Numbers Questions

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.

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

When 16nis divided by 9, we have

 1619, remainder = 7  

1629, remainder = 4 

1639, remainder = 1 

1649, remainder = 7 

1659, remainder = 4 

1669, remainder = 1 

So, we have cyclicity of 3 factors i.e 7,4,1. 

Hence only 3 remainders are possible.

If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible number of books = 15,17,19,21,23,25,27,29
If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible number of books = 17,20,23,26,29
If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible number of books = 15,19,23,27
common number is only 23 so it will be answer

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.

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 = peacocks
y = deers

2x + 4y = 200
x + y = 72
y = 72 - x
2x + 288 - 4x = 200
x = 44 peacocks
y = 28 deers

All powers of 6 has 6 in units place so answer will definitely be 1.