Question: Copper pipe costs x cents per foot in 8-foot lengths, and x + y cents per foot in shorter lengths. What is the lowest possible price, in cents, of 51 feet of pipe in terms of x and y?
- 51(x + y)
- 51x
- 48x + 3y
- 48(x + y)
- 51x + 3y
“Copper pipe costs x cents per foot in 8-foot lengths, and x + y cents per foot in shorter lengths.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
There is only one approach to solve the problem
Given in the question that a copper pipe costs x cents per foot in 8-foot lengths, and x + y cents per foot in shorter lengths. It is asked to calculate the lowest possible price, in cents, of
51 feet of pipe in terms of x and y.
It is said in the problem that if the pipe is in the lengths of 8 feet then each foot will cost x cents. If the length of the given pipe is less than 8 feet then each foot will cost (x+y) cents.
We have to find the cost of 51 feet of pipe.
Firstly we’ll see how many numbers of 8 feet pipes are possible
Dividing the length by 8 we get,
51 / 8 = 6.375
The closest integer number less than equal to 6.375 is 6
Therefore we’ll buy a total of 6 -> 8 feet pipes.
Total length will be = 8*6 = 48
Total price will be = 48*x = 48x
Now remaining length 51 - 48 = 3
Now the remaining 3 feet is less than 8 feet so we have to pay (x+y) per feet.
Price for the remaining 3 feet = 3(x+y)
Total price for the 51 feet pipe = price1 + price2
= 48x + 3(x+y)
= 51x + 3y
Correct Answer: C
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