Showing posts with label Algebra. Show all posts
Showing posts with label Algebra. Show all posts

Thursday, October 27, 2011

CAT 2011: QuantoLogic Analysis

I finished my CAT 2011 journey in the initial phases. So did some other friends who are involved with us at Quantologic. Here is our analysis.

1. CAT 2011 is a tad difficult when compared to CAT 2010/CAT 2009.
2. The data intensive complicated logical reasoning questions have disappeared and the focus is more on basic understanding of problem solving techniques.
3. The onus is on the student to solve the easy questions.
4. Every paper especially the Quant and DI section has enough sitters for an average student to crack. We must also mention that every paper has around 6-8 difficult to very difficult questions which require analytical imagination.
5. Section 1 feels short of time, you need to choose your questions well and take no more than 2-3 minutes to solve any question.
6. There are some DI questions which require lengthy calculations, but the calculations can be remarkably reduced by making smart approximations and using the options well.
7. The number of Data Sufficiency questions have gone down considerably.
8. The questions are focused on basic concepts and formulae and one needs to be able to solve questions from first principles rather than imaginative methods.
9. Read each question carefully before you start solving and try to look at the options as some of the questions will require much less work if you use the options.
10. Overall an intelligent test.

Cheers!
Rahul

Wednesday, October 12, 2011

Problem of the Day 12 Oct 2011

How many factors of 2010^{2010} have last digit 2?

Monday, October 10, 2011

Problem of the Day 10 Oct 2011

Ten identical boxes of dimensions 2 \times 3 \times 5 are stacked flat on top of each other, with the orientation of each box being independent and random. If \frac{m}{n} is the probability that the height of the stack is 31 and \gcd(m, n)=1, find m. All units are in feet.

Sunday, October 9, 2011

Problem of the Day 9th Oct 2011


In an increasing Arithmetic Progression, the product of the 5th term and the 6th term is 300. When
the 9th term of this A.P. is divided by the 5th term, the quotient is 5 and the remainder is 4. What is
the first term of the A.P.?
(a) 12                 (b) –40               (c) –16                     (d) –5

Saturday, October 8, 2011

Problem of the day 8th oct 2011


Rohan is asked to figure out the marks scored by Sunil in three different subjects with the help of
certain clues. He is told that the product of the marks obtained by Sunil is 72 and the sum of the
marks obtained by Sunil is equal to the Rohan’s current age (in completed years). Rohan could not
answer the question with this information. When he was also told that Sunil got the highest marks
in Physics among the three subjects, he immediately answered the question correctly. What is the
sum of the marks scored by Sunil in the two subjects other than Physics?

(a) 6                  (b) 8                (c) 10               (d) Cannot be determined

Friday, October 7, 2011

Problem of the day 7th Oct 2011


Ten books are arranged in a row on a bookshelf. A student has to select three out of these ten books
in such a way that no two books selected by him must have been lying adjacently. In how many
ways can he make the selection?
(a) 56                                (b) 64                           (c) 72                    (d) None of these

Problem of the Day 6th Oct 2011


If xΔ(y +1) = yΔ(x +1), xΔ x = 1 and (x − y)Δ(x + y) = xΔ y, then what is the value of 1001Δ1?
(a) 1000                   (b) 100                    (c) 10                 (d) 1

Wednesday, October 5, 2011

Problem of the day 5th Oct 2011


The set S contains nine numbers. The mean of the numbers in S is 202. The mean of the five smallest of the numbers in S is 100. The mean of the five largest numbers in S is 300. What is the median of the numbers in S?

Monday, October 3, 2011

Problem of the Day 3rd Oct 2011

How many ordered pairs of positive integers (m, n) satisfy the system

\begin{align*}\gcd (m^3, n^2) & = 2^2 \cdot 3^2,\\ \text{LCM} [m^2, n^3] & = 2^4 \cdot 3^4 \cdot 5^6,\end{align*}

where \gcd(a, b) and \text{LCM}[a, b] denote the greatest common divisor and least common multiple of a and b, respectively?



