-gre.qu.10 quantity on 2 means

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karush
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GRE quantitative comparison question 5: arithmetic mean of 100 measurements is 23, arithmetic mean of 50 additional measurements is 27; Quantity A is the mean of the 150 measurements, Quantity B is 25; answer choices A to D.

posted a screenshot because I think the wording is awkward and I think it is easy to setup it up wrong

so to begin with we have a and b being list of added numbers
$\dfrac{a}{100}=23$ and $\dfrac{a+b}{150}=27$

so now what?
 
we have sum of 100 measurements = 2300

sum of 50 additional measurements = 27 * 50 = 1350

total sum = 2300 + 1350 = 2650

so arithmetic mean = $\frac{3650}{150} = \frac{73}{3}$

so B is bigger

for a short cut 25 is mean of 23 and 27

more elements(100) have mean 23 and less (50) elements have 27 so arithmetic mean < 25
 
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mahalo i probably would of missed it