CAT 1 Problem 9

[tkkishore]

Why is B the answer ? What if the sequence is even ? Then the mean wont be the same as the median, right ? Since b tells us the mean but doesnt give us the # of terms, i dont know how we would know the median. anyone understands this solution ?

[RonPurewal]

Please post the question, together with the answer choices (for problem solving questions), so that we can give you an immediate answer.

Thank you.

[tkkishore]

What is the median value of the set R, if for every term in the set, Rn = Rn-1 + 3?

(1) The first term of set R is 15.

(2) The mean of set R is 36.

[Guest]

I think because it's an evenly spaced set and when that happens the median is always equal to the mean. If the mean is 36, then so is the median.

[StaceyKoprince]

Thanks - remember always to post the actual text of the question in future. "test 1 question 9" could be any one of the thousands of questions in our database!

Also, is the formula supposed to say Rn = R(n-1) + 3, or Rn = (Rn) - 1 + 3? And that n is a "sub-n" right? The lack of formatting on the forum makes it hard to know what a problem like this really says.

I'm assuming it's supposed to say R-sub-n = R-sub-(n-1) + 3 and that's how I'll answer the question, but let me know if that's not right.

If that's the formula, then every term is 3 greater than the previous term. For example, if I start with 1, then my sequence is 1, 4, 7, 10, ...
If I start with 3, then my sequence is 3, 6, 9, 12, ...
If I start with 2.5, then my sequence is 2.5, 5.5, 8.5, ...

This means that, no matter what my terms actually are, they are always 3 apart.

Statement 2 says the mean (average) is 36. What are some options that make this true?
- There could be exactly one term, and that term would have to be 36. This would also make the median 36.
- There could be two terms. They would have to be 3 apart and average to 36, so they'd have to be 34.5 and 37.5. And, hmmm... the median would also be 36, because when you have an even number of terms, you average the two middle terms to get the median.
- There could be three terms. They would have to be 3 apart and average to 36, so the middle term would have to be 36 and the two other terms would have to be 33 and 39. And the median would be... 36!

Examine that pattern and see if you can understand why you're proving a rule here. The terms in the sequence are always exactly the same distance apart (3 units). Any time you have evenly spaced terms (as the above guest said), then you can calculate the average simply by averaging the first and last terms. There's one rule.

Also, if you have evenly spaced terms, then the values of the individual terms will be evenly spaced around the median, no matter how many terms you have. If all of the terms are evenly spaced around the median, then the first and last terms are also evenly spaced around the median, by definition. If the first and last terms are evenly spaced around the median, then the two terms will average to the median. Always - regardless of whether there is an even or odd number of terms. Try it out!

[dixitsandeep]

Nth term of set is 3 more than the N-1 th term.


That tells us the Set an evenly spaced Set (each term 3 more than the previous).

Therefore, If all the terms in Set are are positive integers then mean and median of the Set will be equal.
But if there are negative terms then Mean and Median may not be equal.
For example in this evenly spaced set {-1,0,1,2,3}
median=1, mean=2.5

We cannot solve this using statement 2 alone.
To rule out the possibility that there are negative numbers in Set, we must know the first term in this problem.
Statement 1 tells the first term. Statement 2 tells the mean.

We need to use both of these to get the answer.

That's why answer should be C.

I don't know the manhattan's official answer, which appears to be B as per this thread.

[tim]

your calculation is incorrect in your example. the mean and median are both 1. the mean and median will ALWAYS be equal in evenly-spaced sets..