# Numbers & Algebra - Numbers and Algebra MCQ

36:

A = 0.a1a1a1 ... and B = 0.a2a2a2, where aand a2 are multiples of 3 and also, a1 and a2 are distinct integers from 0 to 8. Then value of A + B is

 A. B. C. 1 D. Cannot be determined Answer Report Discuss Option: C Explanation :  Similarly,  Now, a1 and a2 are multiples of 3 and are distinct. Also, these values are less than 8. either a1 = 3 and a2 = 6 or a1 = 6 and a2 = 3 ∴a1 + a2 = 9. Click on Discuss to view users comments. Write your comments here:
37:

Which of the following is true?

 A. √2+√5=√7 B. √2+√5 ≤ √7 C. √2+√5<√7 D. √2+√5 > √7 Answer Report Discuss Option: D Explanation : (√2+√5)² = 2 + 2√10 +5 =7+2√10 (√7)² = 7 ∴ √2+√5> 7 Alternatively: √2 > √1 and √5 > √4 ∴ √2+√5 > 2+1  => √2 + √5 > 3 and √7 < √9 = 3 => √7 < 3.  so √2 + √5>√7 Click on Discuss to view users comments. Write your comments here:
38:

revise20. If a, b, c, d, p and q are non-zero, unequal integers  and (a+bi)/(c+di) equals

 A. p/q B. p2 / q2 C. 1 D. None of the these Answer Report Discuss Option: B Explanation : a + bi p c + di q qa + qbi = pc + pdi Equating real and imaginary parts. qa = pc and qb = pd. a = -P/q -c and b = (p/q)d * a²+b² (p²/q²)c + (p²/q²)d² p² ---- = ------------------- = -- c²+d² c²+d² q² Click on Discuss to view users comments. Write your comments here:
39:

revise 47. Which of the following statementls is/are true?
I.  Average of a set of values will always lie between lowest and the largest of these values.
II. If each of the values in a set is increased by a constant k, then new average of the set is increased by k.
III. If each of the values in a set is multiplied by a constant m, then new average will also be `m' times the old average
Codes

 A. Only I and II B. Only II and III C. Only I and III D. I, II and III Answer Report Discuss Option: D Explanation : I. Average of a set of numbers is greater than smallest and smaller than the greatest number of the set. Thus, I is true. II. Consider five numbers a, b, c, d and e whose average is (a+b+c+d+e) / 5 Now if each of them is increased by k, then we have average =a+k+b+k+c+k+d+k+e+k 5 =a+b+c+d+e + 5k = old average +k. 5 5 Thus, II is true III. Consider three numbers x,y and z whise average is (x+y+z) /3 Now each of them is multiplies by m then new average =(xm +ym+zm) / 3 = m((x+y+x)/3) = 3xodd average Thus III is true Click on Discuss to view users comments. Write your comments here:
40:

What is the least number which on being divided by 5, 6, 8, 9, 12 leaves in each case a remainder 1 but when divided by 13 leaves no remainder?

 A. 2987 B. 3601 C. 3600 D. 2986 Answer Report Discuss Option: B Explanation : L.C.M. of 5, 6, 8, 9 and 12 is 360 Required number = 360 K + 1 = (13 x 27 + 9) K + 1 = (13 x 27) K + (9K + 1) Now this number must be divisible by 13 K = 10 and required number = 3601. Click on Discuss to view users comments. Write your comments here: