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What was the maximum temperature in city A on Saturday

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What was the maximum temperature in city A on Saturday

by BTGmoderatorDC » Mon Mar 12, 2018 9:28 pm
What was the maximum temperature in city A on Saturday, May 14?

(1) The maximum temperature on Saturday, May 14, was 5° greater than the maximum temperature in city A on Sunday, May 8.

(2) The average (arithmetic mean) of the maximum daily temperatures in city A from Sunday, May 8, to Saturday, May 14, was 72°, which was 2° less than the average (arithmetic mean) of the maximum daily temperatures in city A, from Monday, May 9, to Friday, May 13.

Is there a sufficient statement?

OA C
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by s_sandoval » Tue Mar 13, 2018 6:33 pm
Why isn't statement 2 sufficient? It's kind of a monster.
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by ErikaPrepScholar » Wed Mar 14, 2018 5:46 am
Let's break down what each statement tells us. The statements deal with a range of dates from Sunday, May 8th to Saturday May 14th. Since they are all different days of the week, we'll ignore the dates

Statement 1:
The max temp on Sat was 5 degrees higher than the max temp on Sun, or Sat = Sun + 5. We don't know the max temp on Sun, so this doesn't tell us much on its own.

Statement 2:
$$\frac{Sun+Mon+Tues+Wed+Thurs+Fri+Sat}{7}=72$$ $$\frac{Mon+Tues+Wed+Thurs+Fri}{5}=74$$
We can use these two averages as a system of equations to isolate Sun + Sat: $$Mon+Tues+Wed+Thurs+Fri=370$$ $$\frac{Sun+370+Sat}{7}=72$$ $$Sun+370+Sat=504$$ $$Sun+Sat=134$$
So the temperatures on Sun and Sat added together give 134 degrees. However, we don't know how the temp on Sat relates to the temp on Sun (higher? lower? the same?), so this is insufficient on its own.

Both:
We know that Sat = Sun + 5 and Sat + Sun = 134 - we have two variables and two equations, so we should be able to solve, making the statements combined sufficient.

If we want to check, we can work as follows:
Sat = Sun + 5 --> Sun = Sat - 5
(Plugging Sat - 5 in for Sun in the second equation)
Sat + Sat - 5 = 134
2Sat =139
Sat = 69.5 degrees
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