# Missing number in figure [closed]

Question:

Determine the missing number in the right figure on the basis of the numbers arranged in the left figure. My attempt:

I have tried every thing from squares, cubes, products, sum, differences; alternate application of these methods, etc. but cannot at all come close to the options:

(1) 30   (2) 58   (3) 160   (4) 32


I am usually good at these problems but can't solve this one. Please help!

## 2 Answers

Perhaps the answer is

(2) $~58$.

## Argument:

Call the numbers in the outer ring $a,b,c,d,e$, so that in the left figure $a=1$, $b=2$, $c=3$, $d=4$, $e=5$ and in the right figure $a=10$, $b=9$, $c=8$, $d=7$, $e=6$. Call the central number $x$.

Then the numbers are related as

$x=e*(a+b)-c*d$.

Left figure: $~~~~x=5*(1+2)-3*4=3$
Right figure: $~~x=6*(10+9)-8*7=58$

Perhaps the answer is

(2)  $$58$$

### Explanation:

Call the numbers in the outer ring $$a,b,c,d,e$$, so that in the left figure $$a=1$$, $$b=2$$, $$c=3$$, $$d=4$$, $$e=5$$ and in the right figure $$a=10$$, $$b=9$$, $$c=8$$, $$d=7$$, $$e=6$$.  Call the central number $$x$$.
[Thanks, @Gamow, for proposing a concise notation.]

Then,

$$x={a~\times~e}-2$$

But this is silly; we could just as well say

(1)  $$30$$

because

$$x=\lceil\frac{a~\times~e}2\rceil$$

or

$$x=4b-e$$

## or

(3)  $$160$$

because

$$x=a \times c \times (e-4)$$

# or

(4)  $$32$$

because

$$x=c \times (d-3)$$

• Thanks for your answer! But I disagree with you about your thought that this question has many answers. To obtain the central number, we are supposed to use ALL the five numbers encircling it. That's why those five numbers are given. This is how these questions are generally solved. These tricks (of not using all the given numbers) are used when there doesn't exist an answer which can be formed using all the given numbers. – Gaurang Tandon Apr 17 '16 at 6:32