Number of terms

[adi_800]

Source : Mgmat exams....
Q level : 700-800


The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even

(2) n < 9

My question is : How to solve the question under two minutes...

[Gurpinder]

Wouldnt the answer be (E)? Whats the OA?

[von]

To find the sum of consecutive integers you can find the product of the mean and the total number of terms in the set. But in order to find the mean you would need the first and last terms so we could divide by 2 but we don't know how many consecutive integers there are in the set so I'm not sure how we could do this. Wait let me try something... just thinking aloud here:

(1) n is even: okay in this situation n could be 2 (22+23=45) or 6 (5+6+7+8+9+10=45) thus, we don't have a difinite yes or no answer and so statement 1 alone is NOT sufficent to answer the question; eliminated A and D

(2) n < 9: okay, if n is 8 then the sum of n consecutive integers cannot = 45. it's the same for n = 7. if n = 6 then (5+6+7+8+9+10) = 45 but if n = 5 then (7+8+9+10+11)=45 too! so statement 2 alone is NOT sufficent to answer the question either. eliminated B, so it's either C or E.

If we take them both together we know that n can ONLY equal 2, 4, or 6. If n = 6 then n is less than 9 and it's even so it checks out okay. But if n = 2 then (23+23)=45 which would mean n is also less than 9 and positive so C can't work either since we're getting two answers for it. Therefore E must be the answer; but not to your question... took me 15min to get this. Anyone know a quick way to do this??

[adi_800]

Answer is E..
But nt sure how to get this one within 2 minutes...

[Gurpinder]

Answer is E..
But nt sure how to get this one within 2 minutes...

Hmmm......I am not sure if you are aware of this formula but with this one, I did this question in like few seconds.

Avg*# of items = sum

The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even

Clearly this statement is insufficient. N could be anything 10,12,14,16....etc

(2) n < 9

This statement by itself is also insufficient. N could be anything from 2-8.

Both together are also insufficient because now all you know is N is even < 9. Again it could be 2,4,6,8.

Therefore the answer is (E).


The main thing to take away from this is this formula: Avg*# of items = sum

** remember that if you have any of the 2 things in this formula, you can figure out the third one. We have the sum, and need N or AVG. The statements attempt to give us information about N but both are insufficient. Therefore the answer is (E).

I hope this helps!

[uwhusky]

I got an approach to this that might work.

We can look at the sequence of numbers like this: x + (x + 1) + (x + 2) + (x + 3)...

So if it's even, it must be either 2x + 1 = 45, or 4x + 6 = 45, or 6x + 15, or 8x + 28 = 45...and we can keep going until we hit a number that cannot be divided by nx.

1) is insufficient, because there are at least 4 different solutions I have listed above.

2) is also insufficient, because the same 4 solutions still work.

Together it tells you nothing, so E is the right answer.