Data Sufficiency Multiple Variables

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.

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

USING 2)

C+D=D-B

-----> C+B=0

sO THE VALUE OF C+B =0.

Option C makes a logical answer.

Testluv wrote:

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.

Thank you very much. That was very helpful. Got it!

No problem!

You can get complex algebra problems that test your ability to manipulate expressions. However, gmatmachoman's approach was actually the best for this particular problem:

Because D - B = E + F, and because E + F = C + D, we can say:

C + D = D - B

C + B = D - D

C + B = 0

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

C is the answer,

1) A+B=C+D=E+F INSUFF
2) E+F=D-B INSUFF

since E+F = C+D then substitute C+D for E+F

C+D=D-B
C+B =D-D
C+B = 0