Practice MCQ Questions and Answer on Number System
51.
x, y and z are distinct prime numbers where x y z. If x + y + z = 70, then what is the value of z?
(A) 29
(B) 31
(C) 37
(D) 43
Solution:
Since x, y and z are distinct prime number (x y z) y + z = 70 - 2 = 68 31 + 37 = 68 Hence, x = 2, y = 31 and $$\boxed{{\text{z}} = 37}{\text{ Answer}}$$
52.
If sum of two numbers be a and their product be b, then the sum of their reciprocals is :
(A) $$\frac{{1}}{{b}}$$ + $$\frac{{1}}{{b}}$$
(B) $$\frac{{b}}{{a}}$$
(C) $$\frac{{a}}{{b}}$$
(D) $$\frac{{1}}{{ab}}$$
Solution:
Let the two number are P and Q P + Q = a PQ = b ⇒ $$\frac{{1}}{{P}}$$ + $$\frac{{1}}{{Q}}$$ ⇒ $$\frac{{Q + P}}{{PQ}}$$ ⇒ $$\frac{{a}}{{b}}$$
53.
In a certain series, each number except the first and second is obtained by adding the previous two numbers. If the first no is 2 and sixth no is 26, then the seventh number is:
Thrice the square of a natural number decreased by four times the number is equal to 50 more than the number, the number is -
(A) 6
(B) 5
(C) 10
(D) 6
Solution:
Let the number be x According to question $$\eqalign{ & \left( {3 \times {x^2}} \right){\text{ - }}\left( {4 \times x} \right) = 50 + x.....(i) \cr & \Rightarrow 3{x^2} - 4x = 50 + x \cr & \Rightarrow 3{x^2} - 5x - 50 = 0 \cr & \Rightarrow 3{x^2} - 15x + 10x - 50 = 0 \cr & \Rightarrow 3{x^{}}(x - 5) + 10(x - 5) = 0 \cr & \Rightarrow (x - 5)(3x + 10) = 0 \cr & x = 5\,\,or\,\, - \frac{{10}}{3} \cr} $$ Since the natural number is x = 5 Shortcut method : $$ \Rightarrow 3{x^2} - 4x = 50 + x.....(i)$$ Now put the value of x from option (b) $$\eqalign{ & x = 5 \cr & 3 \times {(5)^2} - 4 \times 5 = 50 + 5 \cr & 75 - 20 = 55 \cr & 55 = 55 \cr} $$ LHS = RHS (it satisfies the conditions) $${\text{so, x = 5}}$$
55.
In a farm there are cows and hens. If heads are counted there are 180, if legs are counted there are 420. The number of cows in the farm is :
(A) 130
(B) 50
(C) 150
(D) 30
Solution:
Let the number of cows be x. Then, number of hens would be (180 - x) According to the question (180 - x) × 2 + 4x = 420 ⇒ 360 - 2x + 4x = 420 ⇒ 2x = 420 - 360 = 60 ⇒ 2x = 60 ∴ x = $$\frac{{60}}{2}$$ = 30
56.
The number of prime numbers between 301 and 320 are :
(A) 3
(B) 4
(C) 5
(D) 6
Solution:
Each of the numbers 302, 303, 304, 305, 306, 308, 309, 310, 312, 314, 315, 316, 318 and 319 is clearly a composite number. Out of 307, 311, 313 and 317 clearly every one is prime. Hence, there are 4 prime numbers between 301 and 320.
57.
In doing a question of division with zero remainder. a candidate took 12 divisor instead of 21. The quotient obtained by him was 35. The correct quotient is :
A gardener plants his garden with 5550 trees and arranged them so that there is one plant more per row as there are rows then number of trees in a row is:
(A) 56
(B) 74
(C) 76
(D) 75
Solution:
Let there be n rows, then number of trees in each row = (n + 1) Thus, total number of trees, n × (n +1) = 5550 Now, at this moment this problem can be solved in two ways. First by finding the roots of quadratic equation. Second, by using the values from options. 74 × 75 = 5550 i.e. (n + 1) = 75