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

Answer: (a)

Let the numbers be 3x, 3x + 3 and 3x + 6

3x + 3x + 3 + 3x + 6 = 72

9x + 9 = 72

9x = 72 – 9 = 63

x =$63/9$ = 7

∴ Largest number = 3x + 6 = 3 × 7 + 6 = 27

Answer: (c)

22 + 24 + 26 + ... + 50

= 2 (11 + 12 + 13 + .... + 25)

= 2 [(1 + 2 + 3 + ... + 25) – (1 + 2 + 3 ... + 10)]

= 2$({25×26}/2 - {10×11}/2)$

= 2 (325 – 55) = 2 × 270 = 540

Method 2 :

Sum of first n even numbers = n (n + 1)

Required sum = Sum of 25 even numbers from 1 to 50 – sum of 10 even numbers from 1 to 20

= 25×26 – 10 × 11 = 650 – 110 = 540

Answer: (a)

Series of first 20 odd natural numbers is an arithmetic progression with 1 as the first term and the common difference 2.

Sum of n terms in arithmetic progression is given by.

$S_n =1/2n[2a + (n – 1)d]$

Where a : First term; d : common difference

$S_{20}= 1/2×20[(2×1) + (20 -1) × 2]$

= 10 [2 + 38]=10 × 40 = 400

Note :Sum of first n consecutive odd numbers = $n^2$

Answer: (d)

Series of all natural numbers from 75 to 97 is in A.P. whose first term,

a = 75, last term, l = 97

If number of terms be n, then $a_n$ = a + (n–1)d

97 = 75 + (n – 1)

n = 97 – 74 = 23

$S_n = n/2(a+l)$

$S_23 = 23/2(75+97)$

= $23/2$× 172=1978

Answer: (c)

$10^2 + 11^2 + 12^2$ = 100 + 121 + 144 = 365

Required sum =10 + 11 + 12 = 33