Q14 of 55 Page 79

Complete the magic square:




























14




0



8




6



11



4





7




2



1



12


Here, sum of last column = 0 + 11 + 7 + 12


Solving for last row,


x + 2 + 1 + 12 = 30


∴ x = 15





























14




0



8




6



11



4





7



15



2



1



12



Solving for first column,


x + 8 + 4 + 15 = 30


∴ x = 3




























3



14




0



8




6



11



4





7



15



2



1



12



Solving for first row,


3 + 14 + x + 0 =30


∴ x = 13




























3



14



13



0



8




6



11



4





7



15



2



1



12



Solving for second row,


8 + x + 6 + 11 = 30


∴ x = 5




























3



14



13



0



8



5



6



11



4





7



15



2



1



12



Solving for second column,


14 + 5 + x + 2 = 30


∴ x = 9




























3



14



13



0



8



5



6



11



4



9




7



15



2



1



12



Solving for third column,


13 + 6 + x + 1 = 30


∴ x = 10




























3



14



13



0



8



5



6



11



4



9



10



7



15



2



1



12



More from this chapter

All 55 →
12

Fill in the numbers from 1 to 6 without repetition, so that each side of the triangle adds up to 12.

 13

Fibonacci numbers Take 10 numbers as shown below:

a, b, (a + b), (a + 2b), (2a + 3b), (3a + 5b), (5a + 8b), (8a + 13b), (13a + 21b), and (21a + 34 b). Sum of all these numbers =11(5a + 8b) = 1 1 x 7th number.


Taking a = 8, b =13; write 10 Fibonacci numbers and verify that sum of all these numbers =11 x 7th number.

 1

If 5x6 is exactly divisible by 3, then the least value of x is

 2

If 64y8 is exactly divisible by 3, then the least value of y is