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The rooms on the south side of the corridor

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Junior | Next Rank: 30 Posts
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by darlingriyarai » Tue Nov 27, 2012 1:44 am
The rooms on the south side of the corridor of a certain hotel are numbered with consecutive odd integers. If there are 84 rooms on the south side of the corridor and the lowest room is 501, what is the highest room number on that side?

A. 669
B. 667
C. 587
D. 585
E. 583
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by Anurag@Gurome » Tue Nov 27, 2012 4:34 am
darlingriyarai wrote:The rooms on the south side of the corridor of a certain hotel are numbered with consecutive odd integers. If there are 84 rooms on the south side of the corridor and the lowest room is 501, what is the highest room number on that side?/quote]

1st room is 501 = 500 + 1st odd positive integer = 500 + (2*1 - 1)
2nd room is 503 = 500 + 2nd odd positive integer = 500 + (2*2 - 1)
...
84th room is N = 500 + 84th odd positive integer = 500 + (2*84 - 1) = 500 + 168 - 1 = 667

the correct answer is B.
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by nisagl750 » Tue Nov 27, 2012 8:34 am
darlingriyarai wrote:The rooms on the south side of the corridor of a certain hotel are numbered with consecutive odd integers. If there are 84 rooms on the south side of the corridor and the lowest room is 501, what is the highest room number on that side?

A. 669
B. 667
C. 587
D. 585
E. 583
In an A.P last term = first term + (no. of terms - 1)*common diff.
here first term = 501, no. of terms = 84, common diff = 2 (odd consec. integers)

Last term = 501 + (84-1)*2
= 501 + 83*2
For me Answer is B
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