(A)   0        (B) 1         (C)  2            (3) More than 2

Sunday, October 2, 2011

Problem of The day 2nd Oct 2011

Let [x] and {x} respectively denote the integer and fractional part of of a real number x. If {n} + {3n}=1.4, find the sum of all possible values of 100{n}.

(A) 180           (B) 145                (C) 85      (d) 102

Wednesday, September 21, 2011

Problem of the Week 21 Sept 2011

The leftmost digit of an integer of length 2000 digits is 3. In this integer, any two consecutive digits must be divisible by 17 or 23. The 2000th digit may be either a or b. What is the value of a+b?



Thursday, September 15, 2011

Problem of the day 15 sept 2011

Rachel and Brian are playing a game in a grid with 1 row of 2011 squares. Initially, there is one
white checker in each of the fi rst two squares from the left, and one black checker in the third square
from the left. At each stage, Rachel can choose to either run or ght. If Rachel runs, she moves the
black checker 1 unit to the right, and Brian moves each of the white checkers one unit to the right. If
Rachel chooses to fi ght, she pushes the checker immediately to the left of the black checker 1 unit to
the left, the black checker is moved 1 unit to the right, and Brian places a new white checker in the
cell immediately to the left of the black one. The game ends when the black checker reaches the last
cell. How many diff erent final confi gurations are possible?

a) 2011   b) 2010  c) 2009 d) None

Thursday, September 8, 2011

Problem Set 9 Sept 2011

Q1 The integers from 1 to n are written in increasing order from left to right on a blackboard. David and Goliath play the following game: starting with David, the two players alternate erasing any two consecutive numbers and replacing them with their sum or product. Play continues until only one number on the board remains. If it is odd, David wins, but if it is even, Goliath wins. Find the probability that Goliath wins if n=2011?

a) 0 b) 1 c) 1/2 d) None of these


Q2 A classroom has 30 students and 30 desks arranged in 5 rows of 6.The class has 15 boys and 15 girls.If the students be placed in the chairs such that no boy is sitting in front of, behind, or next to another boy, and no girl is sitting in front of, behind, or next to another girl in x(y!)(z!), where x, y and z are positive integers. Find x+y+z?

a) 32 b) 30 c) 27 d) 29


Q3. Find the sum of all integers x such that 2x^2 + x- 6 is a positive integral power of a prime positive integer?

a) 7 b) 5 c) 4 d) 12

Thursday, July 30, 2009

Problem of the Day 30.07.09

Find the sum of the digits of the least natural number N, such that the sum of the cubes of the four smallest distinct divisors of N is 2N?



1)  9                                2) 8                             3) 7                    4) 6                      5) 10

Tuesday, July 28, 2009

Bonus QUestion 28.07.09

Suppose K be the number of integers n such that (2^n+1)/n^2 is also an integer.
Then K is
a) 0               b) 1               c) 2              d) 3              e) none of these

Problem of the day 28.07.09

if a<b and 12²+4²+5²+3²=a²+b² the find (a+b)?

Monday, July 27, 2009

Problem of the day 27.07.09

Find the number of quadratic polynomials ax² + bx + c such that:

a) a, b, c are distinct.

b) a, b, c ε {1, 2, 3, ...2008}

c) x + 1 divides ax² + bx + c
a) 2013018            b) 2013021            c) 2014024             d) 2018040       e) none of these

Sunday, July 26, 2009

Bonus Question 26.07.09

The perimeter of a right triangle is 60. The height to the hypotenuse is 12 what is the area?
(A) 75 (B) 144 (C) 150 (D) 300 (E) none of these

Problem Of the Day 26.07.09

If x² + y²= 1 and x, y are real numbers. Let p, q be the largest and smallest possible
value of x + y respectively. Then compute pq
a) 0                    b) 1/2         c) −1/2                          d) 2                           e) −2