# Numbers & Algebra - Numbers and Algebra MCQ

26:

Six men A, B, C, D, E, F agree with a seventh man G to provide a sum of money among them. A, B, C, D, E, F are to subscribe Rs.10 each, and G is to pay Rs.3 more than the average of the seven. What is the whole sum to be provided?

 A. Rs.73.50 B. Rs. 74 C. Rs. 73 D. Rs. 72.50 Answer Report Discuss Option: A Explanation : let average of the seven men be x ∴ x = (10x6+(x+3)) / 7 => 60 + x +3 = 7x => x = 63/6 = 10.5 Toal amount = 10.5 x 7 = 73.5 Click on Discuss to view users comments. Write your comments here:
27:

What is the greatest number consisting of six digits which on being divided by 6, 7, 8, 9, 10 leaves 4, 5, 6, 7, 8 as remainders respectively?

 A. 997920 B. 997918 C. 999999 D. 997922 Answer Report Discuss Option: B Explanation : 6 - 4 = 2, 7 - 5 = 2,  8 - 6 = 2,  9 - 7 = 2,  10 -8 = 2 L.C.M. of 6, 7, 8, 9, 10 = 2520; Greatest number of 6 digits = 999999 2520 x 396 + 2079 = 999999 Remainder = 2079. Subtract 2079 from 999999, then we get 999999- 2079 = 997920. Subtract 2 from this number to get required number, which is 997918 and which will give the remainders 4, 5, 6, 7, 8 when divided by 5, 6, 7, 8, 9 respectively. Click on Discuss to view users comments. Write your comments here:
28:

There are N questions in an exam.
For i= 1, 2,..... N ,
there are 2N-1 students who answered i or more questions wrongly. If total number of wrong answers is 8191, N then will be

 A. 12 B. 11 C. 10 D. 13 Answer Report Discuss Option: D Explanation : Number of students who answered 1 or more questions wrongly = 2N-1. Number of students who answered 2 or more questions wrongly = 2N-2 Hence number of students who answered 1 question wrongly = 2N-1- 2N-2 = 2N-2 Similarly it can be shown that number of students who answered 2 questions wrongly = 2N-2 - 2N-3 = 2N-3 Similarly we can find number of students who answered K questions wrongly where K ≥ 3 Hence total number of questions attempted wrongly s = 2N-2+2(2N-3)+3(2N-4 )+...+(N-1)(20) + N(1) ........(1) ∴ s/2 = 2N-3+ 2(2n-4) +.......+ (N-2)(20) + (N-1)/2 + N/2.......... (2) Substracting equations (1) from (2) s/2 = 2N-2 + 2N-3 +...+20+1/2 => s = 2N + 2N-2+2N-3+...+1 = 2N -1 = 8191 => N = 13 Click on Discuss to view users comments. Write your comments here:
29:

In an election for the President, if 261 valid votes are cast, for the 5 contestants then least number of votes a candidate requires to receive to win the election are

 A. 53 B. 54 C. 257 D. 72 Answer Report Discuss Option: A Explanation : Worst scenario is when other four get equal number of votes. Let the winning candidate get x votes. ∴ x > (261-x) / 4 => x > 52  x = 53 Click on Discuss to view users comments. Write your comments here:
30:

If 7x + 6y = 420, x and y are natural numbers, then what can be said about x?

 A. x is always odd B. x is always even. C. x is even only if y is odd. D. x is odd if y is even. Answer Report Discuss Option: B Explanation : 7x + 6y = 420 Equation is of the form: 7x + even number = even number. ∴7x has to be even   Hence x has to be even. Click on Discuss to view users comments. Write your comments here:

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