 4^6 = 2^12.

B.
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Re: Which of the following cannot be the sum of two or more cons [#permalink] New post 04 Apr 2013, 07:43
TheNona wrote:
Which of the following cannot be the sum of two or more consecutive positive integers?

(A) 3^7
(B) 4^6
(C) 5^5
(D) 6^4
(E) 7^3

This Week's Challenge Problem from MGMAT : "Consecutive Positive Madness"

https://www.manhattangmat.com/challenge_thisweek.cfm?submitted=1

I got this wrong ... Can anybody please explain?


Is this a 700 level question ?

answer simply depends upon logic of even and odd number
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Re: Which of the following cannot be the sum of two or more cons [#permalink] New post 04 Apr 2013, 07:44
jbisht wrote:
TheNona wrote:
Which of the following cannot be the sum of two or more consecutive positive integers?

(A) 3^7
(B) 4^6
(C) 5^5
(D) 6^4
(E) 7^3

This Week's Challenge Problem from MGMAT : "Consecutive Positive Madness"

https://www.manhattangmat.com/challenge_thisweek.cfm?submitted=1

I got this wrong ... Can anybody please explain?


Is this a 700 level question ?

answer simply depends upon logic of even and odd number



4^(any Number) = will never be odd
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Re: Which of the following cannot be the sum of two or more cons [#permalink] New post 05 Apr 2013, 01:50
Expert's post
jbisht wrote:
TheNona wrote:
Which of the following cannot be the sum of two or more consecutive positive integers?

(A) 3^7
(B) 4^6
(C) 5^5
(D) 6^4
(E) 7^3

This Week's Challenge Problem from MGMAT : "Consecutive Positive Madness"

https://www.manhattangmat.com/challenge_thisweek.cfm?submitted=1

I got this wrong ... Can anybody please explain?


Is this a 700 level question ?

answer simply depends upon logic of even and odd number


That's the thing about GMAT questions - All 700- 800 level questions will also simply depend on the logic of something simple.
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Re: Which of the following cannot be the sum of two or more cons [#permalink] New post 21 Jun 2014, 06:30
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Re: Which of the following cannot be the sum of two or more cons   [#permalink] 21 Jun 2014, 06:30
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