CAT 2008: Quantitative Questions a Day 1 to 50 - The discussions

rajeev_hts

Quote:

Originally Posted by Aarav

Each candidate's vote % is atleast one less than his/her number of votes.

Isn't it true in this case?if I say

one candidate has 3 votes and total votes are 101

he has 300/101 % => 2.9 % votes that is greater than 3-1= 2.

same as in case when candidates have 4 votes.

Aarav

Quote:

Originally Posted by rajeev_hts

Isn't it true in this case?if I say

one candidate has 3 votes and total votes are 101

he has 300/101 % => 2.9 % votes that is greater than 3-1= 2.

same as in case when candidates have 4 votes.

Please go and wash your face to read the question again -> I think it's still Sunday morning for you in bed.

ankaj

Quote:

Originally Posted by Aarav

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Quantitative Question # 041
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N people vote for one of 27 candidates. Each candidate's vote % is atleast one less than his/her number of votes. What is the smallest possible value of N?

(a) 108 (b) 127 (c) 134 (d) 162 (e) none of these

least possible votes will come...when 26 candidates recieve 1% of the votes and one candidate gets 74% votes

so the total votes of 26 candidates= 26+26= 52 (atleast)

and the one guy gets 75 votes....

So total votes= 52+75=127

answer---B

...this is not a convincing asnwer.....

slam

Quote:

Originally Posted by Aarav

------------------------------------------------------
Quantitative Question # 041
------------------------------------------------------

N people vote for one of 27 candidates. Each candidate's vote % is atleast one less than his/her number of votes. What is the smallest possible value of N?

(a) 108 (b) 127 (c) 134 (d) 162 (e) none of these

The equation I have used is:
x1 - x1*100/N >= 1, similarily for the rest
Add all these to get
N(1-100/N) >= 27
N >= 127

put this back in the original:
x1 >= N / (N-100)
x1 >= 127/27
x1 >= 5 (smallest integer value greater than 127/27)
Now, if N has to be minimum, then each candidate has to have the minimum possible value, which in this case is 5
=> N (min) = 27*5 = 135.

Comments?

rajeev_hts

Quote:

Originally Posted by Aarav

Please go and wash your face to read the question again -> I think it's still Sunday morning for you in bed.

I am not feeling Sunday hangover. Will wait for right one.

ankaj

Quote:

Originally Posted by Aarav

------------------------------------------------------
Quantitative Question # 041
------------------------------------------------------

N people vote for one of 27 candidates. Each candidate's vote % is atleast one less than his/her number of votes. What is the smallest possible value of N?

(a) 108 (b) 127 (c) 134 (d) 162 (e) none of these

here is one moe way...but somewhere i am stuck...

say, V(X) is the percentage of votes by one person....

there fore v1+V2+....+v27= 100

(V1/100)N= X1-1-----------1
(V2/100)N= X2-1-----------2

(V27/100)N= X27-1
adding all

(V1+...v27)N/100= (x1+.....+x27)-27
N=(x1+.....+x27)-27

Now...i am gone...logically N=(x1+.....+x27)

but if go the above way...then...i am gone....some things wrong...for sure...

brain

is not working.....some body help

rajeev_hts

Quote:

Originally Posted by slam

The equation I have used is:
x1 - x1*100/N >= 1, similarily for the rest
Add all these to get
N(1-100/N) >= 27
N >= 127

put this back in the original:
x1 >= N / (N-100)
x1 >= 127/27
x1 >= 5 (smallest integer value greater than 127/27)
Now, if N has to be minimum, then each candidate has to have the minimum possible value, which in this case is 5
=> N (min) = 27*5 = 135.

Comments?

okey lets take for some candidate it is 5

then he has 500/135 % votes= 3.7%

as per the question he/she has at least one less than the votes he received means he shouls have atleast 5-1=4% votes.

but your's come 3.7%, how does it true??

slam

Quote:

Originally Posted by rajeev_hts

okey lets take for some candidate it is 5

then he has 500/135 % votes= 3.7%

as per the question he/she has at least one less than the votes he received means he shouls have atleast 5-1=4% votes.

but your's come 3.7%, how does it true??

I think one of us has misinterpreted the question. The question statement says:
"Each candidate's vote % is atleast one less than his/her number of votes"

This means that the the number of votes should be at least one greater than the vote percentage. If it is more than 1, then it is fine. (look at the equation I've started with, you'll get the point)

In the case you've given, the difference is 1.3, which is greater than 1. So it's alright.

Aarav

Quote:

Originally Posted by slam

The equation I have used is:
x1 - x1*100/N >= 1, similarily for the rest
Add all these to get
N(1-100/N) >= 27
N >= 127

put this back in the original:
x1 >= N / (N-100)
x1 >= 127/27
x1 >= 5 (smallest integer value greater than 127/27)
Now, if N has to be minimum, then each candidate has to have the minimum possible value, which in this case is 5
=> N (min) = 27*5 = 135.

Comments?

Excellent attempt -> but you can better 135 here.

slam

Quote:

Originally Posted by rajeev_hts

okey lets take for some candidate it is 5

then he has 500/135 % votes= 3.7%

as per the question he/she has at least one less than the votes he received means he shouls have atleast 5-1=4% votes.

but your's come 3.7%, how does it true??

The 'at least' is on the '1' and not on the '4' in the equation "5 - 1 = 4". I think that should clear your doubt regarding this.

Aarav, please correct me if I am wrong in interpreting the question here.