kkpatel1 wrote:What is the value of C+B?
1) A+B=C+D=E+F
2) (E+F)=(D-B)
I performed this problem on a Kaplan Quiz. The answer explanation was not that great. If someone has a good way to solve this, it would be greatly appreciated.
OA: 3
Both statements are independently insufficient as you cannot derive the expression C+B from either of them, and so cannot ascertain the value of C + B.
Looking at them in combination:
Statement two tells us that D - B = E + F, and we know from statement one that E + F = A + B = C + D. Therefore:
D - B = E + F = A + B = C + D
Because the "D - B" is the oddball equation, we should work towards figuring something out about that. So, among the other equations, let's look at the equations that have "B" and "D" in them: A + B = C + D
Because A + B = C + D, if we subtract either from the other we will have zero. (When you subtract something from itself you have zero, eg: 5 - 5 = 0). Therefore:
(A + B) - (C + D) = 0
A + B - C - D = 0
A - C = D - B
We have successfully derived D - B, and we have learned that it is equal to A - C. But, among other things, we also know that D - B is equal to A + B. (We are focussing on A + B because, among the other equations, this is the equation that has the "B" term). Therefore:
A - C = D - B = A + B
Therefore:
A - C = A + B (if both A - C and A + B equal to D - B, then A - C and A + B are necessarily equal to each other).
Because A - C equals A + B, again, if we subtract one expression from the other we will have zero:
A + B - (A - C) = 0
A + B - A + C = 0
C + B = 0
The statements, while independently insufficient, are sufficient in combination. Choice C.
