CAT Q&A

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Q1. The number of zeroes in binary notation of 2189 – 289 is: (a) 0 (b) 89 (c) 100 (d) 189 Q2. The average of 60 positive distinct integers all greater than 7 is equal to 41. What could be the maximum possible value of any one of these 60 integers? (a) 277 (b) 217 (c) 210 (d) 224 Q3. N is a natural number which gives remainders 1 and 2 when divided by 6 and 5, respectively. All such N’s are written in the ascending order, side by side from left to right. What is the 99th digit from the left? (a) 2 (b) 0 (c) 1 (d) 7 Q4. Vijay covers 910 km by boat, road and rail in the ratio 4:3:6 respectively. Surprisingly, the speeds at which the journey was covered were also in the ratio 4:3:6 respectively. The total time taken for the journey was 89 hours. The ratio of the time taken by boat, road and rail was: (a) 3:4:2 (b) 1:1:1 (c) 6:3:4 (d) 4:3:6 Q5. A contractor, intending to finish a work in 150 days, employed 75 men. They worked for 8 hours every day for 90 days and completed 2/7th part of the work. Then the contractor increased the number of men by x and thereafter all the men were made to work for 10 hours every day. If the work was completed just in time, then what is the value of x? (a) 225 (b) 150 (c) 75 (d) None of these Q6. Ajay purchased four varieties of rice at the rate of 2 kgs/Re., 3 kgs/Re., 4 kgs/Re.and 5 kgs/Re. If he mixes all the four varities of rice in the ratio 4:3:2:1 in the given order, then the price at which Ajay should sell the mixture to make a profit of 20% is: (a) 2.5 kgs/Re. (b) 3.6 kgs/Re. (c) 3 kgs/Re. (d) 250kgs /111 Re. ******************************************************************************* Answers with explanations: 1. b 2189 has 189 zeroes in the end. 289 has 89 zeroes in the end. 2189 – 289 will have 89 zeroes in the end and the remaining 100 digits would all be 1s. 2. a If we need one of these 60 numbers to be maximum possible then all other 59 should be minimum possible. Minimum possible sum of 59 distinct integers each of which is greater than 7 will be: 8 + 9 + 10 +.....66 = 2183 Sum of the 60 integers = Average × 60 = 41 × 60 = 2460 Maximum possible value of an integer out of these 60 = 2460 – 2183 = 277 3. b Natural numbers which when divided by 5 give a remainder 2 are given by 5K + 2 [‘k’ is a whole number]. Natural numbers which when divided by 6 give a remainder 1 are given by 6m + 1[‘m’ is a whole number] 5k + 2 = 6m + 1 6m – 5k = 1 All such natural numbers are 7, 37, 67, 97, 127, .... Numbers when written one beside the other 7376797127157187217247277307337..... Observe the series The first 4 numbers give first 7 digits. After these 4 numbers, 3 digit numbers follow. These 3 digit numbers from an A.P. with common difference 30. First three digit number = 127 The 30th 3-digit number is = 127 + (30 – 1) × 30 = 997 The first 34 numbers (= 4 + 30) give 97 digits (= 7 + 3 × 30) The next number in this A.P is 997 + 30 = 1027 the 99th digit is 0. 4. b The ratio of the speeds and the distances travelled is the same. So the ratio of time = 1:1:1 5. b 75 × 8 × 90 men-hr = 2/7 th = of work. Therefore, whole work = 75 × 8 × 90 × 7/ 2 men-hr Therefore, 5/ 7 work = 75 × 8 × 90 × 7/2 × 5/7 According to the information given in the question: (75 + x) × 10 × 60 = 75 × 8 × 90 × 5/ 2 x = 150. 6: The prices at which Ajay purchased 4 varieties of rice are 50 paise/kg, 100/ 3 paise / kg, 25 paise/ kg and 20 paise/kg respectively. They are mixed in the ratio 4:3:2:1. Let, the cost price of the mixture be ‘X’. X 1/10 (4 × 50 + 3 × 100/ 3 + 2 × 25 + 1 × 20) = 37 paise / kg. In order to make a profit of 20%, the selling price of the mixture will be 1.2 × 37 paise/kg = 250/ 111 kg/Re.