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18 May 2017, 00:16
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A
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:
83% (01:22) correct
17%
(01:44)
wrong
based on 233
sessions
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In a certain first grade classroom, the average height is x inches for the 5 girls and y inches for the 8 boys. What is the average height for the 13 students in the classroom combined?
(1) 15x + 24y = 1755
(2) x < 40
(1) 15x + 24y = 1755
(2) x < 40
18 May 2017, 08:29
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Bunuel
Target question: What is the average height for the 13 students in the classroom combined?
Given: The average height is x inches for the 5 girls and y inches for the 8 boys.
This is a good candidate for rephrasing the target question.
We can think of this is a weighted averages question. So, we'll apply the following formula:
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
So, Average weight of classroom = (5/13)(x) + (8/13)(y)
= 5x/13 + 8y/13
= (5x + 8y)/13
So, we can REPHRASE the target question...
REPHRASED target question: What is the value of (5x + 8y)/13?
Statement 1: 15x + 24y = 1755
Notice that we have (5x + 8y) "hiding" in the above equation.
Take 15x + 24y = 1755 and factor the left side to get: 3(5x + 8y) = 1755
Divide both sides by 3 to get: 5x + 8y = 585
So, (5x + 8y)/13 = (585)/13 = 45
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: x < 40
No information about y, which means there's no way to determine the value of (5x + 8y)/13
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer:
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22 Sep 2020, 21:40
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what are good questions similar to this one? I decided to start by prime factoring for some reason.
