CAT Analysis

            Being the last paper-based CAT exam, CAT-2008 has got its own significance. From 2009 onwards, CAT is being conducted online and CAT-Exam Q’s are not openly available. Considering CAT-2008 as a bench mark, it is thoroughly analysed here:

Total number of questions given in ‘Quant’ section is 25, each question contributing for 4 marks and there is a negative mark of 1 for each wrong answer. Out of all, 3 set problems each containing 2 questions are given. A set on number theory containing 2- sub questions is a harder and sitter type problem.  Geometry problem on circles is a harder one. I suggest leaving out such type of problems in the examination. Except these, remaining all come under easy to middle level problems. 

Puzzle-24 (CAT-2008)

Directions for Questions 1 and 2:

Choose (1) if Q can be answered from A alone but not from B alone.

Choose (2) if Q can be answered from B alone but not from A alone.   

Choose (3) if Q can be answered from A alone as well as from B alone.

Choose (4) if Q can be answered from A and B together but not from any of them alone. 

Choose (5) if Q cannot be answered even from A and B together.       

In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules:

(a) If the number of players, say n, in any round is even, then the players are grouped in to n/2 pairs.    The players in each pair play a match against each other and the winner moves on to the next round.

(b) If the number of players, say n, in any round is odd, then one of them is given a bye, that is, he automatically moves on to the next round. The remaining (n − 1) players are grouped into (n − 1)/2 pairs. The players in each pair play a match against each other and the winners move on to the next round. No player gets more than one bye in the entire tournament.

Puzzle-23 (CAT-2008)

Directions for Questions 1 and 2:

Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.         

1. Which of the following cannot be true?

                        (1) At least two horses finished before Spotted

                        (2) Red finished last

                        (3) There were three horses between Black and Spotted

                        (4) There were three horses between White and Red

                        (5) Grey came in second      

2.  Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be true?

                        (1) Spotted came in first

                        (2) Red finished last

                        (3) White came in second

                        (4) Black came in second 

(5) There was one horse between Black and White

Solution follows here:

Trigonometry-3 (CAT-2008)

Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves C located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60⁰ to AB. Also C is located between south and southwest of A with AC at 30⁰ to AB. The latest time by which Rahim must leave A and still catch the train is closest to
(1)6:15 am     (2) 6:30 am    (3) 6:45 am    (4) 7:00 am    (5) 7:15 am

Solution follows here:

Geometry-16 (CAT-2008)

Consider a right circular cone of base radius 4 cm and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of the cone. Find the largest possible total surface area (in sq cm) of the cylinder.

(1)   100 π/3          (2) 80 π/3    (3) 120 π/7    (4) 130 π/9    (5) 110 π/7  

Solution follows here:

Algebra-24 (CAT-2008)

Puzzle-22

Directions for Questions 1 and 2:  The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

1. Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the     number of possible shortest paths that she can choose is

(1)  60              (2)   75               (3)     45               (4)   90              (5)   72

2. Neelam rides her bicycle from her house at A to her club at C, via B taking the shortest path. Then the number of possible shortest paths that she can choose is    
(1) 1170              (2)   630            (3)     792               (4)   1200              (5)   936

To enter your answers, click on “comments” below:

Geometry-15 (CAT-2008)

Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote  the line passing through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120°. What is the ratio of the area of ABQCDP to the remaining area inside ABCD?

(1) 4√2/3       (2) 2+√3       (3) (10-3√3)/9        (4) 1+(1/√3)         (5) 2√3-1

Solution follows here:

Quadratic Equations-3 (CAT-2008)

Directions for Questions 1 and 2: 

Let f(x) = ax² + bx + c, where a, b and c are certain constants and a ≠ 0. It is known that f(5) = −3f(2) and that 3 is a root of f(x) = 0.

1. What is the other root of f(x) = 0?

(1)   −7        (2)   − 4         (3)     2         (4)   6        (5)   cannot be determined

2. What is the value of a + b + c?      

(1)  9          (2)   14          (3)     13          (4)   37     (5)   cannot be determined

Solution follows here:

Geometry-14 (CAT-2008)

Two circles, both of radii 1 cm, intersect such that the circumference of each one passes   through the centre of the circle of the other. What is the area (in sq cm) of the intersecting region?

(1) π/3 - √3/4            (2) 2π/3 + √3/2 (3) 4π/3 - √3/2 (4) 4π/3 + √3/2 (5) 2π/3 - √3/2

Solution follows here:

Numbers-16 (CAT-2008)

The integers 1, 2, …, 40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers say a and b, currently on the blackboard are erased and a new number a + b – 1 is written. What will be the number left on the board at the end?

(1)  820        (2) 821     (3) 781      (4) 819      (5) 780

Solution follows here:

Numbers-15 (CAT-2008)

Suppose the seed of any positive integer n is defined as follows:

seed(n) = n, if n < 10

= seed(s(n)), otherwise,

where s(n) indicates the sum of digits of n. For example, seed(7) = 7, seed(248) = seed(2+4+8) = seed(14) = seed(1+4) = seed(5) = 5 etc..

How many positive integers n, such that n < 500, will have seed(n) = 9?

 (1) 39             (2) 72                (3) 81              (4) 108                                   (5) 55

Solution follows here:

Trigonometry-2 (CAT-2008)

In a triangle ABC, the lengths of the sides AB and AC equal 17.5cm and 9cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD=3cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

(1)17.05   (2) 27.85   (3) 22.45   (4) 32.25   (5) 26.25

Solution follows here:

Progressions-7 (CAT-2008)

The number of common terms in the two sequences 17,21,25,….,417 and 16,21,26,….466 is

(1)78          (2) 19              (3)20                    (4)77               (5) 22

Solution follows here:

Algebra-10 (CAT-2008)

A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?

(1)2 ≤ x ≤ 6 (2)5 ≤ x ≤ 8 (3)9 ≤ x ≤ 12 (4)11 ≤ x ≤ 14 (5) 13 ≤ x ≤ 18

Solution follows here:

Algebra-9 (CAT-2008)

Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square whose square root equals to the total of the three original integers. Which of the following best describes the minimum, say m of these three numbers?

(1)1 ≤ m ≤ 3 (2)4 ≤ m ≤ 6 (3)7 ≤ m ≤ 9 (4)10 ≤ m ≤ 12 (5) 13 ≤ m ≤ 15
Solution follows here:

Algebra-8 (CAT-2008)

If the roots of the equation x³-ax²+bx-c=0 are three consecutive integers, then what is the smallest possible value of b?

(A)-1/√3        (B)-1       (C)0      (4)1      (5)1/√3

Solution follows here:

Geometry-7 (CAT-2008)

Consider obtuse angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?
(1)5      (2)21         (3)10           (4) 15          (5) 14
Solution follows here:

P&C-5 (CAT-2008)

How many integers greater than 999 but not greater than 4000, can be formed with the digits 0,1,2,3 and 4, if repetition on digits is allowed?

(1) 499         (2)500                (3)375       (4)376       (5)501

Solution follows here:

Algebra-7 (CAT-2008)

What is the number of distinct terms in the expansion of (a+b+c)²⁰?    

(1)231              (2)253    (3)242   (4)210          (5) 228

Solution follows here: