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[1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/

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154238
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[1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/ [#permalink] New post   11 Oct 2012, 20:50
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0% (00:00) correct 100% (01:40) wrong based on 3 sessions
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Guys plz help me with the question below

[1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/100]

a)52
b)53
c)54
d)55
e)none of these

Thanks

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KarishmaB
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Re: [1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/ [#permalink] New post   11 Oct 2012, 21:41
Expert Reply
154238 wrote:
Guys plz help me with the question below

[1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/100]

a)52
b)53
c)54
d)55
e)none of these

Thanks


There is something wrong in the answer choices or the question (or the answer is (E)).

Ignore the 1/2s right now.
You have 1/100 and you have 99/100 in the series. When you add them, you will get 1.
Similarly, you have 2/100 and 98/100. This will again give you 1.
This will continue till 49/100 and 51/100.
So you have a total of 49.
You are left with 5 terms: 50/100 + 100/100 + 101/100 + 102/100 + 103/100 which add to apprx 4.5
Now you have a 103 times 1/2 which adds up to 51.5

So the total is 49 + 4.5 + 51.5 = 105 apprx
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Re: [1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/ [#permalink] New post   11 Oct 2012, 21:46
Expert Reply
You can also use the concept of sum of first n integers here.
Sum of first n integers = n(n+1)/2

Take all 1/2s together and take out 1/100 common out of the rest of the terms.

103*(1/2) + (1/100)(1 + 2 + 3 + 4 ....+ 103)
= 103/2 + (1/100) (103*104)/2 = 105 apprx
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Re: [1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/ [#permalink] New post   11 Oct 2012, 22:22
VeritasPrepKarishma wrote:
154238 wrote:
Guys plz help me with the question below

[1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/100]

a)52
b)53
c)54
d)55
e)none of these

Thanks


There is something wrong in the answer choices or the question (or the answer is (E)).
Ignore the 1/2s right now.
You have 1/100 and you have 99/100 in the series. When you add them, you will get 1.
Similarly, you have 2/100 and 98/100. This will again give you 1.
This will continue till 49/100 and 51/100.
So you have a total of 49.
You are left with 5 terms: 50/100 + 100/100 + 101/100 + 102/100 + 103/100 which add to apprx 4.5
Now you have a 103 times 1/2 which adds up to 51.5

So the total is 49 + 4.5 + 51.5 = 105 apprx



Even i feel that the answer given was incorrect. Thanks for your help :-D

Cheers :-D

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Re: [1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/ [#permalink]
11 Oct 2012, 22:22
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