M40-94

Question

According to the new estimates, the number of stars in the Milky Way galaxy has increased from 124 billion to 415 billion, while the number of stars in the Andromeda galaxy has doubled. With these updated figures, the number of stars in the Milky Way is still only 42% of the number of stars in the Andromeda galaxy. Prior to the new estimates, approximately how many times more stars did the Andromeda galaxy have compared to the Milky Way galaxy?

A. 2
B. 4
C. 5
D. 8
E. 16

Show Answer

Official Answer

B

A. 2
B. 4
C. 5
D. 8
E. 16

Bunuel · Answer

Official Solution:

According to the new estimates, the number of stars in the Milky Way galaxy has increased from 124 billion to 415 billion, while the number of stars in the Andromeda galaxy has doubled. With these updated figures, the number of stars in the Milky Way is still only 42% of the number of stars in the Andromeda galaxy. Prior to the new estimates, approximately how many times more stars did the Andromeda galaxy have compared to the Milky Way galaxy?

A. 2
B. 4
C. 5
D. 8
E. 16

Show Answer

Official Answer

B

A. 2
B. 4
C. 5
D. 8
E. 16

We are tasked with approximating, so let's proceed with that approach.
 
Consider using 400 billion instead of 415 billion, and 40% instead of 42%. This gives us: 400 billion = 0.4*(Andromeda's new estimate). Notice that the first approximation decreases the new estimate for the Andromeda galaxy, while the second approximation increases it. Therefore, these two approximations roughly balance each other out. Thus, from 400 billion = 0.4*(Andromeda's new estimate), we determine that Andromeda's new estimate is 1,000 billion. Given that the new estimates have doubled the numbers for the Andromeda galaxy, its old number was 500 billion.
 
Consequently, prior to the new estimates, the Andromeda galaxy had  \frac{500}{124} \approx 4  times more stars than the Milky Way galaxy.

Answer: B

RicharddelPino · Answer

415=0,42*2X

X=415/0,84 ...if 415/1 is 415...415/0,84 would be more than that, and close to 500...

So, compared with 124... 2 times is too low, 5 times is too high....124 x 4 ≈ 500

Answer B= 4

magnamut · Answer

Hi  Bunuel  , could you please explain why we took 500/124 and not (500-124)/124? Also, could you elaborate on when we should be taking a/b vs a-b/b

Thank you

Bunuel · Answer

When you ask “how many times more stars did Andromeda have”, you compare the full Andromeda amount to the Milky Way amount. That is why the fraction is Andromeda_old divided by MilkyWay_old, which is 500/124.

If you do (500 - 124)/124, that gives the percent increase, not the number of times larger.

popcorn98 · Answer

This is a great question that’s helpful for learning and I did not quite understand the solution. If the question is asking for "how many times more" shouldn't the answer be 3 times? since 4 times the number of stars in milky way is that of andromeda so it just 33 times "more"?

Bunuel · Answer

Here is my post from another topic addressing this issue:

Agree that it's confusing but check below:

Merriam Webster's  Dictionary of English Usage :

The argument in this case is that times more (or times larger, times stronger, times brighter, etc.) is ambiguous, so that "He has five times more money than you" can be misunderstood as meaning "He has six times as much money as you." It is, in fact, possible to misunderstand times more in this way, but it takes a good deal of effort. If you have $100, five times that is $500, which means that "five times more than $100" can mean (the commentators claim) "$500 more than $100," which equals "$600," which equals "six times as much as $100." The commentators regard this as a serious ambiguity, and they advise you to avoid it by always saying "times as much" instead of "times more." Here again, it seems that they are paying homage to mathematics at the expense of language. The fact is that "five times more" and "five times as much" are idiomatic phrases which have - and are understood to have - exactly the same meaning.

The "ambiguity" of times more is imaginary: in the world of actual speech and writing, the meaning of times more is clear and unequivocal. It is an idiom that has existed in our language for more than four centuries, and there is no real reason to avoid its use.

The "ambiguity" of  times more  is imaginary : in the world of actual speech and writing, the meaning of  times more  is clear and unequivocal. It is an idiom that has existed in our language for more than four centuries, and there is no real reason to avoid its use.

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