It's Equal To One Of The Others?

Adding first four equations we get $3(a+b+c+d)=18 \Rightarrow a+b+c+d=6$ .

Step 1

a + b + c + d = x

When a is removed, the equation is equal to 6.

When b is removed, the equation is equal to 5.

When c is removed, the equation is equal to 4.

When d is removed, the equation is equal to 3.

Therefore, $b = a + 1$ , $c = b + 1$ , and $d = c + 1$

Step 2

$6 = b + (b + 1) + (b + 2)$

Simplify

$6 = 3b + 3$

-3

$3 = 3b$

Divide by 3

$1 = b$

Step 3

a = b - 1 therefore a = 0

b = b therefore b = 1

c = b + 1 therefore c = 2

d = b + 2 therefore d = 3

Step 4

$0 + 1 + 2 + 3 = 6$

If we examine the formulas, we can see that if we combine the first three equations, then we will get the next formula here:

$3(a+b+c+c)$ $=$ $3a+3b+3c+3d$ $=$ $18$

We can then see that the final equation is equal to the sum of all of the different variables, we can divide both sides by $3$ to find the final value. We don't need to find the values of the individual variables so we simply carry out this operation to get the answer.

$3a+3b+3c+3d$ $=$ $18$

$\frac{3a+3b+3c+3d}{3}$ $=$ $\frac{18}{3}$

$a+b+c+d$ $=$ $6$

Avoid any calculations by just paying attention to the possible answers - if b+c+d=6 then all answers below 6 are automatically excluded as possible solutions. ;)