Quantitative Ability Tech Test Numbers Test 3

5358 x 51= 5358 x$\left(50 + 1\right)$= 5358 x 50 + 5358 x 1= 267900 + 5358= 273258.

Required sum = 2 + 3 + 5 + 7 + 11 = 28.

Note: 1 is not a prime number.

Definition: A prime number [or a prime] is a natural number that has exactly two distinct natural number divisors: 1 and itself.

Let the smaller number be $ x $. Then larger number = $x$ + 1365.

$\therefore x $ + 1365 = 6$ x $ + 15

$\Rightarrow$ 5$ x $ = 1350

$\Rightarrow x $ = 270

$\therefore$Smaller number = 270.

Given Exp. =$ \dfrac{(12)^3 \times 64}{432} = \dfrac{(12)^3 \times 64}{12 \times 6^2} $= (12)² x 6² = (72)² = 5184

72519 x 9999= 72519 x $\left(10000 - 1\right)$= 72519 x 10000 - 72519 x 1= 725190000 - 72519= 725117481.

Local value of 7 - Face value of 7 = 70000 - 7= 69993

6$n$² + 6$n$ = 6$n$ $\left(n + 1\right)$, which is always divisible by 6 and 12 both, since $n$ $\left( n + 1\right)$ is always even.

Let $ x $ be the number and $ y $ be the quotient. Then,

$ x $ = 357 $x y $ + 39

  = $\left(17 \times 21 xy\right )$ + $\left(17 \times 2\right)$ + 5

  = 17 x $\left(21y + 2\right) + 5$

$\therefore$Required remainder = 5.

Given sum

= [1 + 1 + 1 + ... to n terms]-$(\dfrac{1}{n}+\dfrac{2}{n}+\dfrac{3}{n}+ ... $)to n terms

= $ n $ -$\dfrac{ n }{2}$$\left(\dfrac{1}{ n }\right)$+ 1    [ Ref: $ n $th terms = $\left( n / n\right )$ = 1]

= $ n $ -$\dfrac{ n + 1}{2} $

=$ \dfrac{1}{2} \left( n - 1\right)$

S_n = $\left(1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100\right)$ - $\left(1 + 2 + 3 + ... + 50\right)$

    =$ \dfrac{100}{2} $ x (1 + 100) -$ \dfrac{50}{2} $x (1 + 50)

    = $\left(50 \times 101\right)$ - $\left(25 \times 51\right)$

    = 5050 - 1275

    = 3775.