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

comradeharsh

My mistake. Thanks for pointing it out.

nbangalorekar

Quote:

Originally Posted by Aarav

Ok - same problem but we now have six natural numbers whose sum is 100 such that a(a+1) + b(b+1) + c(c+1) + d(d+1) + e(e+1) + f(f+1) = 9130.
Find the numbers.

My post after a looooong time:

with the given condition, the sum 'a(a+1)+b(b+1)........' will be max only when one of a,b,c,... is max n all others are equal. i.e. one of them is 95 n all others are equal to 1.
now the max value comes to 9130.
so only possible answer set is {1,1,1,1,1,95}
CHEERS....

warrior

Quote:

Originally Posted by Aarav

Expecting many to come out with the right answer

let's see who writes the solution with correct reasoning.

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Quantitative Question # 001
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Let the sum S = 20 of four natural numbers a, b, c, d be such that a(a+1) + b(b+1) + c(c+1) + d(d+1) = 312. Which among the a, b, c, d is/are uniquely determinable ?

(1) None if a = b (2) Atleast 2 if a ≠b (3) All if a > b (4) All of the foregoing (5) Exactly 2 of the foregoing

we can get a^2 + b^2 + c^2+d^2

now as a b c d are natural the max sum can be 292

289 +1+1+ 1

so all are 1 except one

2 and 3 are correct

so (5) is the ans

kavita_iet

Quote:

Originally Posted by Aarav

Ok - same problem but we now have six natural numbers whose sum is 100 such that a(a+1) + b(b+1) + c(c+1) + d(d+1) + e(e+1) + f(f+1) = 9130.
Find the numbers.

a^2 + b^2 + c^2 + d^2 + e^2 + f^2 = 9030
Solving for maximum value we equalize b, c, d, e,f = 1 ( as in typical set theory problems)
a^2 = 9025 or a = 95 and soln is 95,1,1,1,1,1.

Thanks for the reasoning implex
correct ans should be we can uniquely determine exactly 2

OperationBLACKI · 10:10 AM

Quote:

Originally Posted by Aarav

Expecting many to come out with the right answer

let's see who writes the solution with correct reasoning.

------------------------------------------------------
Quantitative Question # 001
------------------------------------------------------

Let the sum S = 20 of four natural numbers a, b, c, d be such that a(a+1) + b(b+1) + c(c+1) + d(d+1) = 312. Which among the a, b, c, d is/are uniquely determinable ?
(1) None if a = b (2) Atleast 2 if a ≠b (3) All if a > b (4) All of the foregoing (5) Exactly 2 of the foregoing

Even I got Option(5) .......The approach remains same as most of you puys have taken . The only concept I used here was to maximise the sum of squares we need to keep the numbers as far as possible we got to maximise one and minimise the others . Followed this approach and ended up with 17,1,1,1 in the first case and 95,1,1,1,1,1 in the latter . Put in the options and arrived at the answer.

OperationBLACKI · 10:11 AM

Quote:

Originally Posted by Aarav

Expecting many to come out with the right answer

let's see who writes the solution with correct reasoning.

The reasoning was fine as the sum total we had required us to maximise our number . Had it been a total somewhere in the middle ranges, then a lot of trial and error would be involved in the above approach which for more numbers wouldn't be practical.

warrior

Quote:

Originally Posted by Aarav

Expecting many to come out with the right answer

let's see who writes the solution with correct reasoning.

------------------------------------------------------
Quantitative Question # 001
------------------------------------------------------

Let the sum S = 20 of four natural numbers a, b, c, d be such that a(a+1) + b(b+1) + c(c+1) + d(d+1) = 312. Which among the a, b, c, d is/are uniquely determinable ?

(1) None if a = b (2) Atleast 2 if a ≠b (3) All if a > b (4) All of the foregoing (5) Exactly 2 of the foregoing

we can get a^2 + b^2 + c^2+d^2

now as a b c d are natural the max sum can be 292

289 +1+1+ 1

so all are 1 except one

2 and 3 are correct

so (5) is the ans

implex

Quote:

Originally Posted by warrior

we can get a^2 + b^2 + c^2+d^2

now as a b c d are natural the max sum can be 292

289 +1+1+ 1

so all are 1 except one

2 and 3 are correct

so (5) is the ans

why u posted the same thing again??

IG87 · 10:29 AM

Quote:

Originally Posted by Aarav

Expecting many to come out with the right answer

let's see who writes the solution with correct reasoning.

------------------------------------------------------
Quantitative Question # 001
------------------------------------------------------

Let the sum S = 20 of four natural numbers a, b, c, d be such that a(a+1) + b(b+1) + c(c+1) + d(d+1) = 312. Which among the a, b, c, d is/are uniquely determinable ?
(1) None if a = b (2) Atleast 2 if a ≠b (3) All if a > b (4) All of the foregoing (5) Exactly 2 of the foregoing

the second eq. reduces into:a^2 +b^2 +c^2 +d^2=292
putiing d minimum values ie 1,1,1,17 we get the ans.. as 292
now making any two f these equal...the eq is not satisfied.. n also 1st option is clearly ruled out!!
making any changes wth no.17 ie reducing its value and increasing d other no...the difference produced on changing 17 cannt be substituted by increasing the other three...
thus v have only single ans..17,1,1,1 .. and values of a,b,c,d r hence determined..
e is the rite optn

monk4lif

can u recommand ny gud buk 4 quant