model 6 operations of consecutive numbers (odd, even, square, etc.) Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (c)

Let the three consecutive natural numbers be x, x + 1 and x + 2.

According to question,

$x^2 + (x + 1)^2 + (x + 2)^2$ = 2030

or $x^2 + x^2 + 2x + 1 + x^2 + 4x + 4$ = 2030

or $3x^2 + 6x + 5 = 2030 $

or $3x^2 + 6x – 2025$ = 0

or $x^2 + 2x – 675$ = 0

or $x^2 + 27x – 25x – 675$ = 0

$x (x + 27) – 25 (x + 27)$ = 0

or $(x – 25) (x + 27)$ = 0

$x = 25 and – 27$

∴ Required number = $x$ + 1 = 25 + 1 = 26

Answer: (c)

Prime numbers upto 17⇒ 2, 3, 5, 7, 11, 13, 17

Required sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 = 58

Answer: (a)

Sum of all multiples of 3 upto 50

= 3 + 6 + ..... + 48

= 3 (1 + 2 + 3 + .... + 16)

= 3×${16(16+1)}/2$= 3 × ${272}/2$ = 408

[Since 1+2+3+…+n = ${n(n+1)}/2$]

Answer: (a)

$(x + 2)^2 – x^2 = 84$

or $x^2 + 4x + 4 – x^2$ = 84

4x = 84 – 4 = 80

x = $80/4$ = 20

x + 2 = 20 + 2 = 22

∴ The required sum = 20 + 22 = 42

Answer: (a)

1 + 2 + 3 + ... + n = ${n(n+1)}/2$

1 + 2 + 3 + .. + 25 = ${25(25 + 1)}/2$ = 25 × 13

Hence, 13 is a factor of required sum.