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Updated on: Monday, July 26, 2010

The country’s most reputed management entrance examination — CAT 2010 will be held in a 20-day window, between October 27 and November 23, 2010 and the test will be held in two slots on each day. We bring you mock test papers and tips on each section (Quantitative Aptitude, Verbal Ability, Data Interpretation and Reasoning) of the exam to help you assess your conceptual clarity and preparation.

Let’s begin with the section on Quantitative Ability. To start with, you need systematic practice and well-honed skills to be able to do well in this test as this is a blend of ‘attempt’ and ‘accuracy’. As of today, speed is not required. Keep in mind that if you can attempt 60 per cent questions with 90 per cent accuracy (in each section), you stand a good chance of getting a call from the venerated IIMs. Since Quant questions can be scattered anywhere in the test, first ‘skim and scan’ the test and mark the questions so that you can find them easily later.

Let’s say you get 20 questions like last year. Now, with the aim of attempting 12 questions with over 90 per cent accuracy, start with questions that have the least amount of data, i.e. the one-line questions. With less data, the chances of getting bogged down are cut drastically. If you can find five one-line questions and correctly attempt four of them in 5 minutes, suddenly you are left with 35 minutes for eight questions that you must attempt. That’s almost 5 minutes per question! Now you can move on to two-line questions and so on.

In many cases, the correct answer can be reached at by a combination of elimination of visibly wrong options and substituting options in question rather than solving the question itself. For example:
The value of 3 + 1/ [2 + (1/(2 + 1/2 .....))] is
(A) 2 – ^2 (B) 3 – ^2
(C) 2 + ^2 (D) 3 + ^2
Since the given expression will be greater than 3 but less than 4, we can simply eliminate the options (A), (B) and (D). Hence, the answer is (C).

QUANTITATIVE ABILITY

1. P = 73n – 35n, where n is a positive integer. Which of the following would always divide P?
(1) 100 (2) 150 (3) 225
(4) 250 (5) 175

2. If N = 10008 – 8, what is the sum of its digits?
(1) 200 (2) 207 (3) 208
(4) 209 (5) 175

3. What is the remainder when

is divided by 4?

(1) 0 (2) 1 (3) 2 (4) 3 (5) 4

4. P is a point on the side AD of a square ABCD whose area is 64 cm2. The perpendicular to the line PC at C meets the line segment AB extended at Q. If the area of DCQP is 50 cm2, the length of BQ is
(1) 12 cm (2) 6 cm (3) 4 cm
(4) 3 cm (5) 2 cm

5. If m is an integer, how many values of m are there for which m4 – 20m2 + 4 is a prime
number?
(1) 0 (2) 1 (3) 2 (4) more than 2 (5) None of these

Questions 6-7 are based on the following information...
The distance between TCY Ludhiana and TCY Jalandhar is less than 100 km. Aman started from TCY Ludhiana and after 10 hours he came across a milestone showing the distance between it and TCY Ludhiana. He moved further and 2 hours later he came across another milestone showing the distance, exactly reverse of that shown by the previous milestone.

6. The total distance covered by Aman when he reaches the
second milestone is
(1) 64 km (2) 54 km (3) 76 km (4) 65 km (5) 70 km

7. What is Aman’s speed?
(1) 4.5 km/hr (2) 4.6 km/hr
(3) 4.6 km/hr (4) 5.6 km/hr
(5) 3.2 km/hr

8. If P is a number having exactly two divisors, what is the remainder when (P – 2)! is divided by it?
(1) 1 (2) –1 (3) –6 (4) –5
(5) Cannot be determined

9. A vessel contains V litres solution of milk and water in the ratio 3 : 2. If 10 litres of water is added and the concentration of milk in the resultant solution lies between 40% and 50%, find the range of values of V.
(1) 50 £ V £ 60 (2) 20 £ V £ 50 (3) 30 £ V £ 40 (4) Data insufficient (5) None of these

10. In a survey, it was found that the number of students in the college has increased by 20% over the previous year. The number of boys has increased by 10%, whereas the number of girls has increased by 35%. Find the present percentage of girls in the college.
(1) 40% (2) 45% (3) 55%
(4) 75% (5) Can’t determine

11. 10000! = (100!)K × P, where P and K Î I. What can be the maximum value of K?
(1) 97 (2) 102 (3) 103 (4) 104 (5) 107
12. There are two cubes
painted. The first cube has 5 faces painted red and one face painted blue. The second cube has some faces painted red and some painted blue. When the two cubes are rolled simultaneously, the probability of both the cubes coming up with the same colour is ½. How many faces of the second cube are painted red?
(1) 1 (2) 2 (3) 3 (4) 4 (5) 5

Direction for questions 13-14...
In a question paper, there are 30 questions. If a person answers a question correctly, he is awarded 5 marks and if he gives the wrong answer, he gets –2 marks. There is no negative marking for not attempting any question.

13. Priya secured 60% of the maximum marks in the paper. If a denotes the number of correct attempts and b denotes the number of incorrect attempts, the total number of pairs of attempts (a, b) by Priya can at most be
(1) 2 (2) 4 (3) 6 (4) 8
(5) None of these

14. How many natural numbers less than 150 can never equal the marks secured by any student taking the test?
(1) 0 (2) 6 (3) 10 (4) 8 (5) 12

15. How many quadratic polynomials; ax2 + bx + c are there which satisfy the following conditions?
I. a, b and c are distinct.
II. a, b, c Î {1, 2, 3, 4, 5, 6}
III. x + 1 divides ax2 + bx + c
(1) 8 (2) 12 (3) 10 (4) 0
(5) Infinite

ANSWERS
1. (1) 2. (4) 3. (1) 4. (2) 5. (1) 6. (2) 7. (1) 8. (1)
9. (2) 10. (2) 11. (3) 12. (3) 13. (1) 14. (5) 15. (2)

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