(22 + 42 + 62 + ... + 202) = ?

(22 + 42 + 62 + ... + 202) = (1 x 2)2 + (2 x 2)2 + (2 x 3)2 + ... + (2 x 10)2

= (22 x 12) + (22 x 22) + (22 x 32) + ... + (22 x 102)

= 22 x [12 + 22 + 32 + ... + 102] Ref: (12 + 22 + 32 + ... + n2) =1/6 n(n + 1)(2n + 1)

=(4 x 1/6x 10 x 11 x 21)

= (4 x 5 x 77)= 1540.

.
Jane and Naura are age fellows. The total age of Miley and Naura is 7 years more than the total age of Jane and Bell

Bell is how many years younger than Miley.

Let's

Naura and jane have same age = X

Miley + x = 7 + x + Bell

=> Miley - Bell = 7 + X - x = 7

=> Bell is younger than Miely by 7 years

.
Choose or find odd letter group

VT , MQ , PR , DF , FG

Putting A = 1, B = 2, ....... and so on, we have:

VT = V + T = 22 + 20 = 42 (even);

MQ = M + Q = 13 + 17 = 30 (even);

PR = P + R = 16 + 18 =34 (even);

DF = D + F = 4 + 6 = 10 (even);

FG = F + G = 6 + 7 = 13 (odd).

.