Brain Teasers
Circular System?
Given that:
a + b = 12
c + d = 7
b-c = 2
a-d = 3
Find (a-b) + (c - d).
a + b = 12
c + d = 7
b-c = 2
a-d = 3
Find (a-b) + (c - d).
Hint
It doesn't hurt to "regroup".Answer
The answer is 1. If you tried to get each letter individually, you'd probably go in circles. Instead, notice that (a-b) + (c-d) = (a+c) - (b+d).Also, (a+c) = [(a+b) - (b-c)], and (b+d) = [(a+b) - (a-d)], so:
(a+c) - (b+d)
= [(a+b) - (b-c)] - [(a+b) - (a-d)]
= [(12 - 2)] - [(12 - 3)]
= 10 - 9
= 1
or
(a-b) + (c-d)
= (a-d) - (b-c)
= 3 - 2
= 1
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