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

[themystique]

QQAD 41:

given : total no. of votes = N

vote % of candidate 1 = (x1/N)*100

vote % of candidate 2 = (x2/N)*100 and so on....


also given:

vote % is atleast = (no. of votes in favor) - 1

i.e.,

for 1, (x1/N)*100 <= x1 - 1.
for 2, (x2/N)*100 <= x2 - 1.. and so on..


adding the above eq. for all candidates:

(x1/N)*100 + (x2/N)*100 + ..... + (x27/N)*100 <= (x1 + x2 + .....x27) - 27

if x1 + x2 +.... x27 = X, then

(X/N) * 100 <= X - 27

(X/N) * 100 - X <= -27

but X = N

thus,

100 - N <= -27

or N >= 127

hence option (b)

[Aarav]

Originally Posted by themystique

100 - N >= -27

or N <= 127

hence option (b)

This is wrong -> can you write the values and confirm your answer if this matches with what is being asked in the question?

[Aarav]

@All
The NL will reach you in few hours time. I think this system is stubborn and doesn't work as expected when NL is fired immediately without setting a time well in advance. I have fired 2 NLs and when the system lies by saying, delivered to all, there is little I can do in it.

[naga25french]

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

answer should be d) 162

[Aarav]

Originally Posted by naga25french

answer should be d) 162

Justify your answer -> why "should be"?

[sandeep jha]

Originally Posted by rajeev_hts

Let 1st candidate's votes =x1
2nd's = x2 and so on...

so N= x1+x2+x3+.....+x27

since (x1*100)/N >= x1-1
or x1 <= N/(N-100)
such as x2 <= N/(N-100)

adding all Xs. (N*27) /(N-100) <= N
N(N-100) >=27N
or N^2 -127N >= 0
N(N-127)>=0
N>=127

So least value of N=127 (b)

I think it should be (x1*100)/N <= x1-1 !
then, x1>=N/(N-100)
x2>=N/(N-100)
............
x27>=>=N/(N-100)
Adding all these...(x1+x2+...x27)>=N*27/(N-100)
or, 27>=N*27/(N-100)
or,N(N-127)>=0
so, N>=127...option(b)

p.s.: m back..m i?

[rajeev_hts]

Originally Posted by Aarav

This is wrong -> can you write the values and confirm your answer if this matches with what is being asked in the question?

oops ... couldn't recheck..

lemme try again..

(X1*100)/N >= X1-1

X1 <= N/(N-100)

adding all such Xs

27*N/(N-100) >= N

N <= 127

For N=127 => X1 <= 4.7

So Maximum integer X can take is 4, so max value of N comes 108.

Min value of X is > 100 and < 108 i.e. 101.

Let put the values back in que.
7 candidate of 3 votes
20 candidates of 4 votes

Total votes = 101

for 3 pointers :-

300/101 >= 3-1 true

for 4 pointers

400/101 >= 4-1 True.

So answer is (e) None of these.

How is this Arav?

[themystique]

Originally Posted by Aarav

This is wrong -> can you write the values and confirm your answer if this matches with what is being asked in the question?

the equations i have formed seem correct.
not able to find why mine is wrong..
seems i am overlooking some point..
shall wait for your official answer..

[arbit_rageur]

Let us assume that candidate i receives ni votes.

Then clearly 100ni/x<ni-1

or rearranging x>100ni/ni-1......call this equation (1)

This is true for all i i=1,2.....27.

Furthermore 27ni<=x for atleast one ni.(i.e the least ni)....eqn 2

Weknow that y/y-1 is a decreaing fn of y, so if ni<=x/27, then

100ni/ni-1>100x/27/(x/27-1)

or x>100x/27/(x/27-1).

Solving we get x>127.

For x>127 but x<=133, we get ni>=5 from equation 1, which leads us to x>135....which means that no solutions exist for x>127 but x<=133.

For x=134 we get ni=4 from eqn1...which also satisfies eqn 2

We also find that the 26 candidates getting 4 votes and one candidate getting 30 votes satisfies the given condition.

Therefore answer is c)134.

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

[Aarav]

Originally Posted by rajeev_hts

Let put the values back in que.
7 candidate of 3 votes
20 candidates of 4 votes

Total votes = 101

for 3 pointers :-

300/101 >= 3-1 true

for 4 pointers

400/101 >= 4-1 True.

So answer is (e) None of these.

How is this Arav?

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