CAT 2008: QQAD Practice Test Discussions

[implex]

Originally Posted by Aarav

Problem 24

For a natural number n, f(p) - f(q) is divisible by p-q since p^n-q^n is divisible by p - q (from X)

Thus, [f(p) - f(q)]/(p-q) is an integer. The quadratic equation that has 2 solutions f(p)/(p-q) and -f(q)/(p-q) is x^2 - x[f(p) - f(q)]/(p-q) + 1 = 0 (from Y).

If the roots of x^2 + ax + b = 0 are rational where a and b are integers then the roots are integers => f(p)/(p-q) is an integer

nice solution for the best problem of the paper!

the two Ds problem, the thief problem and the blue card and green problem classify as difficult problems. And all the four are little gems !

[Aarav]

Originally Posted by implex

nice solution for the best problem of the paper!

the two Ds problem, the thief problem and the blue card and green problem classify as difficult problems. And all the four are little gems !

@Implex, nbangalorekar and All -> among the 11 Practice Tests in QQAD so far, in my opinion the best has been Test 6 Last year. Do ensure that you attempt this paper It's attached in this thread only.

[Aarav]

Originally Posted by nbangalorekar

Extremely sorry for spamming but i absolutely cant stop praising the beauty of this soln...
Kudos to you yaar Aarav....Awesum man!!!
but it wud have been impossible to spot this in an exam...

It was tough, almost impossible to do in exam considering no one could do this last year as QQAD problem. The answer is (e), but everyone ended up with finding some error or the other.

The problem read as following:

Reema tries to prove her conjecture that f(a)/(a-b) is an integer for two distinct integers a and b for a given polynomial f(x) which satisfies the following properties I and II
(I) Every coefficient in f(x) is an integer (II) f(a)f(b) = -(a-b)^2

Find out the mistake in her proof if there is any

Proof

(a) For a natural number n, f(a) - f(b) is divisible by a-b since a^n-b^n is divisible by a - b (from I)

(b) Thus, [f(a) - f(b)]/(a-b) is an integer. The quadratic equation that has 2 solutions f(a)/(a-b) and -f(b)/(a-b) is x^2 - x[f(a) - f(b)]/(a-b) + 1 = 0 (from II)

(c) Since, f(a)/(a-b) is rational, (from I) and [f(a) - f(b)]/(a-b) is integer => f(a)/(a-b) is an integer

(1) (a) (2) (b) (3) (c) (4) exactly 2 of the foregoing (5) none of these

[Aarav]

In the above problem last year, students were foxed to think this as purely a quadratics problem when the killer blow was the fact, that require number theory to prove that -> If roots of x^2 + mx + n = 0 are rational where m, n are integers => roots are integers.

[nbangalorekar]

Originally Posted by Aarav

In the above problem last year, students were foxed to think this as purely a quadratics problem when the killer blow was the fact, that require number theory to prove that -> If roots of x^2 + mx + n = 0 are rational where m, n are integers => roots are integers.

to say the least... im completely dazzled by the beauty of math..
Aarav one more request: also provide a formal soln to 25th prob...
cant just wait...

[Aarav]

Originally Posted by nbangalorekar

to say the least... im completely dazzled by the beauty of math..
Aarav one more request: also provide a formal soln to 25th prob...
cant just wait...

X and Y alone are inconclusive, combine both we get C = 4, B = 2, A = 3.
Here we go -> Consider the parities of the differences N(A) - N(B), N(B) - N(C), N(C) - N(A), where N(X) is the number of type X insect. These parities do not change in the merging process. This means, in particular that in the end the number of C-insect and B-insect have the same parity, which is possible only if the only insect left belongs to type A.

[arun_juee]

Originally Posted by arun_juee

Hi,

My Take ( after 2 peg of Smirnoff )
Time 12:20 am to 1:10 am ( July 4th 2008 ).

6-D,11-B,14-B,15-E,17-A,20-A,21-B,22-B,23-D,24-E
Where are the options/solutions available?


Later.
Arun

Hi,

My Take
Attempt 10
Correct 6
Wrong 4
Score : 20

Any suggestions for improvement?

Later.
Arun

[Aarav]

Originally Posted by arun_juee

Hi,

My Take
Attempt 10
Correct 6
Wrong 4
Score : 20

Any suggestions for improvement?

Later.
Arun

Can you please tell as how this test could have been better to test student's ability - since you have filled this in poll? Suggestion for improvement is simple to start with, work on your accuracy. I'm sure 2 wrongs among the 4 were kinda fluke attempts by you. Also, enlarge your competency area in quant.

[arun_juee]

Originally Posted by Aarav

Can you please tell as how this test could have been better to test student's ability - since you have filled this in poll? Suggestion for improvement is simple to start with, work on your accuracy. I'm sure 2 wrongs among the 4 were kinda fluke attempts by you. Also, enlarge your competency area in quant.

Hi,

I checked the options.
Whichever suited to me,i marked.
I am yet to start preparation.
So I thought without revising the formulas, I am at least able to get a 20.
So, I thought of improvement.

You are the master,I am only a critic.

If I created any inconvenience, I apologize.

Later.
Arun

[niyant14]

hey,
cud u plz upload the answer keys too for QQAD CAT 07

Thnx