Q16 - Comets do not give

[ocho34]

Just overall confused when I first saw the problem. Am I interpreting the stimulus correctly?

new estimate of halley's comet by the satellite probe show that:
1. brightness is now x (I am thinking of brightness in terms of x rather than x/60 because it is easier to understand that way).
2. previous estimate of the brightness is shown to be 60 times greater: 60(x)

Since the previous estimates of brightness is shown to be much greater, the previous estimates of the mass should have also been greater (greater mass, more light).

Does this inference translate into answer choice (B) that the previous est. of mass was "too low"?

[ManhattanPrepLSAT1]

This question is a classic. Thanks for the oldie!

I like your thought process but there was a simple mix up. It's not that there are old and new estimates of the brightness of Halley's comet. But rather a new understanding of the amount of light that can be reflected from the COMPOSITION of the material from which Halley's comet is made.

That means that before, they thought that the stuff that Halley's comet was made from reflected let's say x amount of light for every ton of mass. Now they know that the stuff reflects a 60 times less light for every ton of mass. So to reflect the same amount of light Halley's comet would have to be 60 times more massive than they thought.

Let's put numbers on this. Suppose x=1. So, for every unit of light reflected under the old calculation Halley's comet would have one ton of mass. If there were 50 units of light reflected then that meant that Halley's comet had 50 tons of mass. Under the new system for every unit of light reflected Halley's comet should have 60 tons of mass. The amount of light being reflected hasn't changed. So, if 50 units of light are being reflected then that means Halley's comet must be 3000 tons.

This translates into answer choice (B) that the previous estimates were way too low.

[backupbecool]

I understand why B is the answer, but for what reason would you eliminate answer choice D?

[ManhattanPrepLSAT1]

I think a read of answer choice (A) will help us with eliminating answer choice (D). In that sense the test-writer was kind enough to include answer choice (A).

(A) says that some comets are composed of material that reflect 60 times more light than the material of which Halley's comet is composed. Unfortunately, we do not know the composition of any other comet.
(D) says that reflective properties of the material of which comets are composed of varies widely from one comet to the next. However, we do not know the composition of any other comet besides Halley's comet. So, while the reflective property of Halley's comet was way off, that does not mean that there is a large variance in the reflective properties of comets in general. Maybe it's just the case that all comets have been revised with respect to their reflective properties.

Does that help clear things up?

[backupbecool]

Ah tricky tricky. Yes that helps. I think I also misunderstood what the correct answer C stated...because initially I think I just did bad math thinking that if Halley's comet reflects 60 times less light per unit of mass than had been previously thought, then that would mean the weighed less as well, but the inverse is actually true. Thank you!

[gmatalongthewatchtower]

Question -

The question states that initially scientists thought that comets reflect light relative to their mass. However, the new satellite probe has determined that Halley's comet reflects 60 times less light than had been previously thought.

One of the interpretations is that :

Initially -

Mass | Brightness

1 unit | 1 unit (I am assuming 1:1 ratio)

Now

>1unit | 0.6 unit

Hence, the mass is more than what was thought previously.

However, another interpretation could be that :

1unit | 0.6 unit (i.e. the satellite probe helped to improve the measurement of the amount of light. Essentially, previously they were using a bad measuring device, but now they have satellite probes, which are better than the previous instruments.

In the second case, B) won't be correct.

Can anyone please help me?

Thanks
Voodoo

[cyt5015]

Question -

The question states that initially scientists thought that comets reflect light relative to their mass. However, the new satellite probe has determined that Halley's comet reflects 60 times less light than had been previously thought.

One of the interpretations is that :

Initially -

Mass | Brightness

1 unit | 1 unit (I am assuming 1:1 ratio)

Now

>1unit | 0.6 unit

Hence, the mass is more than what was thought previously.

However, another interpretation could be that :

1unit | 0.6 unit (i.e. the satellite probe helped to improve the measurement of the amount of light. Essentially, previously they were using a bad measuring device, but now they have satellite probes, which are better than the previous instruments.

