Numbers Questions

Let the Number be Y.

Then  Y = 296 q + 75

= (37 x 8)q +( 37 x 2) + 1

= 37 (8q + 2) + 1

Thus, when the number is divided by 37, the remainder is 1

Here a = 3 and r = 6/3 = 2. Let the number of terms be n.
Then, t = 384 => a * r^(n-1) = 384
=> 3 * 2^(n-1) = 384 => 2^(n-1) = 128 = 2^(7)

=> n-1 = 7 => n = 8.

The best approach is to pick a number that satisfies the rules that x and y are greater than 0. So for example you could choose 25 for y.

The value of x before doubling is then 25 - 50/25 = 23

The value after doubling y will be 50 - 50/50 = 49, which is more than double.

6)4456(742
42
--------
25
24
-------
16
12
-----
4
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Required number = (6-4) = 2.

The pattern is -4, +9,-16, +25, -36

The next number=119+49=168

The pattern followed is *1.5 , * 2 , *2.5 , *3 , *3.5

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

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = ( 22 + x ), which must be divisible by 3.

When x=2. [(22 + 2) = 24 is divisible by 3]

So, the answer is 2