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Sequence A is defined by the equation An = 3n + 7

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by BTGmoderatorDC » Tue Feb 27, 2018 6:37 pm
Sequence A is defined by the equation An = 3n + 7, 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 275.
(2) The range of the terms in set B is 30

Which of the statements is sufficient? can some experts explain why?

OA D
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by mbawisdom » Tue Mar 06, 2018 5:37 am
lheiannie07 wrote:Sequence A is defined by the equation An = 3n + 7, 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 275.
(2) The range of the terms in set B is 30

Which of the statements is sufficient? can some experts explain why?

OA D
Let's look at the sequence:

A1 = 10
A2 = 13
A3 = 16
...
An = 3n + 7

(1) the sum of the sequence is going to equal 7n + (n)(n+1)3/2. We are told this equals 275.
7n + 3/2(n^2 + n) = 275
14n + 3n^2 + 3n = 550
3n^2 + 17n - 550 = 0
If you like you can solve this and you will get n = 11. The point though is not to solve it. If we know we can solve it, we know N and hence we know all the elements in B. Once we know all the elements in B we can work out the median.
SUFFICIENT

(2) the range is 30 implies that the last term is 30 more than the first --> the first is 10 so the last is 40.
40 = 3n + 7
33 = 3n
n = 11
Once again we know N and hence we know all the elements in B. Once we know all the elements in B we can work out the median.
SUFFICIENT

Do let me know if you have any questions - I imagine it the sum formula "7n + (n)(n+1)3/2" could be a bit tricky but I'll let you have a crack at it and can explain in further detail if needed.
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by Jay@ManhattanReview » Wed Mar 07, 2018 3:34 am
lheiannie07 wrote:Sequence A is defined by the equation An = 3n + 7, 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 275.
(2) The range of the terms in set B is 30

Which of the statements is sufficient? can some experts explain why?

OA D
We have

Sequence A is defined by the equation An = 3n + 7, where n ≥ 1

Set B is comprised of the first x terms of sequence A

We have to get the value of median of Set B.

If we get the values of first x terms of Set B, we can calculate the value of the median.

Let's take each statement one by one.

(1) The sum of the terms in set B is 275.

The first term of Set A = 3*1 + 7 = 10;
The second term of Set A = 3*2 + 7 = 13;
The third term of Set A = 3*3 + 7 = 16;

So Set B: {10, 13, 16, 19, ... }

If we keep adding the terms of Set B (10 + 13 + 16 + 19 + 22 + ...), we will certainly reach 275; thus, the number of terms would be known. When the numbers of terms would be known, the middle-most term can be identified and thus, we can get the unique value of median. Sufficient.

Since this is a DS question and we only need to be sure that there would be a unique answer to the question, we need not necessarily calculate the value.

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

Range = Highest term - Smallest term

30 = Highest term - (3*1 + 7)

Highest term = 30 + 10 = 40

Set B: {10, 13, 16, 19, 22, ... 40}

Again, we have the finite number of terms, thus, the unique value of median can be computed. Sufficient.

The correct answer: D

Hope this helps!
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by farsar » Fri Jun 28, 2019 12:13 pm
mbawisdom wrote:
lheiannie07 wrote:Sequence A is defined by the equation An = 3n + 7, 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 275.
(2) The range of the terms in set B is 30

Which of the statements is sufficient? can some experts explain why?

OA D
Let's look at the sequence:

A1 = 10
A2 = 13
A3 = 16
...
An = 3n + 7

(1) the sum of the sequence is going to equal 7n + (n)(n+1)3/2. We are told this equals 275.
7n + 3/2(n^2 + n) = 275
14n + 3n^2 + 3n = 550
3n^2 + 17n - 550 = 0
If you like you can solve this and you will get n = 11. The point though is not to solve it. If we know we can solve it, we know N and hence we know all the elements in B. Once we know all the elements in B we can work out the median.
SUFFICIENT

(2) the range is 30 implies that the last term is 30 more than the first --> the first is 10 so the last is 40.
40 = 3n + 7
33 = 3n
n = 11
Once again we know N and hence we know all the elements in B. Once we know all the elements in B we can work out the median.
SUFFICIENT

Do let me know if you have any questions - I imagine it the sum formula "7n + (n)(n+1)3/2" could be a bit tricky but I'll let you have a crack at it and can explain in further detail if needed.

Thank you so much for this. I had a question. In the part where:

3n^2 + 17n - 550 = 0
If you like you can solve this and you will get n = 11.

I would like to understand why we can assume this equation to not have two solutions? Because I got till here and assumed n will have two values and dismissed it. Could you suggest a faster way of solving it as well? Appreciate it a lot!
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by Ian Stewart » Sat Jun 29, 2019 5:37 am
farsar wrote: Thank you so much for this. I had a question. In the part where:

3n^2 + 17n - 550 = 0
If you like you can solve this and you will get n = 11.

I would like to understand why we can assume this equation to not have two solutions? Because I got till here and assumed n will have two values and dismissed it.
I wouldn't solve this problem by generating a formula -- we know exactly what our sequence is. The sequence is 10, 13, 16, 19, etc. Every term is positive, so as you add more and more terms, the sum gets larger and larger. If we know the sum of the first n terms is 275, there can thus only be one value of n, and with that value we can answer the question.

But if you did generate that formula, 3n^2 + 17n - 550 = 0, if you solved completely, you will find two different solutions for n. But because the quadratic has that "-550" at the end, one of the solutions will be negative (if you solve, you'll find it is -50/3), and the other will be positive (the positive solution is 11). In this question, n must be a positive integer, so you'd discard the meaningless negative solution, and you'd have only one possible value of n.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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