Sequence A is defined by the equation An = 3n + 7, where n is an integ

Question

Sequence A is defined by the equation  A_n = 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.

TestPrepUnlimited · Answer

We already know  A_n = 10, 13, 16, 19 ...  so once we know what  x  is we know the entire set B and the median of set B. Hence we only need to know x for sufficiency.

Statement 1:

We can keep adding the terms of A in order, and stop when the sum reaches 275. We would know x is the index of the last term we added, so x is a confirmed value, sufficient.

Statement 2:

The range is 30 while the common difference is 3, so there are 10 differences and 11 terms in total. Then x = 11, sufficient.

Ans: D

sthahvi · Answer

can someone explain this inn more detail  TestPrepUnlimited

TestPrepUnlimited · Answer

sthahvi  sure!

First of all, this sequence A(n) = 3n + 7 is what we call an arithmetic sequence, each term has equal spacing between its neighbors. The sequence is 10, 13, 16, 19 ... infinitely increasing and this type of sequence has a clear pattern. Since we already know the full sequence, if we want to find the median/anything on the first x terms we only need to know what x is.

Statement 1  says the sum of terms in B is 275. If we add first 5 terms it is only 10 + 13 + 16 + 19 + 22, not even close to 275. If we add the next 5 terms, we might be close with 10 + 13 + 16 + .... + 37. Anyhow, we can keep adding terms until we hit exactly 275 so we know exactly where to stop. Thus x is a known value, sufficient.

Statement 2  says the range is 30. We start at 10 so we must end on 40. Then we know there are  \frac{40 - 10}{3} + 1 = 11  terms, sufficient.

rsrighosh · Answer

sthahvi Took me quite a lot of time to solve...

but here's what I did Statement 1:- (1) The sum of the terms in set B is 275. n is a positive integer. Therefore 3n+7 is evenly spaced consecutive integer. 1st term = 10 xth term = 3x+7 Going by AP formula: \frac{(10 + 3x+7)x}{2} = 275 Solved the quadratic equation to find x => 11,\frac{ -50}{3} (Took time to frame the equation and solve for x --> if anyone can help with a faster method would be helpful) As x should be an integer, hence x=11. So by this we can find median Sufficient. Statement 2:- (2) The range of the terms in set B is 30. 3x+7-10 = 30 x=11 So again x is integer. Sufficient.

keyuwang · Answer

Where in the question states that n has to start from 1 in Sequence A?

It simply says n is an integer greater than 1. I pick A because of that.

FitnessforFriends · Answer

I may be missing something but how is B sufficient?

If T1 = 10, Last Term = 40 and Median then = 50/2 = 25
If T1 = 13, Last Term = 43 and Median then = 56/2 = 28

The wording "first x terms" here may be the key. Can we take this to mean the sequence must include the first term? If that is the case then i would agree with B. Please clear doubts

FitnessforFriends · Answer

I may be late on this but it says greater than or equal to 1. Also it says first x terms which would mean starting from the first term. Example x could be 5,7,9 all the number of terms where each one includes the first term

puneetfitness · Answer

Hi Brunel please advise as in data sufficiency any issues if we can get a unique number answer is yes

But here in statement it says n= or > 1 start value can be 3(1)+7= 10 or 3(2)+7=13 or any number that fits this case.

How can we reach unique number as we will not sure about starting point

Posted from my mobile device

DUMDUM21 · Answer

Number of terms = (Last term - First term)/ common difference. If you can find number of terms then you can find Median.

bumpbot · Answer

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Sequence A is defined by the equation An = 3n + 7, where n is an integ

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Sequence A is defined by the equation An = 3n + 7, where n is an integ

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