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what is the sum of the first four terms of sequence S?
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Author:  AbdurRakib [ 01 Jul 2016, 03:57 ]
Post subject:  what is the sum of the first four terms of sequence S?

What is the sum of the first four terms of sequence S?

(1) After the first two terms of S,the value of each term of S is equal to the average (arithmetic mean) of the last two preceding terms.

(2) The average (arithmetic mean) of the first three terms of S is 10.

OG Q 2017 New Question(Book Question: 219)

Author:  Nick90 [ 01 Jul 2016, 05:33 ]
Post subject:  Re: what is the sum of the first four terms of sequence S?

AbdurRakib wrote:
What is the sum of the first four terms of sequence S?

(1) After the first two terms of S,the value of each term of S is equal to the average (arithmetic mean) of the last two preceding terms.

(2) The average (arithmetic mean) of the first three terms of S is 10.

OG Q 2017 New Question(Book Question: 219)


E

Assume 1st term a nd 2nd term b.

From 1st statement, 3rd term (c) = (a+b)/2

4th term = (b +c)/2

From 2nd statement, (a+b+c)/3 =10
a+b+ (a+b)/2 =30

a+b = 20
Therefore, c=10

4th term = (b+c)/2

( we find out the sum of a and b but we can't say anything about individual values. Since, a can be 1,2.....so on and correspondingly b can be 19,18....so on)

So the answer is E






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Author:  MikeScarn [ 05 Aug 2018, 15:54 ]
Post subject:  Re: what is the sum of the first four terms of sequence S?

AbdurRakib wrote:
What is the sum of the first four terms of sequence S?

(1) After the first two terms of S,the value of each term of S is equal to the average (arithmetic mean) of the last two preceding terms.

(2) The average (arithmetic mean) of the first three terms of S is 10.

OG Q 2017 New Question(Book Question: 219)


(1) We could make S anything.

Not Sufficient.


(2) Plug in numbers.

9, 10, 11, 100. Satisfies statement and sum is 130
9, 10, 11, 12. Satisfies statement and sum is 42.

Not Sufficient.


(1) + (2) Plug in numbers.

9, 11, 10, 10.5. Satisfies both statments and sum is 40.5

5, 15, 10, 12.5. Satisfies both statements and sum is 42.5

Not Sufficient.

Answer: E

Author:  09173140521 [ 06 Aug 2019, 04:55 ]
Post subject:  Re: what is the sum of the first four terms of sequence S?

WHAT IS THE BEST APPROACH TO SOLVE SUCH PROBLEM ?

Author:  Hanzel101 [ 17 Aug 2019, 19:51 ]
Post subject:  Re: what is the sum of the first four terms of sequence S?

09173140521 wrote:
WHAT IS THE BEST APPROACH TO SOLVE SUCH PROBLEM ?


According to statement 1 = x + y + (x+y)/2 + [(x+y)/2 + y]/2 = S

No info about Sum, NS.

St 2- x+y+z = 30.

NS.

On combining,

x + y + (x+y)/2 = 30 => x+y = 20.

We can find the 3rd term with this info but since we have no idea what type of sequence it is w.r.t first three terms, we cannot determine x & y.

FYI, 3rd term will be (x+y)/2 = 10. (replacing x+y with 20). But, can you find x & y ? (x+y =20 ...x & y could be multiple values)

Author:  Doryhihii [ 24 Aug 2020, 19:58 ]
Post subject:  Re: what is the sum of the first four terms of sequence S?

AbdurRakib wrote:
What is the sum of the first four terms of sequence S?

(1) After the first two terms of S,the value of each term of S is equal to the average (arithmetic mean) of the last two preceding terms.

(2) The average (arithmetic mean) of the first three terms of S is 10.

OG Q 2017 New Question(Book Question: 219)


Hi Bunuel, could you please help to provide the answer? Thank you.

Author:  twistedphoton [ 15 Sep 2020, 15:12 ]
Post subject:  Re: what is the sum of the first four terms of sequence S?

What is the sum of the first four terms of sequence S?

(1) After the first two terms of S,the value of each term of S is equal to the average (arithmetic mean) of the last two preceding terms.

(2) The average (arithmetic mean) of the first three terms of S is 10.


Let first 2 terms be a,b
As per statement 1, sequence is: a, b, (a+b)/2, b +(a+b)/2 = a, b, (a+b)/2, (a+3b)/2
Sum = (4a + 6b)/2 (Sum can be anything, since we don't know values of a and b, so eliminate option A and D)

Let first 3 terms be a,b,c
As per statement 2, a+b+c = 3*10 = 30
Now, 4th term can be any term, thus eliminate option B

Combining both statements:
a + b + (a+b)/2 = 30
a+b = 20
Sum = (4a+6b)/2 = [(4a+4b) + 2b] / 2
Sum = 2(a+b) + b
Sum = 2*20 + b = 40 + b
Since, we don't know the value of b, still not sufficient, Select Option E

Author:  samsung1234 [ 16 Jun 2021, 22:56 ]
Post subject:  Re: what is the sum of the first four terms of sequence S?

ScottTargetTestPrep

Hi Scott, would you be able to post an efficient solution to this? It took me 4 minutes to solve this... which is way too long.

Author:  ScottTargetTestPrep [ 30 Jun 2021, 09:43 ]
Post subject:  Re: what is the sum of the first four terms of sequence S?

AbdurRakib wrote:
What is the sum of the first four terms of sequence S?

(1) After the first two terms of S,the value of each term of S is equal to the average (arithmetic mean) of the last two preceding terms.

(2) The average (arithmetic mean) of the first three terms of S is 10.

OG Q 2017 New Question(Book Question: 219)

Solution:

Question Stem Analysis:


We need to determine the sum of the first four terms of sequence S. If we can determine the values of the four terms, then we can determine their sum.

Statement One Alone:

Since we don’t know the value of any of the 4 terms, statement one is not sufficient.

Statement Two Alone:

Even though we don’t know the value of any of the first 3 terms, we know their sum is 30. However, since we don’t know the 4th term, statement two is not sufficient.

Statements One and Two Together:

We can let a and b be the first two terms, then using the first statement, the 3rd term is (a + b)/2 = a/2 + b/2, and the 4th term is (b + (a + b)/2)/2 = b/2 + a/4 + b/4 = a/4 + 3b/4. From the second statement, we can create the equation:

a + b + a/2 + b/2 = 30

3a/2 + 3b/2 = 30

3a + 3b = 60

a + b = 20

However, since we don’t know the individual values of a and b, we can’t determine the 4th term. For example, if a = 8 and b = 12, then the 4th term is a/4 + 3b/4 = 2 + 9 = 11 and the sum of the first 4 terms is 30 + 11 = 41 (recall that the sum of the first 3 terms is 30). However, if a = 12 and b = 8, then then the 4th term is a/4 + 3b/4 = 3 + 6 = 9 and the sum of the first 4 terms is 30 + 9 = 39. Both statements together are not sufficient.

Answer: E

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Post subject:  Re: what is the sum of the first four terms of sequence S?

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