Hi, there. I'm happy to help with this.
Prompt:
The construction of a garage will increase the value of a house in $20,000. What is the ratio between the cost of construction of the garage and the price of the house after the construction?
Let's introduce the variables:
A = price of house before garage
B = price of house with garage
C = cost of the garage
From the prompt, we know A + 20000 = B.
The prompt asks for C/B
Statement #1:
The cost of construction of the garage is $10,000
This tells us C = 10000. Now, we know C, but we still have no idea about B, so we can't answer the prompt question. Statement #1, by itself, is
insufficient.
Statement #2:
The ratio between the price of the house before the construction of the garage is 5/4
There's something funky about the wording here. A ratio is specified, but we are given only one of the two terms of the ratio. I will assume what they mean is --- the ratio of house with garage to house before garage is 5/4. In our language:
B/A = 5/4 -----> B = (5/4)A
Combine that with the information in the prompt:
A + 20000 = B ------> A + 20000 = (5/4)A ----> 20000 = (1/4)*A
A = 80000
B = 100000
This statement allows us to calculate the values of A and B. Unfortunately, we don't know C. (This is an example of a GMAT DS questions where we have to be very careful not to carry over information from Statement #1 when we are trying to consider Statement #2 on its own.) Statement #2, by itself, is
insufficient.
Combined Statements #1 & #2
From #1, we get C = 10000
From #2, we get B = 100000
Therefore, the ratio is 100000/10000 = 10.
Together, the statements are
sufficient.
Answer =
C
Does that make sense? Please let me know if you have any additional questions.
Mike
