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Senior Manager  Joined: 24 Mar 2011
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Location: Texas
Sequence A is defined by the equation An = 3n + 2, where n  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 62% (02:00) correct 38% (02:18) wrong based on 276 sessions

### HideShow timer Statistics Sequence A is defined by the equation An = 3n + 2, where n is an integer greater than or equal to 1. If set B is comprised of the first x terms of sequence A, what is the median of set B ?

(1) The sum of the terms in set B is 220.

(2) The range of the terms in set B is 30.

Originally posted by agdimple333 on 08 Jun 2011, 12:45.
Last edited by Bunuel on 21 Oct 2013, 12:03, edited 2 times in total.
Retired Moderator Joined: 20 Dec 2010
Posts: 1736
Re: DS - Arithmetic Seq  [#permalink]

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agdimple333 wrote:
Sequence A is defined by the equation An = 3n + 2, where n is an integer greater than or equal to 1. If set B is comprised of the first x terms of sequence A, what is the median of set B ?

(1) The sum of the terms in set B is 220.

(2) The range of the terms in set B is 30.

$$A_n=3n+2$$
$$A_1=3*1+2=5$$
$$A_2=3*2+2=8$$
$$A_3=3*3+2=11$$
.
.
.
As we can see that the set
A={5,8,11,14,17,20,23,26,29,32,35,38..................}
B={5,...}

We just need to know the number of terms to get the median.

1.
Sum of an arithmetic series:
$$S_n=\frac{n}{2}[2a_1+(n-1)d]$$
We know,
$$a_1=5$$
$$d=5$$
Solving, we get n=11 and the median.
Sufficient.

2.
Range is known:
Min=5, we know
Max=35, as the range=30
Thus, B={5,8,11,14,17,20,23,26,29,32,35}
Median=20
Sufficient.

Ans: "D"
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Re: DS - Arithmetic Seq  [#permalink]

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1
agdimple333 wrote:
Sequence A is defined by the equation An = 3n + 2, where n is an integer greater than or equal to 1. If set B is comprised of the first x terms of sequence A, what is the median of set B ?

(1) The sum of the terms in set B is 220.

(2) The range of the terms in set B is 30.

Fluke's solution is great, but you don't need to go through all the work. If we see that the sequence is

5, 8, 11, 14, 17, ....

then certainly the more terms we have, the bigger the sum will be. So Statement 1 simply has to be sufficient: there can only be one number of terms that will give a sum of exactly 220, and if we know the number of terms, we can find the median. Similarly, the more terms we have, the bigger the range will be, so there can only be one number of terms that gives a range of exactly 30. The answer is D.
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Senior Manager  Joined: 24 Mar 2011
Posts: 332
Location: Texas
Re: DS - Arithmetic Seq  [#permalink]

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fluke wrote:
2.
Range is known:
Min=5, we know
Max=35, as the range=30
Thus, B={5,8,11,14,17,20,23,26,29,32,35}
Median=20
Sufficient.

Ans: "D"

What if i take min = 11 and as range = 30 implies B = 41
so set = {11,14,17,20,23,26,29,32,35,38,41}
than the median = 26

what i am confused here is that in such kind of Q, are they asking if we can find the median based on the given information or not.
Or
are we suppose to determine that with given info there exists only single median (you know what i mean)?

But now when i see statement 1, according to which also we can construct different sets, just that the sum of all elements should be 220. So basically i think the Q is asking if we can find the median based on the given info or not.
Retired Moderator Joined: 20 Dec 2010
Posts: 1736
Re: DS - Arithmetic Seq  [#permalink]

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agdimple333 wrote:
fluke wrote:
2.
Range is known:
Min=5, we know
Max=35, as the range=30
Thus, B={5,8,11,14,17,20,23,26,29,32,35}
Median=20
Sufficient.

Ans: "D"

What if i take min = 11 and as range = 30 implies B = 41
so set = {11,14,17,20,23,26,29,32,35,38,41}
than the median = 26

what i am confused here is that in such kind of Q, are they asking if we can find the median based on the given information or not.
Or
are we suppose to determine that with given info there exists only single median (you know what i mean)?

But now when i see statement 1, according to which also we can construct different sets, just that the sum of all elements should be 220. So basically i think the Q is asking if we can find the median based on the given info or not.

