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CAT Mock Test Paper - 31 Questions & Explanations

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CAT Mock Test Paper - 31 Questions & Explanations SECTION - I QUANTITATIVE ABILITY 1. Salim purchased three different varieties of chocolates namely A, B and C. The number of chocolates of each variety bought by him is equal to the price of one chocolate of that particular variety. The price of one chocolate of each of these three varieties is an integer. The aggregate amount spent by him on these chocolates is less than Rs.100. The price of one chocolate of variety A is greater then the price of one chocolate of variety B and the cost of one chocolate of variety C is less than the price of one chocolate of variety B. The price of one chocolate of a particular variety is greater than the price of one chocolate of another variety by Rs. 5. If Salim paid an average of Rs.7 for each chocolate bought by him, then find the price of one chocolate of variety A. (a) Rs. 4 (b) Rs. 6 (c) Rs. 9 (d) Rs. 7 2. In three distinct regular polygons, it is known that the measure of the internal angle of one regular polygon exceeds the measure of the internal angle of the other two regular polygons by 15° and 27° respectively. Furthermore, the sum of the measures of the external angles of all the three regular polygons is 177°. What is the sum of the number of sides of all these three regular polygons ? (a) 17 (b) 18 (c) 19 (d) 20 3. Let M be a three-digit number denoted by ‘ABC’ where A, B and C are numerals from 0 to 9. Let N be a number formed by reversing the digits of M. It is known that M – N + (396 × C) is equal to 990. How many possible values of M are there which are greater than 300? (a) 10 (b) 18 (c) 30 (d) 20 4. There is a group of 11 people namely: A1, A2, A3 ...... A11. The number of balls with A1 through A11 in that order is in arithmetic progression. If the number of balls with A1, A3, A5, A7, A9 and A11is equal to 72, then what is the number of balls with A1, A6 and A11 put together? (a) 24 (b) 36 (c) 48 (d) Cannot be determined 5. In an island, which had a total population of 55009, a war was fought between ‘Benos’ and ‘Malos’ the only tribes residing in the island. During the war every ‘Benos’ fought with a different number of ‘malos’. One of them fought with exactly 140 ‘Malos’, a second one fought with exactly 141 ‘Malos’, a third one fought with exactly 142 ‘Malos’, a fourth one with with exactly 143 ‘Malos’ and so on till one of them fought with every ‘Malos’ residing in the island. Find the number of ‘Malos’ residing in the island. (a) 27435 (b) 33000 (c) 27574 (d) 30000 6. After the addition of 35 liters of water to a can of diluted milk, the concentration of milk in the can becomes 30%. Now, further 40 liters of water is added to the can and the concentration of milk in the can gets reduced by 10 percentage points. How many more liters of water must be added to the can now such that the concentration of milk in the can becomes 8%? (a) 160 (b) 180 (c) 175 (d) 200 7. When Sunil will be as old as his father is at present, Sunil will be five times as old as his son is at present. Also, by then Sunil’s son will be six years older than the age of Sunil at present. The sum of the ages of Sunil’s father and Sunil is 85 years at present. What is the sum of the ages of Sunil’s son and Sunil at present? (a) 36 years (b) 39 years (c) 41 years (d) 45 years Page 1 MBA Online Mock CAT 16 - Unproctored Test Prep 8. P is the product of first 30 multiples of 30. N is the total number of factors of P. In how many ways N can be written as the product of two natural numbers such that the HCF of these two natural numbers is 19? (a) 3 (b) 4 (c) 5 (d) 6 9. g(P) represents the product of all the digits of P, e.g. g(45) = 4 × 5. What is the value of g(67) + g(68) + g(69) + ..... + g(122) + g(123)? (a) 1381 (b) 1281 (c) 1481 (d) None of these 10. Mandeep has to create a password having 5 distinct characters using at least 2 digits (from 7 to 9) and at least 2 English vowels (from A, E, I, O and U). No character other than digits