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Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.

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Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.  [#permalink]

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New post 19 Nov 2016, 06:05
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Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}. In how many ways can three numbers be chosen from Set S such that the sum of those three numbers is 54?

A)five
B)four
C)three
D)two
E)zero

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Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.  [#permalink]

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New post 19 Nov 2016, 08:29
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stonecold wrote:
Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}. In how many ways can three numbers be chosen from Set S such that the sum of those three numbers is 54?

A)five
B)four
C)three
D)two
E)zero


The set S is a set of Odd numbers

Sum of 3 odd Numbers will be Odd..

Hence correct answer will be 0, since an even number ( 54 ) can never be obtained....
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Re: Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.  [#permalink]

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New post 19 Nov 2016, 08:38
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Abhishek009 wrote:
stonecold wrote:
Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}. In how many ways can three numbers be chosen from Set S such that the sum of those three numbers is 54?

A)five
B)four
C)three
D)two
E)zero


The set S is a set of Prime ( ODD number except 2 )

Sum of 3 odd Numbers will be Odd..

Hence correct answer will be 0, since an even number ( 54 ) can never be obtained....


Hi Abhishek

Your answer is absolutely correct.
But Set S isn't a set of primes
33,49 => not primes
Although they are all odd.
So it wont make a difference.

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Re: Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.  [#permalink]

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New post 19 Nov 2016, 09:14
stonecold wrote:
Abhishek009 wrote:
stonecold wrote:
Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}. In how many ways can three numbers be chosen from Set S such that the sum of those three numbers is 54?

A)five
B)four
C)three
D)two
E)zero


The set S is a set of Prime ( ODD number except 2 )

Sum of 3 odd Numbers will be Odd..

Hence correct answer will be 0, since an even number ( 54 ) can never be obtained....


Hi Abhishek

Your answer is absolutely correct.
But Set S isn't a set of primes
33,49 => not primes
Although they are all odd.
So it wont make a difference.

Regards
Stone

Thanx for point out... :-D

I have edited my post...
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Re: Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.  [#permalink]

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New post 20 Nov 2016, 07:51
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stonecold wrote:
Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}. In how many ways can three numbers be chosen from Set S such that the sum of those three numbers is 54?

A) five
B) four
C) three
D) two
E) zero


Great question, stonecold!!

It illustrates a point I often make about the fact that the test-makers are reasonable people. That is, they don't expect us to engage in long/hard/tedious/time-consuming calculations.
So when I started working on this question, I started looking for at least one set of 3 values that added to 54. After 20 seconds of this, I realized that, IF I were able to find 3 such values, it would be difficult for me to find another set of 3 values, AND it would be super difficult to know when I had found ALL possible sets.

So, knowing what I know about the testmaker being reasonable, I abandoned my search of values that worked and started looking for other approaches.
That's when I realized that all of the values in the set were ODD integers.
Once I noticed this, I recalled what I know about the sums of ODD integers.
Since we know that ODD + ODD + ODD = ODD, we can see that it's impossible to select three ODD values from the given set that add to 54 (an EVEN number)

Answer:

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Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.  [#permalink]

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New post 20 Nov 2016, 09:08
GMATPrepNow wrote:
stonecold wrote:
Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}. In how many ways can three numbers be chosen from Set S such that the sum of those three numbers is 54?

A) five
B) four
C) three
D) two
E) zero


Great question, stonecold!!

It illustrates a point I often make about the fact that the test-makers are reasonable people. That is, they don't expect us to engage in long/hard/tedious/time-consuming calculations.
So when I started working on this question, I started looking for at least one set of 3 values that added to 54. After 20 seconds of this, I realized that, IF I were able to find 3 such values, it would be difficult for me to find another set of 3 values, AND it would be super difficult to know when I had found ALL possible sets.

So, knowing what I know about the testmaker being reasonable, I abandoned my search of values that worked and started looking for other approaches.
That's when I realized that all of the values in the set were ODD integers.
Once I noticed this, I recalled what I know about the sums of ODD integers.
Since we know that ODD + ODD + ODD = ODD, we can see that it's impossible to select three ODD values from the given set that add to 54 (an EVEN number)

Answer:

RELATED VIDEO




Thanks Brent
I am taking away a Big Lesson from your Post=>

"HAVE FAITH IN THE GMAT TESTMAKERS"



Regards
Stone Cold
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Re: Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.  [#permalink]

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New post 20 Nov 2016, 12:44
stonecold wrote:
Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}. In how many ways can three numbers be chosen from Set S such that the sum of those three numbers is 54?

A)five
B)four
C)three
D)two
E)zero

Great question and a great reminder to always think before hammering away with calculations. I got it right but it took me two minutes and I totally did a bunch of calculations before arriving at my conclusion.
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Re: Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.  [#permalink]

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New post 25 Nov 2016, 05:52
The of 3 odd numbers is always always odd, so it can't be 54 (even)

So the Answer is 0
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Re: Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.  [#permalink]

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New post 16 Feb 2018, 22:31
gracie90 wrote:
stonecold wrote:
Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}. In how many ways can three numbers be chosen from Set S such that the sum of those three numbers is 54?

A)five
B)four
C)three
D)two
E)zero

Great question and a great reminder to always think before hammering away with calculations. I got it right but it took me two minutes and I totally did a bunch of calculations before arriving at my conclusion.


Major takeaway -> Always look for smart ways to solve extra hard questions.
The questions that appear the scariest might actually be the easiest
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Re: Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.  [#permalink]

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New post 17 Feb 2018, 04:04
All the numbers in the given set of numbers are odd numbers.Sum of 3 odd numbers can never be an even number.So there is no way to get sum as 54.So answer would be zero.
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Re: Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.  [#permalink]

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Re: Set S is given as S = {1,3,7,13,17,23,29,31,33,37,39,49,51}.   [#permalink] 27 May 2019, 10:06
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