Numbers Questions

$$\begin{gathered} 2211 x 75 x 112 \\ => 222 x 75 x 112 \end{gathered}$$

 Total number of prime factors is (22+5+2) = 29

we can treat every two consecutive terms as one.
So, we will have a total of 100 terms of the nature:
(2 + 5) + (7 + 6) + (12 + 7).... => 7, 13, 19,....

We know the sum of n terms  nn+12

Now, a= 7, d=6 and n=100
Hence the sum of the given series is
S= 100/2 x[2 x 7 + 99 x 6]
=> 50[608]
=> 30,400.

The pattern followed is *1 + 1, *2 +2 , *3 + 3 , *4 + 4 , *5 + 5

Sum of Interior angle is 180 .
and it is given that interior angle is 150 more than exterior,
so let exterior angle is x then interior will be x+150

now , interior + exterior =180
x+150+x=180
x=15

now , number of sides of polygon = 360 / exterior angle
n = 360 / 15
n = 24

The pattern followed is +3 , +6 , +12 , +24 , +48

From the given series of numbers, if half of the second highest number is subtracted from the third highest number, what will be the value ?

Now arranging the given numbers in descending order.
837 746 519 495 328

519 - 746/2 = 519 - 373 = 146.

Let x be the number.

Given: x = 296n + 75 [where n is quotient] 

 --> (378n) +( 372 + 1) 

 -->37(8n + 2) + 1

Hence, when x divided by 37, 1 is the remainder.