from 7 to 9 and vowels of English alphabets are allowed in that password. If the password starts with a digit, then it must end with an alphabet and if it starts with an alphabet, then it must end with a digit. Find the number of possible passwords that Mandeep can create. (a) 1260 (b) 4480 (c) 3620 (d) 2880 11. The product of three positive integers is 6 times their sum. One of these integers is the sum of the other two integers. If the product of these three numbers is denoted by P, then find the sum of all distinct possible values of P. (a) 432 (b) 252 (c) 144 (d) 336 12. Given that the equation x3 + ax2 + bx + c = 0 has three real roots αβ, and γ . If []α=β=γ= [][]1, then which of the following cannot be a combination of the values of the constants ‘c’ and ‘a’? {Here, [x] denotes the greatest integer less than or equal to x.} (a) a = –3.3 and c = –1.25 (b) a = –5.7 and c = –6.75 (c) a = –4.8 and c = –3.75 (d) a = –4.2 and c = –2.85 13. 78 identical cubes each with 2 cm edge are joined together to form a cuboid. If the perimeter of the base of the cuboid is 64 cm, then the number of cubes along the height of the cuboid is (a) 3 (b) 6 (c) 2 (d) Cannot be determined 14. Three distinct numbers are randomly selected from the first 20 natural numbers. Find the probability that the selected numbers are in a geometric progression having common ratio greater than 1. 2 11 3 1 (a) (b) (c) (d) 285 1140 285 114 15. Given that the cost price of 10 oranges is equal to the cost price of 1 kg of apples and the cost price of 12 apples is equal to the cost price of 1 kg of oranges. If the selling price of 15 oranges is equal to the selling price of 1 kg of apples, then the selling price of 1 kg of oranges is equal to selling price of (Assume that all the apples are identical and this holds true for the oranges as well.) (a) 8 apples (b) 9 apples (c) 10 apples (d) 12 apples Page 2 MBA Online Mock CAT 16 - Unproctored Test Prep 16. In the figure given below, ABCD is a parallelogram, P is a point on the extended line DA such that PQ = 73.5 units and QR = 11.2 units. What is the length of RC? D C R A Q B P (a) 30.8 units (b) 44.1 units (c) 25.9 units (d) 21.9 units 17. Let f(x) be a polynomial of degree 51 such that when f(x) is divided by (x – 1), (x – 2), (x – 3),...and (x – 51), it leaves 1, 2, 3,... and 51 respectively, as the remainders. Find the value of f(52) + f(0). (a) 52 (b) 101 (c) 100 (d) 0 18. Consider the set P = {–5, –3, –1, 1, 3, 5….} consisting of 1998 numbers. If ‘a’ be the average of the elements in P and ‘b’ be twice the average of the first 1998 natural numbers, then which of the following is equal to (a – b)? (a) –6 (b) 5 (c) –7 (d) –8 19. S is a set containing all the integers less than 21000, which are the product of three consecutive prime numbers. N is a non-empty subset of S, in which all the elements are relatively prime to each other. If the number of elements in N is maximum possible, then how many such distinct subsets are possible? (a) 1 (b) 10 (c) 3 (d) 6 20. In a triangle ABC, the incircle touches the three sides AB, BC and CA at the points D, E and F respectively. If the length(in cm) of the sides AB, BC and CA are three consecutive even numbers, then which of the following cannot be the radius(in cm) of the incircle? (a) 3 (b) 7 (c) 15 (d) 32 Page 3 MBA Online Mock CAT 16 - Unproctored Test Prep SECTION - II DATA INTERPRETATION DIRECTIONS for Questions 21 to 23: Answer the questions on the basis of the information given below: In KAT exam there are three sections namely QA, VA and DI with 50, 40 and 30 questions respectively. Each correctly answered question fetches 1 mark. There is progressive negative marking in each section for incorrectly 1 attempted questions with first 6 wrong answers carrying negative marks each, next 6 incorrectly attempted 4 1 1 questions carrying negative marks each and beyond that every wrong answer carries negative marks. 3 2 Following bar graph shows the sectional cut-offs and the overall cut-off marks required to get oneself qualified for the next round of evaluation.
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