Quantitative Aptitude - Numbers and Algebra
41. Which of the following is true?
- 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
42. If a, b, c, d, p and q are non-zero, unequal integers and (a+bi)/(c+di) equals
- 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
- 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) = 3x odd average Thus III is true.
- 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.
