3
$\begingroup$

Source: SOF World IMO Class 9

Find the missing number, if the same rule is followed in all the three figures.

2 1 4    2 3 3    4 6 7
\ | /    \ | /    \ | /
 693      374       ?
/ | \    / | \    / | \
2 5 2    3 2 2    1 1 2
  • (A) 937
  • (B) 824
  • (C) 769
  • (D) 606

I have tried adding, multiplying, squaring, etc. but to no avail. What is the answer?

$\endgroup$
8
$\begingroup$

I finally got it!

Answer is (D) 606

Below is a detailed explanation

First of all we can split central numbers in dividers: 693 = 3*3*7*11 and 374 = 2*11*17
Then we can try to make any pair of dividers (for example 693 = 21*33) by using the 3 figures above, and the 3 figures below..
Finally, we can find that 2*2+1*1+4*4 = 21 and 2*2+5*5+2*2 = 33
So, sum the squares of the 3 figures above, then sum the squares of the number below and multiply the 2 results to get the central number.
In other words, if A, B, C are the 3 top figures, and D, E, F are the 3 figures below, then the central number is
(A^2+B^2+C^2) * (D^2+E^2+F^2)

We can check that this rule works for 374: (2*2+3*3+3*3 = 22 and 3*3+2*2+2*2 = 17, and 374 = 22*17)

For the next one, we have 101 (4*4+6*6+7*7) and 6 (1*1+1*1+2*2) , so the answer is 101*6=606 (answer D)

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.