 This Section
 Latest
 New gut virus lives in half the world`s population
 Solar storm could have plunged world into darkness in 2012
 Black boxes from Taiwan air crash investigated
 One dead as Shia protest in Lucknow turns violent, cleric blames Azam Khan
 Invertebrate numbers slashed by 45% on average over 3 decades
 SGPC row: Sukbir Badal calls its constitutional crisis, meets Rajnath, Jaitley
 Modi to address Nepal Parliament, pray at Pashupatinath temple
 Congress sweeps Uttarakhand Assembly bypoll
 Islamist militants planning attack in West have left Syria: Norway
 Earth missed solar catastrophe two years ago: NASA
 Jihadist assault on Syria regime territory kills 74: Monitor
 Planes with Ukraine bodies arrive in Netherlands
 15 cases of laundering in terror financing booked by ED: Govt
 Tourist shot dead in Kenya was German: Police
 Syria becoming home to two competing Islamic states
 Sushil Modi describes Sharad Yadav as his `political guru`
 China orders probe after man castrates 4 in hospital
 Earth`s 6th mass extinction begins
 Recep Tayyip Erdogan to be `active` Turkish President: Deputy PM
 Emerge as creative leaders: Kalam to IIM students
 Tripura University to attract Bangladeshi students
 Dropout rate matter of concern: Smriti Irani
 `PR and journalism are both extremely competitive fields`
 Lok Kala Academy keeps passion for indigenous performing folk arts alive
 GEO  IT HUB
 Taking Stand
 Comedy Central
 Lowquality education should not be tolerated: CNR Rao
 DU academic session begins today after FYUP row
 DU clears 3year format for UG courses
 DU announces 7th cut off list, most colleges close admissions
 IITJ offers starting salary of Rs 25 L to attract faculties
 Himachal Pradesh govt warns MM Medical College over affiliation
 Developing Skills
 Web Wrap
CAT Q&A
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 3digit 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 menhr = 2/7 th = of work. Therefore, whole work = 75 × 8 × 90 × 7/ 2 menhr 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.
(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

(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 3digit 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 menhr = 2/7 th = of work. Therefore, whole work = 75 × 8 × 90 × 7/ 2 menhr 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.
First Published: Tuesday, September 03, 2013, 21:20
Most Popular in News
More from other sections