Numbers & Algebra - Numbers and Algebra MCQ

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Average marks of 15 students in a class is 145, maximum marks being 150. If two lowest scores are removed, the average increases by 5. Also, two lowest scores are consecutive multiples of 9. What is lowest score in the.class?

 A. 126 B. 117 C. 108 D. None of these Answer Report Discuss Option: C Explanation : Total marks of 15 students = 15 x 145 = 2175. Average marks of 15 students (excluding two lowest scores) = 13 x (145 + 5) = 1950. ∴ Total of two lowest scores = 2175 1950 = 225 Given that two scores are consecutive multiples of 9 * 9x + 9x + 9 = 225 18x = 216 => 18/x = 216 => x = 216/18 Lowest score = 9x = (216/18) x 9 = 108 Click on Discuss to view users comments. Write your comments here:
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revise 39. What is the sum upto 20 terms of the series?
2 8 26 80
- + - + -- + -- + ....?
3 9 27 81

 A. (19.3²⁰+1) / 3²⁰ B. (19.3²⁰ + 1)/ 2.3²⁰ C. (19.3²⁰-1)2.3²⁰ D. (39.3²⁰+1)+2.3²⁰ Answer Report Discuss Option: D Explanation : 2 8 26 80 - + - + -- + -- + up to 20 terms 3 9 27 81 =(1-1/3)+(1-1/9)+(1-1/9)+(1-1/27) +(1-1/81)+...up to 20 terms =20-(1/3+1/3²+1/3³+1/3⁴+...+1/3²⁰) =20-1/3((1-(1/3)²⁰) / 1-1/3) =20-(3²⁰-1)/2.3²⁰ =(40.3²⁰-3²⁰+1)/2.3²⁰ =(39.3²⁰+1) / 2.3²⁰ Click on Discuss to view users comments. Write your comments here:
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revise 48. Three people A, B and C weigh themselves in a particular order. First A, B, C weigh themselves individually and then AB, BC CA and ABC together respectively. Recorded weight for the
last measured is 180 kgs. Then average of the 7 measures is

 A. 320 kgs B. 360/7 kgs C. 720/7 kgs D. Cannot be determined Answer Report Discuss Option: C Explanation : Order of measures is A,B,C,A+B,B+C,C+A,A+B+C. Given: A + B + C = 180 Hence, average of the 7 measures [[(A)+(B)+(C)+(A+B)(B+C)+(C+A)+(A+B+C)]] =--------------------------------------- 7 = 4/7 (A+B+C) = 4/7 x 180 = 220/7 kgs Click on Discuss to view users comments. Write your comments here:
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A gardener had a number of shrubs to plant in horizontal rows. At first he tried to plant 5 shrubs in each row, then 6, then 8 and then 12, but had always 1 left. On trying 13, in one row he had none left. What is the smallest number of shrubs that he could have had?

 A. 481 B. 477 C. 468 D. 121 Answer Report Discuss Option: A Explanation : Number is 120K + 1= ((13 * 9 + 3) K + 1)  = 13 * 9K + 3 K + 1, which is divisible by 13. 3K + 1 is divisible by 13.  ∴  K = 4. Number = 481 Click on Discuss to view users comments. Write your comments here:
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Average age of a team of 15 employees is 36. Youngest of them is 20 years old and eldest is 56 years old. Two of them with average age 28 leave the team. If one of the two comes back on the condition that he will be made the team leader, then which of the following can possibly be average age of the new team so formed?

 A. 35 B. 36 C. 38 D. 39 Answer Report Discuss Option: B Explanation : Total age = 15 x 36 After two left, total age = 15 x 36 - 2 x 28 = 540 - 56 = 484 years. Let the age of the person who returns be x years. Then new average = (484 +x) / 14 Now x lies between 20 and 36 (both inclusive) New average min = (484 + 20) /14 = 36 years And New average max = (484 +36)/14 = 520/14 = 37.14. years Click on Discuss to view users comments. Write your comments here: