PUZZLE-16

FIND OUT THE LAST DIGIT IN THE FOLLOWING MATHEMATICAL OPERATION

ANSWER : 1
SOLUTION :

        Procedure to be followed to find last digit for a number like (xyz)ⁿ

First divide power n with 4.

If 0 is remainder,

                  If z=even; last digit=6;

                  If z=odd(except 5); last digit =1;

                  If z=5; for all n values last digit=5;

If 1 is remainder then last digit is z¹ ;

If 2 is remainder then last digit is z² ;

If 3 is remainder then last digit is z³ ;

Keep visiting for problems like this.

In above problem 1999/4 gives remainder 3,

so last digit in first number is 7³

last digit in second number is 1³

last digit in last number is 7³

so answer =  7³ + 1³ -7³ = 1 

keep visiting to know more like this…

PUZZLE-15

FIND THE NUMBER IN THE BELOW NUMBER SEQUENCE PUZZLE

ANSWER : 1
SOLUTION :
In the given number sequence puzzle
1st row  = 17*17   =  289
2nd row = 18*18   =  324
3rd row  =  19*19  =  361

PUZZLE-14

FIND THE NUMBER IN THE FOLLOWING NUMBER SEQUENCE PUZZLE

ANSWER     :    8
SOLUTION   :
                        In the above table middle number of each row is equal to half of the sum of the other numbers in the respective row.
So, sum of other numbers of middle row is
      6+1+2+3+3+1=16
half of 16 is 8.

PUZZLE-13

ANSWER : 42.42 km
SOLUTION :
                 The travelling route of the shalini is shown as below.

So, 1.the shortest distance is 42.42 kms. 
      2.bank is in North-East direction from her house.

PUZZLE-12

FIND THE NUMBER IN THE BELOW NUMBER SEQUENCE PUZZLE

ANSWER : 22 
SOLUTION :
In the given puzzle numbers are following specific sequence.

4+2=6;
6+3=9;
addition of 2,3 gives 5 will be added to next number in sequence.
9+5=14;
addition of 3,5 gives 8 will be added to next number in sequence.
14+8=22;

PUZZLE-11

ANSWER : 4 numbers, they are 32,46,96,69.
SOLUTION:
Let 2 digits of number are x,y.
The given condition is
x+y=5(x-y);
x+y=5x-5y;
4x=6y;
x/y=3/2:
from the above condition we can get following pairs.
(x=3,y=2);(x=6,y=4);(x=9,y=6);
combinations of above pairs are 32,23,64,46,96,69.
in those numbers 64 is perfect square, 23 is prime number.
so the 2-digit numbers are 32,46,96,69.

PUZZLE-10

FIND THE WHOLE NUMBER 

ANSWER : (2^96-1)
SOLUTION : 

let x=2^32;
so (2^32+1)=(x+1);
Given that (x+1) is divided by whole number.
in option d,
 (2^96)=(2^32)^3=x^3;
(x^3+1)=(x+1)(x^2-(x*1)+1);
it is also divided by whole number because it has term (x+1) in it.