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Numbers & Algebra - Numbers and Algebra MCQ

16:

Sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is

 A. 7 B. 29 C. 41 D. 67 Answer Report Discuss Option: D Explanation : x + (x + 36) + y = 100 ⇒2x + y = 64 Therefore y must be even prime which is 2  2x + 2 = 64 ⇒x = 31. ∴ Third prime number = x + 36 = 31+ 36 = 67 Click on Discuss to view users comments. Write your comments here:
17:

A school has 5 divisions in a class IX having 60, 50, 55, 62 and 58 students. Mean marks obtained in a History test were 56, 64, 72, 63 and 50 by each division respectively. What is overall average of the marks per students?

 A. 56.8 B. 58.2 C. 62.4 D. 60.8 Answer Report Discuss Option: D Explanation : Average = (60x56+50x64+55x72+62x63+58x50)/ (60+50+55+60+58 ) = (3360+3200+3960+3906+2900)/285 = 60.8 Click on Discuss to view users comments. Write your comments here:
18:

What is the smallest number which when increased by 3 is divisible by 27, 35, 25 and 21?

 A. 4722 B. 4725 C. 4728 D. 4731 Answer Report Discuss Option: A Explanation : L.C.M. of 27, 35, 25 and 21 = 4725 ∴ Number = 4725-3 = 4722. Click on Discuss to view users comments. Write your comments here:
19:

Which of the following is true?

 A. Sum of four consecutive even numbers is always divisible by 8. B. Sum of four consecutive odd numbers is always divisible by 8. C. Product of any n consecutive natural numbers may not be divisible by n!. D. Product of 4 consecutive odd numbers is always divisible by 15. Answer Report Discuss Option: B Explanation : (A) Four consecutive even numbers can be written as 2n, 2n + 2, 2n + 4 and 2n + 6,where n is any natural number. Sum = 2n +(2n + 2) + (2n + 4) + (2n +6) = 8n + 12 = 4(2n + 3) not always divisible by 8. Thus, (A) is not true. (B) Four consecutive odd numbers can be written as 2n-1, 2n+ 1, 2n + 3, 2n + 5 where n is a natural number Sum = (2n-1) + (2n + 1) + (2n + 3) + (2n + 5) = 8n + 8 = 8(n + 1) divisible by 8 Thus, (B) is true (C) In product of n consecutive natural numbers atleast one is divisible by n, atleast one by n - 1 ... till 1. Thus product is atleast divisible by n * (n - 1) * (n - 2) *1  =  n!. Thus, (C) is not true. (D) Take four consecutive odd numbers as 7 x 9 x 11 x 13 which is not divisible by 15. Thus, (D) is not true. Click on Discuss to view users comments. Write your comments here:
20:

Sum of all odd numbers up to 100 is

 A. 5050 B. 2500 C. 2525 D. 5000 Answer Report Discuss Option: B Explanation : Given numbers are 1, 3, 5.....99. This is an A.P with a = 1, d = 2 Let it contain n terms ∴ 1 +(n-1)2 = 99 => n = 50 Hence required sum = n/2 (first term +last term) = 50/2(1 + 99) = 2500 Click on Discuss to view users comments. Write your comments here:

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