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

[Aarav]

Originally Posted by monk4lif

can u recommand ny gud buk 4 quant

Frankly, not aware if there is any single good book that can take care of CAT quant requirements. However, I can suggest you few resources that might be useful.

(1) Arithmetic - coaching classes study material
(2) Algebra - TMH for JEE (only CAT related topics)
(3) Number system - PG is the best source
(4) Geometry - Just remember the basics here of 9th and 10th standard and practice problems - should suffice.

Besides this if you can lay your hand on Mathematical Circles (50% of the book has CAT quant related topics) then it would be a good learning. The way the problem solving has been approached in this book makes you fall in love with mathematics again and it is not that over the board kinda book.

[Aarav]

The problem has been solved correctly by most of you in the 1st attempt. Very well done

Here is the official solution to 001 - we might change this if by end of the day someone comes with a better approach

Solution:

Given a(a+1) + b(b+1) + c(c+1) + d(d+1) = 312 => (a-1)^2 + (b-1)^2 + (c-1)^2 + (d-1)^2 = 312 - 3S + 4 = 256. Let a-1 = A, b-1 = B, c-1 = C, d-1 = D => we have non-negative integers A, B, C, D such that A^2 + B^2 + C^2 + D^2 = (A+B+C+D)^2 (the LHS <= RHS always) and can only be true if all but one number is zero => three among a, b, c, d are 1 and fourth number is 17.

Thus (3) holds true - (2) can guarantee the values for c and d. For a=b we have exactly 2 determinable values - thus (1) is not true.

=> choice (5) is the right answer

[implex]

Originally Posted by Aarav

The problem has been solved correctly by most of you in the 1st attempt. Very well done

Here is the official solution to 001 - we might change this if by end of the day someone comes with a better approach

Solution:

Given a(a+1) + b(b+1) + c(c+1) + d(d+1) = 312 => (a-1)^2 + (b-1)^2 + (c-1)^2 + (d-1)^2 = 312 - 3S + 4 = 256. Let a-1 = A, b-1 = B, c-1 = C, d-1 = D => we have non-negative integers A, B, C, D such that A^2 + B^2 + C^2 + D^2 = (A+B+C+D)^2 (the LHS <= RHS always) and can only be true if all but one number is zero => three among a, b, c, d are 1 and fourth number is 17.

Thus (3) holds true - (2) can guarantee the values for c and d. For a=b we have exactly 2 determinable values - thus (1) is not true.

=> choice (5) is the right answer

beautiful solution, I am dumb! I should have found it !!!

[Aarav]

Originally Posted by implex

beautiful solution, I am dumb! I should have found it !!!

I think this has been 1st time in 3 years that someone has come out with right answer to QQAD # 1 in such a short time. Kudos to you Really heartening to see many come out and crack the 1st problem. Keep it up!

Tomorrow's problem might take slightly longer time to solve but seeing the response today - I feel no QQAD problem will remain unsolved till end of the day as it had been the case in previous years.

[ramkumarps]

Quote:
Originally Posted by monk4lif
can u recommand ny gud buk 4 quant


Well,

An approach to good thinking is primarily important than having conceptual knowledge.
For the latter case,many books are available which gives you conceptual knowledge and problems.
But for the former case,i think the only book i have come across is "THINK WITHOUT INK".

[sandhyavenkat]

yes,option (5) is correct. I took a longer method of trial and error,ie i took pairs of consecutive nos that were lesser than 20 to see which one would give me the closest value of 312. so i took options 18*19=342,(more than 312,so obviously impossible) and 17*18=306.Also,there had to be a number 1 among a,b,c,d to get 2 in the final ans 312(310+2). hence, the values i had now were 1 and 17. since the other 2 nos could add upto only 2(20-1, they had to be 1 and 1. Hence only 2 unique values could be obtained. hence option (5).

i've just started my cat prep, so maybe this method was a bit longer... is it a wrong method?

[convivial]

Originally Posted by Aarav

Frankly, not aware if there is any single good book that can take care of CAT quant requirements. However, I can suggest you few resources that might be useful.

(1) Arithmetic - coaching classes study material
(2) Algebra - TMH for JEE (only CAT related topics)
(3) Number system - PG is the best source
(4) Geometry - Just remember the basics here of 9th and 10th standard and practice problems - should suffice.

Besides this if you can lay your hand on Mathematical Circles (50% of the book has CAT quant related topics) then it would be a good learning. The way the problem solving has been approached in this book makes you fall in love with mathematics again and it is not that over the board kinda book.

hello aarav
u mentioned abt mathematical circles.....wats it.......a book or any kinda material......where can i get it.......plz enlighten


cogito,ergo,sum................

[implex]

Originally Posted by convivial

hello aarav
u mentioned abt mathematical circles.....wats it.......a book or any kinda material......where can i get it.......plz enlighten


cogito,ergo,sum................

I guess he is telling about this
Amazon.com: Mathematical Circles: Russian Experience (Mathematical World, Vol. 7) (Mathematical World, V. 7): Dmitri Fomin,Sergey Genkin,Ilia V. Itenberg: Books

I used to read one book in high school, challenges and thrills in mathematics, its a very good book. If you can find it, it will be fun.

Also there are books like

Art of problem solving
Art and craft of problem solving.
High school algebra by hall and knight

and many others, they are good, but I must warn that if you are not into maths, it will chase you away as well. Some of the problems I recently posted have been from these books, but I have reduced them to cat level. i will keep posting more.!!

[sharadgupta]

Originally Posted by Aarav (CAT 2008: Quantitative Questions a Day 1 to 50 - The discussions)
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.

Originally Posted by implex

again we see that a^2+b^2+.. +f^2=9030

and clealry 1<=a,b,..f<=95

(95)^2=9025
one of the solutions comes to 95,1,1,1,1,1.

if we go lower than 95 we are going to lose much more than we can gain by adding one to one of the smaller nos

the fact being x^2 increases very fast for a higher x

clearly this is the only solution possible

now i think i am closer to a better logic

I too agree with this logic..
Cheers..!

[Aarav]

Originally Posted by convivial

hello aarav
u mentioned abt mathematical circles.....wats it.......a book or any kinda material......where can i get it.......plz enlighten


cogito,ergo,sum................

Implex is right - the Indian edition would cost Rs 200 - the publishers are Universities Press.

Art of Problem Solving Forum is highly recommended - especially the Intermediate section.