Numbers & Algebra - Numbers and Algebra MCQ

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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:
27:

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:
28:

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:
29:

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:
30:

Two new charity organizations C1 and C2 were formed, with x members each, on January 1, 2012. On first day of each, subsequent month, in C1, number of members increases by a certain number a, while in C2, number of members increases in such a way that ratio of the number of members in a month to the preceding month bear a ratio equal to b. On May 1, 2012, both organizations had the same number of members. If a = 20x, then b will be

 A. 2 B. 3 C. 2.5 D. 3.5 Answer Report Discuss Option: B Explanation : Number of members in C1 on May 1, 2012 = x + 4ya Number of members in C2 on May 1, 2012= xb4 x + 4a = xb4 and a = 20x ∴ x(b4 - 81) As x   ≠ 0, b4 - 81 = 0 ∴ b = 3 Click on Discuss to view users comments. Write your comments here:

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