HirePro Number System Quiz-1

exp->Given that :
3/7 of the oranges are sour to eat.
Total no. of oranges = 3,80,205
Sour oranges = 3/7 of 3,80,205
= 3 × 54315 = 162945
Oranges that can be sold = total no. of oranges - sour oranges
= 3,80,205 - 1,62,945
= 2,17,260
so 2,17,260 oranges can be sold by the farmer.

exp-> On dividing 7884 by 7, the remainder is 2. So, 2 is the smallest number which should be subtracted from 7884 to make it divisible by 7.

exp-> The given number is divisible by 6 only if it is divisible by 2 and 3. As the last digit is 4, whatever be the value of X, it would be divisible by 2.
Now, 8 + X + 4 = 12 + 3, must be divisible by 3.
So, X = 3 makes the number divisible by 3
So 3 is the required digit.

Correct Option: C
Let the number = 8x, 12x

8x – 4 : 12x – 4 = 3 : 6

(8x – 4) × 6 = (12x – 4) × 3

48x – 24 = 36x – 12

48x – 36x = 24 – 12

x = 1

Numbers = 8, 12

Now Ratio = (8 + 4) : (12 + 4)

= 12 : 16 = 3 : 4

Answer: -1474
Explanation: Given a = 8 and b = -2
On putting the values in the given equation, we will get -
(8)^2 - 3 x (8)^3 + 3 x (8) + 3 x (-2) + 3 x (-2)^3 + (-2)^2
= 64 - 1536 + 24 - 6 - 24 + 4
= -1474

exp-> Given x = a(b - c), y = b(c - a), z = c(a - b)
x = a(b - c)
or, x/a = (b - c) …..(i)
y = b(c - a)
or, y/b = (c - a) …..(ii)
z = c(a - b)
or, z/c = (a - b) …..(iii)
Add equation (i), (ii), and (iii), we will get
x/a + y/b + z/c = b - c + c - a + a - b
x/a + y/b + z/c = 0
So, (x/a)3 + (y/b)3 + (z/c)3 = 3 (x/a) * (y/b) * (z/c) [because if a + b + c = 0, then a3 + b3 + c3 = 3abc]
= 3xyz/abc

Correct Option: 67.5
Let the number be z. then, z – 48 = 92– z

⇒ 2z = 92 + 48 ⇒ 2z = 145

⇒ z = 72.5
Hence, the required number is 72.5

» Explain it
Correct Option: 5
Let, the number be z,
Then, 10z – 32 = 2z + 8

⇒ 8z = 40 ⇔ z = 5

Hence, the required number is 5.

exp-> let numbers be ab
Thus a + b = 12 and a - b = 4
=> (a + b) + (a - b) = 16
=> 2a = 16 => a = 8
=> b = 12 - 8 = 4
∴ number is 84.

Correct Option: 40
1470 = 7 × 7 × 8 × 5

To make it a perfect square, it must be divided by 5 × 8 = 40.