# Numbers & Algebra - Numbers and Algebra MCQ

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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:
22:

Sum of an infinite geometric series is 3 and sum of an infinite geometric series formed from squares of the terms of the original series is 6. First term of the first series will be

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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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If x+y+z=0,then x2/yx + y2/zx + z2/xy equal

 A. 0 B. 1 C. 2 D. 3 Answer Report Discuss Option: D Explanation : x2/yx + y2/zx + z2/xy              ...(since, x+y+z=0  'x3+y3+z3=3xyz) (x3+y3+z3) / xyz = 3xyz / xyz = 3. Click on Discuss to view users comments. Devanshu said: (1:20am on Friday 1st July 2016) Let x=2 y =-1 z=-1 then x y z=0 but RHS is - 3?????Btw if x y z = 0 then x^3 y^3 z^3=3xyz???? I think it should be - 3xyz then ans satisfied Write your comments here:
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Average age of a committee of seven trustees is the same as it was five years ago, a younger man having been substituted for one of them. How much younger was he then trustee whose place he took?

 A. 32 years B. 35 years C. 33 years D. 34 years Answer Report Discuss Option: B Explanation : Increase after 5 years should have been 7 x 5 = 35 years. But since average remains same, diference in their age is 35 years. Click on Discuss to view users comments. Write your comments here: