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BMAT explanation of problem

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Reply 40
Original post by sherazhar
Thank you so much dude! i know it's bad 2 ask u again but can u pls explain me q 20 same paper!
are u sitting for BMAT this year?


Is it the one with the three triangles on top of each other? If so, there are several ways of doing it. I'll however, outline the quickest one.

For starters, you have to be familiar with what is meant by 'similar triangles' as it is impossible to solve it otherwise. The term means that the sides of all three triangles follow the same ratio.

The first step is calculating the length of the hypotenuse, which is the sqrt of 10 (hopeully you can see this, ask otherwise.)

Now, since the triangles are similar, it means that the length of the other non-hypotenuse side is one third or that, or sqrt(10)/3.

Now, since the hypotenuse of one is the bigger non-hypotenuse side of the one above and they are all similar triangles, it means that the growth in side and consequently the change in area follow the same patterns. Hence, we can deduce the area of the largest one based on the areas of the two smaller ones.

The area of the first triangle is 3/2 and the area of the second one is (sqrt(10)*sqrt(10)/3)/2=10/6=5/3. Hence, the ratio between the areas is (5/3)/(3/2)=10/9, or you can say that the area of the second triangle is 10/9 times bigger than the first.

Consequently, you can deduce that the area of the third triangle is 10/9 times bigger than the second one, or, mathematically: (10/9)*(5/3)=50/27.

This seems like a long method but really, if you write it down on paper it's not at all much.

What you could also have done is to continue on with the first part, i.e. to find the hypotenuse of the second triangle, which would be the long non-hypotenuse side of the third one, divide that one by 3 in order to get the other non-hypotenuse side and then calculate the area directly.

A third method is very similar to the second one, with the difference being that you calculate the hypotenuse of the second directly, based on the hypotenuse of the first and its relation to one of the other sides.

And yes, I'm sitting the BMAT this year.
Reply 41
wow you have such a brain! how come? thanks btw :smile:
Reply 42
Original post by sherazhar
wow you have such a brain! how come? thanks btw :smile:


Haha, no problem! Feel free to PM me if you have more questions, this helps me revise as well!
Reply 43
Original post by Doppel
In order to fit the criteria, we have two possible scenarios:

1) YRYRYR
2) RYRYRY

Let's work with the first scenario. We've got 3 bulbs to choose from when planting the first and second bulb (since it has to be the alternating colour), 2 to choose from when planting the third and fourth bulb and then only one choice when planting the last two, so we can ignore those.

Mathematically, this can be written as: 3*3*2*2=36. However, as I said in the beginning, two scenarios fit, where we start with the other colour instead. Hence, the number of possibilites doubles, yielding 72.

Now, in total, there are 6!=720 ways of arranging the bulbs. 72/720=1/10.


I get everything in bold, but I don't understand the first part. What do you mean when you say there are 3 bulbs to choose from when planting the first and second bulb? Sorry to be a pain!

Original post by sherazhar
where do you find the mark scheme for 2008 paper?


http://www.admissionstests.cambridgeassessment.org.uk/adt/digitalAssets/109681_BMAT_Past_Paper_Section_1_answer_key_and_score_conversion.pdf and you can find a load of past papers/ mark schemes on here: http://www.admissionstests.cambridgeassessment.org.uk/adt/bmat/Test+Preparation
Reply 44
Original post by salsharifi
I get everything in bold, but I don't understand the first part. What do you mean when you say there are 3 bulbs to choose from when planting the first and second bulb? Sorry to be a pain!



http://www.admissionstests.cambridgeassessment.org.uk/adt/digitalAssets/109681_BMAT_Past_Paper_Section_1_answer_key_and_score_conversion.pdf and you can find a load of past papers/ mark schemes on here: http://www.admissionstests.cambridgeassessment.org.uk/adt/bmat/Test+Preparation


It's okay, don't worry. If you're having problems with these types of questions I recommend revising 'permutations'. The question is asking for the probability that the bulbs alternate along the whole row. In other words, they are asking for the probability that we get the order YRYRYR or RYRYRY (both show alternating colours).

Imagine you have 6 bulbs in front of you, 3 red and 3 yellow ones. Now, you want to plant them in an alternating way. This means that you have 3 bulbs to choose from when planting the first one (as you have to start with ONE of the colours). When planting the next one, you still have 3 bulbs to choose one as you are choosing one of the OTHER colour. Afterwards, you have planted one of each, so you have 2 of each left. Is it clearer now?
(edited 11 years ago)
Reply 45
Original post by Doppel
It's okay, don't worry. If you're having problems with these types of questions I recommend revising 'permutations'. The question is asking for the probability that the bulbs alternate along the whole row. In other words, they are asking for the probability that we get the order YRYRYR or RYRYRY (both show alternating colours).