In the second case, B) won't be correct.

Can anyone please help me?

Thanks
Voodoo

From the premise, we know that scientists estimate the mass of comets by their brightness, therefore, we knew the brightness first, and then use it to calculate the mass. Here is equation we can use to express this calculation: Mass*x=Brightness, x is the brightness per mass.
In this equation, we know brightness and x, but mass is unknown.Let's assume Halley's Brightness=10, x=1(like you use 1:1 ratio), original Mass equals 10.
According to new data, the material of Halley's comet reflects 60 times less light per unit of mass than previously thought.
Now:x no longer equals 1, but becomes 60 times less (1/60),
then we get Mass=60*Brightness=60*10=600. You can see that the actual mass is much higher than they previously thought.

[tommywallach]

Yep! You nailed it, Cyt!

-t

[mharr]

I have come to the conclusion that I am retarded because I still do not understand why answer choice B is correct. Can someone provide a different explanation, please?

This is my understanding; a comet's mass is based on how bright it is. So, if a comet's brightness is at a level of 10, for example, then the mass is 10. The light reflected off Halley's comet is 60 times less than previously thought. So now brightness is 0.60 in stead of 10 which means the mass is 0.60 instead of 10. That would make the initial mass number (10) bigger than the new number. What am I missing here? This question is really frustrating me.

[tommywallach]

Hey M,

Matt's explanation is as clear as it gets, unfortunately (it's a confusing prompt!). But look at your first sentence: Is it really possible for an object's mass to be based on how bright it is?

-t

P.S. If it's really killing you, remember that it's only one question!

[laura.bach]

I too had a hard time understanding this problem in terms of numbers, but here's a way of thinking about the problem that helped me (although it's kind of silly).

Let's say the majority of comets are made of glass (a highly reflective surface).

So one scientist sees Halley's comet and notices "This comet has a brightness of 1. Because of this brightness, I calculate it has a mass of 1." She makes an assumption that Halley's comet is made of glass, and if that were true, then her estimate of the mass would be accurate.

But then this probe goes to Halley's comet and finds that the comet is actually made of cardboard (a highly non-reflective surface).

The brightness is still 1 -- the scientist observed correctly. But, in order to achieve this brightness with a non-reflective material, there must be much more of the material. For a comet of glass, there would only need to be 1 unit of mass to reflect enough light to achieve a brightness of 1, but for a comet of cardboard, there needs to be 100 units of mass to reflect enough light to have a brightness of 1.

-----

This is kind of a ridiculous example, but for some reason it helped make (B) click and explained why (C) is wrong (that the total amount of light doesn't change because we can observe the light independent of the composition of the comet).

[pa.perezelias]

I also got this problem wrong but as I was selecting my answer I thought about B and thought that I was interpreting the problem wrong. I ignored my intuition and picked the wrong answer anyways. Oh well.

After reading these explanations, I tried to come up with my own that may/may not be able to explain the question. Basically, please let me know if this explanation is wrong or if it helps clarify.

So say the brightness scientists measured = 1

Previously, the mass to light reflected ration was proportional so say that the light reflected was 1, therefore the mass is 1 (1*1=1)

Now, however, we discover that the light reflected is actually .60 less of the original. Remember, the brightness measured is still 1 so you will have something like this:

x * .60 = 1
x = 1.7

The mass x (1.7) is greater than the mass previously thought (1). Therefore, the mass previously thought is too low.

[donghai819]

It is something like:

previously thought: Constant(lightness/mass) * X (mass) = L (lightness) ... (mass and lightness could swap)

Revised one: 1/60 Constant * (?times)X(Mass) = same amount of L

So, the result is kept; one variable becomes much smaller; therefore, the other variable has to become much larger.

One takeaway is: when we see something like "the more A, the more B," we can tell that the author assumes a constant.

If one is interested in another example of "math" question, please see 7-4-13.

[keonheecho]

How do we know that the original estimate of the brightness was right?