GMAT Practice Question: Terry needs to purchase some pipe for a plumbing job that requires pipes with lengths of 1 ft 4...
Question
Terry needs to purchase some pipe for a plumbing job that requires pipes with lengths of 1 ft 4 in, 2 ft 8 in, 3 ft 4 in, 3 ft 8 in, 4 ft 8 in, 5 ft 8 in, and 9 ft 4 in . The store from which Terry will purchase the pipe sells pipe only in 10-ft lengths. If each 10-ft length can be cut into shorter pieces, what is the minimum number of 10-ft pipe lengths that Terry needs to purchase for the plumbing job? (Note: 1 ft=12 in )
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Topics: conversions, word problems
Solution
Step 1
We convert each of the listed required lengths from the question (\textbf{\text{"1 ft 4 in"}}, \textbf{\text{"2 ft 8 in"}}, \textbf{\text{"3 ft 4 in"}}, \textbf{\text{"3 ft 8 in"}}, \textbf{\text{"4 ft 8 in"}}, \textbf{\text{"5 ft 8 in"}}, \textbf{\text{"9 ft 4 in"}}) into inches using the relation 1\text{ ft}=12\text{ in}.
1\text{ ft }4\text{ in} = 1 \times 12 + 4 = 16\text{ in} 2\text{ ft }8\text{ in} = 2 \times 12 + 8 = 32\text{ in} 3\text{ ft }4\text{ in} = 3 \times 12 + 4 = 40\text{ in} 3\text{ ft }8\text{ in} = 3 \times 12 + 8 = 44\text{ in} 4\text{ ft }8\text{ in} = 4 \times 12 + 8 = 56\text{ in} 5\text{ ft }8\text{ in} = 5 \times 12 + 8 = 68\text{ in} 9\text{ ft }4\text{ in} = 9 \times 12 + 4 = 112\text{ in}
Step 2
We sum all these lengths in inches to find the total required pipe length.
16 + 32 + 40 + 44 + 56 + 68 + 112 = 368\text{ in}
Step 3
We convert the available length sold by the store (\textbf{\text{"10-ft"}}) into inches using 1\text{ ft}=12\text{ in}.
10\text{ ft} = 10 \times 12 = 120\text{ in}
Step 4
We divide the total required length by the available length per pipe to see how many full 10-ft pipes we can use, and to find any leftover.
\frac{368}{120} = \frac{240}{120} + \frac{120}{120} + \frac{8}{120} = 2 + 1 + \frac{8}{120} = 3 \text{ remainder } 8
Step 5
Since there is a remainder of 8 inches after using 3 full pipes, we need one more 10-ft pipe, for a total of 4 pipes.
3 + 1 = 4
Answer
4
