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A certain manufacturer produces an engine lift with three pulleys and
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12 Feb 2021, 06:37
12 Feb 2021, 06:37
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A certain manufacturer produces an engine lift with three pulleys and seven levers. If each box contains eight pulleys and the manufacturer is starting with unopened boxes and does not want to have a partial box of pulleys remaining, which of the following could not be the number of levers used in the manufacturing job?
A 56
B 84
C 112
D 168
E 196
F 224
Kudos for the right answer and explanation
A 56
B 84
C 112
D 168
E 196
F 224
Kudos for the right answer and explanation
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A certain manufacturer produces an engine lift with three pulleys and
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12 Feb 2021, 12:42
12 Feb 2021, 12:42
Levers be L and Pulleys be P
1 Lift = 7L + 3P
1 Box = 8P
Now, the manufacturer does not want to have a partial box of pulleys remaining
which means that the number of pulleys can only be a multiple of 8 and at-least 3 boxes
Why?
Lets see, If we have 1 box then we can make 2 Lifts out of it, leaving 2 Pulleys extra, which will violate the given condition
i.e. 3 + 3 + 2
Also, The levers are always a multiple of 7
Conclusion: Divide the number of Levers by 7, if the remainder is divisible by 8, then we can have those number of Levers without violating the condition
A. \(\frac{56}{7}\) = 8; divisible by 8
B. \(\frac{84}{7}\) = 12; not divisible by 8
C. \(\frac{112}{7}\) = 16; divisible by 8
D. \(\frac{168}{7}\) = 24; divisible by 8
E. \(\frac{196}{7}\) = 28; not divisible by 8
F. \(\frac{224}{7}\) = 32; divisible by 8
Hence, option B and E
1 Lift = 7L + 3P
1 Box = 8P
Now, the manufacturer does not want to have a partial box of pulleys remaining
which means that the number of pulleys can only be a multiple of 8 and at-least 3 boxes
Why?
Lets see, If we have 1 box then we can make 2 Lifts out of it, leaving 2 Pulleys extra, which will violate the given condition
i.e. 3 + 3 + 2
Also, The levers are always a multiple of 7
Conclusion: Divide the number of Levers by 7, if the remainder is divisible by 8, then we can have those number of Levers without violating the condition
A. \(\frac{56}{7}\) = 8; divisible by 8
B. \(\frac{84}{7}\) = 12; not divisible by 8
C. \(\frac{112}{7}\) = 16; divisible by 8
D. \(\frac{168}{7}\) = 24; divisible by 8
E. \(\frac{196}{7}\) = 28; not divisible by 8
F. \(\frac{224}{7}\) = 32; divisible by 8
Hence, option B and E
gmatclubot
A certain manufacturer produces an engine lift with three pulleys and [#permalink]
12 Feb 2021, 12:42
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