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26 Mar 2018, 00:34
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
84% (01:48) correct
16%
(02:08)
wrong
based on 70
sessions
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Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, weighing an average of 15.25 kilograms, are shipped to the same location. What is the average weight, in kilograms, of the 20 boxes shipped to the location?
(A) 13
(B) 13.25
(C) 14
(D) 14.25
(E) 15
(A) 13
(B) 13.25
(C) 14
(D) 14.25
(E) 15
26 Mar 2018, 01:12
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Bunuel
We know 1.25 = \(\frac{5}{4}\). Hence \(\frac{5}{4}*8 = 10\) and \(\frac{5}{4}*12 = 15\)
Average = \(\frac{(14 - 1.25)*8 + (14 + 1.25)*12}{20} = \frac{14*20 - 10 + 15}{20} = 14 + \frac{5}{20} = 14.25\)
Therefore, the average of 20 boxes shipped is 14.25(Option D)
P.S In order to solve problems such as these, it is important to identify a pattern to reduce unnecessary calculations.
26 Mar 2018, 01:46
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pushpitkc
Great way to simplify this pushpitkc,
Another way to look at it is -
\(12.75 = 12 \frac{3}{4} improper fraction ... (12*4 +3 )/4 = 51/4\)
\(15.25 = 15 \frac{1}{4} = 61/4\)
Numerator is : \(\frac{51}{4}* 8 + \frac{61}{4}*3 = 50*2 + 60*3 + 2 + 3 = 285\)
On dividing by 20 .. which is 10 * 2
Divide by 2 first and move decimals point one to the left.
Hence \(285 / 2 = 142.5 / 10 = 14.25\)
Hence Option (D) is correct.
Always try to simplify the calculations as much as possible...
Best,
Gladi
