Question

*Logic* While driving from city A to B, a car got 22 MPG and while returning on the same road, it got 30 MPG.

Answer 1

Which quantity is greater?

A: Car's average MPG for both trips MPG
B: 26

Answer 2

The answer is 26...But I do not understand.

Answer 3

Like, why are they not equal?

Answer 4

(22+30)/2 MPG = 26 MPG

Answer 5

They just want you to get the average of going and coming back

Answer 6

Yep! The GRE book says they are not equal though, that quantity A comes out to be about 25.38.

Answer 7

They say the average will be weighted more to the side of 22 for some reason.

Answer 8

They say A--> B is 22*30 = 660
B--> A is 30 *22 = 660
Total is x * 52 = 1320

x is 25.38

Answer 9

I don't understand, what is the question?

Answer 10

While driving from city A to B, a car got 22 MPG and while returning on the same road, it got 30 MPG.
Which quantity is greater?

A: Car's average MPG for both trips MPG
B: 26

That is literally it.

Answer 11

I was thinking of it as Astro was,
a simple arithmetic mean of the two rates...

but I guess they're doing something else here.. hmm

Answer 12

I have spent awhile trying to figure their solution out but can't. I think it is just poorly worded. But that's what the question and their solution says. I would never get that right on a test.

Answer 13

@Astrophysics do you think it is something we are missing or is it just worded poorly? This is GRE review book.

Answer 14

Hey, sorry I'm not really sure :\

Answer 15

It's all good! Thanks for trying!

Answer 16

They have some sort of ratio going on, but I don't see the logic

Answer 17

I mean, if A--->B was longer than b-->A, it would make sense.

Answer 18

@ganeshie8

Answer 19

the average gas mileage is not the average of the gas mileages

Answer 20

That short and supposingly simple statement just blew me away.

Answer 21

exactly the same as "the average speed is not the average of the speeds"
an example with numbers will make it clear

Answer 22

lets say the distance from A to B is 100 miles (not that it makes any difference)

Answer 23

I'm following. Thanks.

Answer 24

do you still need help

Answer 25

if they got 22 miles per gallon then they used up how many gallons?

Answer 26

Like 4.5, right?

Answer 27

oh ok if you still don't get it just tag me

Answer 28

just as a fraction, not as a decimal it would be \[\frac{100}{22}\]

Answer 29

Right.

Answer 30

Ok, so if they got 30 MPG it would be 100/30

Answer 31

which is not 4.5, but whatever
now coming back, they use up \[\frac{100}{30}\]

Answer 32

how far have they gone?
200
how much did they use? \[\frac{100}{22}+\frac{100}{30}\]

Answer 33

i realize you can reduce these fractions, but no need
so what is there average miles per gallon? \[\frac{200}{\frac{100}{22}+\frac{100}{30}}\]

Answer 34

25.38

Answer 35

That makes so much more sense.

Answer 36

that is the total distance 200 divided by the total amount used

Answer 37

Thank you SO MUCH!

Answer 38

now if you want to do it with D instead of 100, you get the same answer

Answer 39

wanna try it?

Answer 40

Nice! I'm going to say I didn't get it because it wasn't using a metric system yeah! :)

Answer 41

yw btw
wanna try with D?

Answer 42

Well, if we used D, it would give the same answer. I mean, it is just sub for miles.

Answer 43

\[\frac{2D}{\frac{D}{22}+\frac{D}{30}}\] is the start
then a bit of algebra, the D will go away

Answer 44

Just multiply by inverse, right?

Answer 45

So many viewing this! We are famous.

Answer 46

add in the denominator might be easiest

Answer 47

\[\frac{2D}{\frac{22D+30D}{22\times 30}}\] is a start

Answer 48

btw this has a name, think it might be "harmonic mean" but i could be wrong

Answer 49

lol it would help if I used the equation feature.

Answer 50

yeah it is
replace D by 1 you get \[\frac{2}{\frac{1}{22}+\frac{1}{30}}\] pretty sure this is harmonic mean
google

Answer 51

=25.38. Thanks.

Answer 52

https://en.wikipedia.org/wiki/Harmonic_mean

Answer 53

yup harmonic mean it is

Answer 54

That's neat we ran into this in this supposingly simple problem. Thanks of all your help. I learned a lot.

Answer 55

:)

Answer 56

oh also improtant inequatly
arithmetic mean > geometric mean > harmonic mean
by > it is really \(\geq\)