The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even
(2) n < 9
OA is E. What will be the quickest way to solve this?
DS question on Sum of consecutive postive integers
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I agree with Calista
The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even
Now 45 is an odd nos
so if n is even, it must have half even nos & half odd nos which will when summed up will lead to an odd nos, there are many possibilities like 22,23 5,6,7,8,9,10 etc INSUFF
(2) n < 9
again the above possibilities will arise and we can have odd value of n also
as 14,15,16 INSUFF
Combine again n can assume odd as well as even vals below 9 INSUFF
E
The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even
Now 45 is an odd nos
so if n is even, it must have half even nos & half odd nos which will when summed up will lead to an odd nos, there are many possibilities like 22,23 5,6,7,8,9,10 etc INSUFF
(2) n < 9
again the above possibilities will arise and we can have odd value of n also
as 14,15,16 INSUFF
Combine again n can assume odd as well as even vals below 9 INSUFF
E
Regards
Samir
Samir

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 Posts: 158
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The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even
(2) n < 9
22 + 23 = 45; here n = 2 which is even and less than 9.
5+6+7+8+9+10 = 45; here n = 6 which is even and less than 9.
Simple. Answer must be E and hence MGMAT is wrong.
Calista.
(1) n is even
(2) n < 9
22 + 23 = 45; here n = 2 which is even and less than 9.
5+6+7+8+9+10 = 45; here n = 6 which is even and less than 9.
Simple. Answer must be E and hence MGMAT is wrong.
Calista.
The Most easy way to solve this equation is
1) as the elements are consecutive integer they are in AP
hence Sum of n consecutive elements is = a(2a+n1)/2
Hence we can form the Equation as
a(2a+n1)/2 = 45
Where a the First integer in the series.
n no of integers in the series.
as it is equation of two variables unless you get the value of the a we can solve the problems.Hence both the conditions are insufficient.
E
Hope this will help you understand easily
1) as the elements are consecutive integer they are in AP
hence Sum of n consecutive elements is = a(2a+n1)/2
Hence we can form the Equation as
a(2a+n1)/2 = 45
Where a the First integer in the series.
n no of integers in the series.
as it is equation of two variables unless you get the value of the a we can solve the problems.Hence both the conditions are insufficient.
E
Hope this will help you understand easily

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 Posts: 158
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 Thanked: 7 times
Auzbee,
I checked the MGMAT explanation just now, they too say that the answer is E.
However in your first post, you gave the OA as D.
That's why this confusion.
Calista.
I checked the MGMAT explanation just now, they too say that the answer is E.
However in your first post, you gave the OA as D.
That's why this confusion.
Calista.
[quote]Auzbee,
I checked the MGMAT explanation just now, they too say that the answer is E.
However in your first post, you gave the OA as D.
That's why this confusion.
[/quote]
My apologies for being in a haste while replying. Let me correct my previous post on this thread.
I checked the MGMAT explanation just now, they too say that the answer is E.
However in your first post, you gave the OA as D.
That's why this confusion.
[/quote]
My apologies for being in a haste while replying. Let me correct my previous post on this thread.