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# Product of 2 consecutive odd integers is 783. Find their

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Senior Manager
Joined: 04 Mar 2007
Posts: 442
Followers: 1

Kudos [?]: 17 [0], given: 0

Product of 2 consecutive odd integers is 783. Find their [#permalink]  21 May 2007, 10:49
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Product of 2 consecutive odd integers is 783. Find their sum.

A) 44
B) -56
C) -76
D) 64
E) -36
VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 128 [0], given: 0

x*(x+2) = 783 (two consecutive numbers i.e x=3,x+2=5)

x^2+2x = 783

x^2+2x-783 = 0

factoring 783

783:3
261:3
87:3
29

3*3*3*29 = 29*27

(x+29)(x-27) = 0

x can be either -29,27

if x = 27 then x+2 = 29 and 27+29 = 56

if x = -29 then x+2 = -27 and -29+(-27) = -56

the only possible answer is (B)

Director
Joined: 13 Mar 2007
Posts: 545
Schools: MIT Sloan
Followers: 4

Kudos [?]: 28 [0], given: 0

factorize 783

783 = 3 x 3 x 3 x 29

hence all factors - 1,783,3,9,27,29,87,261

only two consecutive odds = 27,29

Hence B
Director
Joined: 18 Jul 2006
Posts: 531
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Kudos [?]: 30 [0], given: 0

Re: PS - consecutive odds [#permalink]  23 May 2007, 00:03
Caas wrote:
Product of 2 consecutive odd integers is 783. Find their sum.

A) 44
B) -56
C) -76
D) 64
E) -36

As two integers are next to each other, one quick way of sloving this is look for square root of 783 = 28 appx (as 28*28 =784).

so integers could be 27 & 29 OR -27 & -29.
VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 128 [0], given: 0

Re: PS - consecutive odds [#permalink]  23 May 2007, 00:36
Juaz wrote:
Caas wrote:
Product of 2 consecutive odd integers is 783. Find their sum.

A) 44
B) -56
C) -76
D) 64
E) -36

As two integers are next to each other, one quick way of sloving this is look for square root of 783 = 28 appx (as 28*28 =784).

so integers could be 27 & 29 OR -27 & -29.

Nice thanks ! a real time saver !

Senior Manager
Joined: 04 Mar 2007
Posts: 442
Followers: 1

Kudos [?]: 17 [0], given: 0

Thank you for the discussion guys
You are all right. OA is B indeed.
For those who wonder - another way of solving it
(2n-1)*(2n+1)=783
4n^2-1=783
n^2=784/4
n=+/- 14
2n=+/- 28 ----> so the consecutive odd integers are +/- 27 and +/- 29 and their sum is +/- 56
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