sud21 wrote:A, B, C and D play cards, the total score of A, B, C and D is 400, is B>C?
1). A+B=100+C+D
2). A+C=80+B+D
In other words, "
If A+B+C+D=400, is B>C?"
(Aside: We can also reword the target question as "
Is B-C > 0?")
Statement 1:
A+B=100+C+D
Rewrite as:
A+B-C-D=100
Add this to:
A+B+C+D=400 to get:
2A+2B=500
Divide both sides by 2 to get: A+B=250, which means that C+D=150
There are lots of different values of A, B, C, and D that satisfy this.
case a: A=100, B=150, C=100, D=50 --> B
is greater than C
case b: A=200, B=50, C=100, D=50 --> B
is not greater than C
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2:
A+C=80+B+D
Rewrite as:
A-B+C-D=80
Add this to:
A+B+C+D=400 to get:
2A+2C=480
Divide both sides by 2 to get: A+C=240, which means that B+D=160
There are lots of different values of A, B, C, and D that satisfy this.
case a: A=100, B=150, C=140, D=10 --> B
is greater than C
case b: A=40, B=150, C=200, D=10 --> B
is not greater than C
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 & 2
Given:
A+B-C-D=100
A-B+C-D=80
Subtract the second equation from the first equations to get: 2B-2C=20
Divide both sides by 2 to get B-C=10
If B-C=10, then B
must be greater than C (since B-C >0)
As such, statements 1&2 combined are SUFFICIENT and the answer is
C
Cheers,
Brent
