mnjoosub wrote:Together, Andrea and Brian weigh p pounds; Brian weighs 10 pounds more than Andrea. Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea. In terms of p, What is Cubby's weight in pounds?
(A) (p/2)-10
(b) (3p/4)-5
(c) (3p/2)-5
(d) (5p/4)-10
(e) (5p)-5
The OA is B.
I can get the answer by plugging, but I would like to have the mathematical explanation.
Thanks.
The problem seems to be with interpretation of the information, in particular the phrase:
Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea.
Most people are interpreting this as "the sum of Brian and Andrea's dog is p/4 pounds more than Andrea".
However, when I first read it, I interpreted it as "the dog belonging to Brian and Andrea weighs p/4 pounds more than Andrea does".
I'm 100% certain that my interpretation is correct (and not just by reverse engineering the question from the answer).
We have to remember that math questions will be gramatically correct. Let's look at the verb in the sentence.
"Weighs" is a singular verb. In order for the first interpretation to be right, the sentence would have had to read:
Brian and Andrea's dog, Cubby, WEIGH p/4 pounds more than Andrea
since "Brian and Cubby" form a plural noun and require a plural verb.
So, now that we know how to interpret the question, our equations are:
A + B = P
B = A + 10
C = A + P/4
We want to solve for C, so let's get rid of A and B by getting A in terms of P and then subbing into the Cubby equation:
A + 10 = B
A + A + 10 = P
2A = P - 10
A = P/2 - 5
C = P/2 - 5 + P/4
C = (2P/4) + P/4 - 5
C = (2P + P)/4 - 5
C = 3P/4 - 5
Choose (b).