Number System - Study Mode

[#266] A number is successively divided by 8, 7 and 3 giving residues 3, 4 and 2 respectively and quotient 31. The number is :
Correct Answer

(B) 5355

Explanation

Solution: z = 3 × 31 + 2 = 95 y = 7 × z + 4 = 7 × 95 + 4 = 669 x = 8 × y + 3 = 8 × 669 + 3 = 5355 ∴ Required number = 5355

[#267] If x - y = 8, then which of the following must be true ? I. Both x and y are positive. II. If x is positive, y must be positive. III. If x is negative, y must be negative.
Correct Answer

(D) III only

Explanation

Solution: It is given that x - y = 8 I. We may have x = 5 and y = - 3 So, it is not necessary that both x and y are positive. II. If x positive, then it is not necessary that y is positive, as x = 5 and y = -3 III. If x < 0, then y = x - 8 which is clearly less than 0 So, if x is negative, then y must be negative.

[#268] ? × $$left( {|a| imes |b|}
ight) = - { ext{ ab}}$$
Correct Answer

(B) -1

Explanation

Solution: Let x × $$left( {|a| imes |b|}
ight) = - { ext{ ab}}$$ Then, x = $$frac{{ - left( {{ ext{ab}}}
ight)}}{{|ab|}}$$ = -1

[#269] If you subtract - 1 from + 1, what will be the result ?
Correct Answer

(D) 2

Explanation

Solution: (+ 1) - (- 1) = (+ 1 + 1) = 2

[#270] All natural numbers and 0 are called the ..... numbers.
Correct Answer

(C) whole

Explanation

Solution: All natural numbers and 0 are called the whole numbers.