Based on the given info, you can just create ONE set:
set B can't start from 11.
We know
A={5,8,11,14....}
AND it is given in the stem that:
"If set B is comprised of the first x terms of sequence A".
Thus, B can't start from 11.

And now, when a series is starting with 5, we know this for sure. We also know the summation of the series from st1. We will know the exact set to form. Once we know the set, we can find the median.

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Re: DS - Arithmetic Seq  [#permalink]

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one thing we must remember is in DS the 2 statements can never contradict each other.

If your statement 2 stats with 5..................41
then the st.1 should mention the sum of set B as 226 and not 220.

Hope that helps.
Director  Joined: 01 Feb 2011
Posts: 629
Re: DS - Arithmetic Seq  [#permalink]

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Sequence is like 5 8 .....

1. Sufficient

sum of terms is 220

so enough to find the last term and all the terms upto the last term (as the series is in A.P.)

=> enough to find median

2. Sufficient

from the range and the first term , we can find the last term and all the terms upto the last term (as the series is in A.P.)

=> enough to find median

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Re: DS - Arithmetic Seq  [#permalink]

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a1=5,a2=8,a3=11 and so on.

a gives 120 = n/2[2a+ (n-1)d] where d = 3 and a = 5 here.

thus the xth element can be found out. Hence the median.

Sufficient.

b gives a = 5 and xth element = 35.
thus median can be found out for AM.
Sufficient.

D it is.
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Re: Sequence A is defined by the equation An = 3n + 2, where n  [#permalink]

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Hi Bunnel and Fluke,

The problem reads that Sequence A is defined by the equation An = 3n + 2, therefore Sequence A is definitely in Arithmetic progression.

Then it reads If set B is comprised of the first x terms of sequence A- How can we assume from this that set B in Arithmetic progression.

As per Fluke's solution, statement A is only sufficient if it is assumed that set B is in AP.

From statement B we know that the t1= 5 and tn=35

set B could be = {5, t2, t3, t4, ...t(n-1),35}

But if we combine both the information then

Assuming that set B is not in AP

5+t2+t3+t4+...+t(n-1)+35=220
t2+t3+t4+...+t(n-1)=180

Therefore set B could be= (5,30,30,30,30,30,30,35) [as the problem does not read that set B consists of different integers], median 30
or set B could be=(5,24,28,29,31,32,36), median 30
or set B could be= (5,7,16,18,20,22,27,30,35), median 20

The way I understand the problem, if we assume that set B is in AP then the answer choice is D
If we assume that set B is not in AP and can consist of both different or same integers then the answer choice is E

It would be very helpful if you can please provide some insight on my understanding.
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Re: Sequence A is defined by the equation An = 3n + 2, where n  [#permalink]

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samikpal01 wrote:
Hi Bunnel and Fluke,

The problem reads that Sequence A is defined by the equation An = 3n + 2, therefore Sequence A is definitely in Arithmetic progression.

Then it reads If set B is comprised of the first x terms of sequence A- How can we assume from this that set B in Arithmetic progression.

As per Fluke's solution, statement A is only sufficient if it is assumed that set B is in AP.

From statement B we know that the t1= 5 and tn=35

set B could be = {5, t2, t3, t4, ...t(n-1),35}

But if we combine both the information then

Assuming that set B is not in AP

5+t2+t3+t4+...+t(n-1)+35=220
t2+t3+t4+...+t(n-1)=180

Therefore set B could be= (5,30,30,30,30,30,30,35) [as the problem does not read that set B consists of different integers], median 30
or set B could be=(5,24,28,29,31,32,36), median 30
or set B could be= (5,7,16,18,20,22,27,30,35), median 20

The way I understand the problem, if we assume that set B is in AP then the answer choice is D
If we assume that set B is not in AP and can consist of both different or same integers then the answer choice is E

It would be very helpful if you can please provide some insight on my understanding.

Set A = {5, 8, 11, 14, 17, 20, ...}, an arithmetic progression as you noted.

Set B is comprised of the first x terms of set A, so set B must also be an arithmetic progression. For example, if x=3, so if set B is comprised of the first 3 terms of set A, then set B = {5, 8, 11}.

Does this make sense?
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