For any integer greater than 1, n* denotes the sum of all integers fro

Question

For any integer greater than 1,  n*  denotes the sum of all integers from 1 to n, inclusive. How many even numbers are there from 15* to 20*, inclusive?

(A) 42
(B) 43
(C) 44
(D) 45
(E) 46

chetan2u · Answer

Source please.

15* is sum of all integers from 1 to 15.
So from 15* to 20*, we will have 6 integers: 15*, 16*…..20*.
How can you have answers in 40s?

filipembribeiro · Answer

So, the official answer is:

Right answer: (E) 46

Explanation:
Essentially  n*  is the sum of an arithmetic sequence in the first term is 1 and each term increases by 1. To find the sum of such a sequence, take the average of the first and last terms and multiply this by the number of terms in the sequence. To this end:
15* =  \frac{(15+1)*15}{2} = 120

20* =  \frac{(20+1)*20}{2} = 210

And to find the number of multiples of a given number within in a range, we first take
the difference between the endpoints and divide them by the number in question:
 \frac{(210-120)}{2}  =  \frac{90}{2}  =  45

Now add 1 because both of the endpoints are even and the question specifies
"inclusive." (E) is correct: it is 46.

chetan2u · Answer

It can be easily taken as 15*, 16*, 17*, 18*, 19* and 20*. 
Ambiguous wordings, and that is why the source is asked.

filipembribeiro · Answer

I agree 100% with you.
This question was taken from a random set for consulting applications and therefore is not official from GMAT or other reliable source, but the question is written here as it is on their font.

Crytiocanalyst · Answer

Sum of intergers from 1 to 15 ---->120

Sum of integers from 1 to 20 ---->210

no terms a+n-1*d = last term

Since both the sum are inclusive

120 +n-1*2 = 210
n-1=45
n=46
Hence IMO E

udaypratapsingh99 · Answer

Actually, I read it that way, i.e. "15*, 16*, 17*, 18*, 19* and 20*", so it didn't make any sense to me. But after reading the solution, I think, the language is NOT ambiguous. It's a good question. Can be made even trickier by introducing a couple of options between 1 to 5, including 3.

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For any integer greater than 1, n* denotes the sum of all integers fro

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