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M is the sum of three consecutive odd integers, the least o

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M is the sum of three consecutive odd integers, the least o [#permalink] New post 07 Jun 2017, 02:02
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M is the sum of three consecutive odd integers, the least of which is \(t\). In terms of M, which of the following is the sum of three consecutive odd integers, the greatest of which is t ?

A) \(M + 12\)

B) \(M + 6\)

C) \(M - 6\)

D) \(M - 12\)

E) \(\frac{M}{2}\)
[Reveal] Spoiler: OA

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Re: M is the sum of three consecutive odd integers, the least o [#permalink] New post 20 Sep 2017, 05:55
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The sum of three consecutive integers, the least being t is M = t + (t+2) + (t+3) = 3t +6. The sum of three consecutive odd integers, the largest being t is (t-4) + (t-2) + t = 3t - 6. To get the answer in terms of M, we can substitute for 3t that from the first equation is equal to M-6 obtaining that the sum becomes M-6-6 = M-12. Thus answer D!
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Re: M is the sum of three consecutive odd integers, the least o [#permalink] New post 12 May 2018, 01:55
IlCreatore wrote:
The sum of three consecutive integers, the least being t is M = t + (t+2) + (t+3) = 3t +6. The sum of three consecutive odd integers, the largest being t is (t-4) + (t-2) + t = 3t - 6. To get the answer in terms of M, we can substitute for 3t that from the first equation is equal to M-6 obtaining that the sum becomes M-6-6 = M-12. Thus answer D!



If possible can you please explain your solution in a bit simpler way. will be thankful.
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Re: M is the sum of three consecutive odd integers, the least o [#permalink] New post 12 May 2018, 09:30
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IshanGre wrote:
IlCreatore wrote:
The sum of three consecutive integers, the least being t is M = t + (t+2) + (t+3) = 3t +6. The sum of three consecutive odd integers, the largest being t is (t-4) + (t-2) + t = 3t - 6. To get the answer in terms of M, we can substitute for 3t that from the first equation is equal to M-6 obtaining that the sum becomes M-6-6 = M-12. Thus answer D!



If possible can you please explain your solution in a bit simpler way. will be thankful.



the wording is a bit convoluted but the question is not difficult.

The question says: 3 consecutive odd integers and the least is t. The best way is to pick numbers: 5+7+9=21

Only D is the answer because M -12 = 21 -12 = 9 and our t was 9.

Hope this helps.

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Re: M is the sum of three consecutive odd integers, the least o [#permalink] New post 21 Nov 2018, 20:51
IshanGre wrote:
IlCreatore wrote:
The sum of three consecutive integers, the least being t is M = t + (t+2) + (t+3) = 3t +6. The sum of three consecutive odd integers, the largest being t is (t-4) + (t-2) + t = 3t - 6. To get the answer in terms of M, we can substitute for 3t that from the first equation is equal to M-6 obtaining that the sum becomes M-6-6 = M-12. Thus answer D!



If possible can you please explain your solution in a bit simpler way. will be thankful.


The solution is logical. May be you are confused by a typo. Instead of (t+3), it should be (t+4) because the question is about consecutive odd. The later part is just simplification.
Re: M is the sum of three consecutive odd integers, the least o   [#permalink] 21 Nov 2018, 20:51
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