Imagine you have 6 bulbs in front of you, 3 red and 3 yellow ones. Now, you want to plant them in an alternating way. This means that you have 3 bulbs to choose from when planting the first one (as you have to start with ONE of the colours). When planting the next one, you still have 3 bulbs to choose one as you are choosing one of the OTHER colour. Afterwards, you have planted one of each, so you have 2 of each left. Is it clearer now?


Thanks, I understand it better now :smile: But I've never done permutations before so I guess it's time to start teaching myself that eh. But thanks a lot for your help!
Reply 46
Permutations is quite straightforward, it has a lot to do with logic. I'm sure it won't take long to teach yourself.
Reply 47
Do how is the BMAT session coming?
Reply 48
Original post by sherazhar
but the answer you get when you divide 1.59/2 and multiply by 100 is 79.5%!

hey this is probably a printing mistake. Sorry but i cud only make this out of the question. Since this is a complete combustion reaction all the carbon from the carbon containing compound must be int the CO2. I find no other way but to use the atomic ratio to find the mass of carbons. Please some one correct me if i am wrong.
(edited 11 years ago)
Reply 49
Original post by tim3
hey this is probably a printing mistake. Sorry but i cud only make this out of the question. Since this is a complete combustion reaction all the carbon from the carbon containing compound must be int the CO2. I find no other way but to use the atomic ratio to find the mass of carbons. Please some one correct me if i am wrong.


Exactly! even i believe there's some printing mistake because even i dont get that answer! if anybody else think i am wrong please correct me!
Reply 50
Original post by tim3
Here is the solution,
First of all you know that the total carbon atoms remain same b4 and after the reaction.
so.................the ratio of carbon is to oxygen in the compound is 1:2 in CO2
so divide 4.77 by 3 which is equal to 1.59g! ( please trust the fact that in BMAT most calculation are really easy and can be done quickly)
so CO2 has 1.59g of carbon. So original 2 gram carbon containing compound, there must have been 1.59g of carbon
and 1.59 percentage of 2 is around 65% ( here they are probably testing the power of estimation) and the answer is E!!!!


You are completely wrong. That is definitely not how to solve it. What you are doing, is assume that 1 mol of carbon has the same mass as 1 mol of oxygen, which is not true. Hence, your ratio is wrong.

Original post by sherazhar
Exactly! even i believe there's some printing mistake because even i dont get that answer! if anybody else think i am wrong please correct me!


It's not a printing mistake, I did the question just now and got 64,5%. First of all, what you do, is calculate the percentage of carbon in 1 mol of carbon dioxide, i.e. 12/(12+32)=12/44=3/11=0,27

Now, since there are 0.27% of carbon in 1 mol, it means that 0,27% of the 4.77g of CO2 is just carbon. Hence, 0.27*4,77=1.29

Finally, as the other person said earlier, the mass of carbon (and any other element) is conserved (i.e. same before & after reaction). Hence, there are 1.29g of carbon in the 2g of the carbon compound. Thus: 1.29/2 = 64.5/100=64.5%
Reply 51
I have now also solved your other two questions (20 & 26), but I'll wait with typing them out until you see the above.
Reply 52
wow! yeah why didnt i get it! i feel so bad! :frown:
Reply 53
For question 20, this "The cylinder has the same internal diameter and length as the diameter of the sphere. " is absolutely crucial. What it is saying is that the height=diameter of sphere=2r and that the radius of the circular opening is also r.

Formula for volume of a cylinder: pi*r^2*h. Now, if h=2r, we get: 2pi*r^3.

We are told (and should know) that the volume of a sphere is 4/3pi*r^3.

To calculate the fraction the sphere takes up, we simply do (4/3pi*r^3)/(2pi*r^3). pi*r^3 cancels out on both sides, giving (4/3)/2=4/6=2/3. Hence, the answer is D.

-----------------------------------------------------------------------

When it comes to 26, I actually had a bit trouble with grasping the last sentence (and what I'm supposed to find) due to, in my opinion, the poor phrasing. Nevertheless, after reading it several times, it finally made sense to me.

What they are basically asking is: out of all possible compounds of CH2BrCl, which ones will have the relative molecular mass of 128? In other words, this is a probability question within chemistry.

Now, we are told to assume that the relative atomic mass of carbon and hydrogen is 12 respectively 1 (i.e. always that) which means that we can subtract 128 by 14, giving us 114.

We have two possible masses of chlorine, 35 and 37 and two possible masses of bromine, 79 and 81. If you study these numbers, you will see that the only combination which adds up to 114 is 35 respectively 79.

Now, what is the "probability" that the chlorine in the compound has a mass of 35? We are told that the abundance of Chlorine-35 is three times that of Chlorine-37, or, in other words, that the "probability" is 3/4.

The "probability" of having bromine-79 is the same as having bromine-81, i.e. 1/2.

Hence: 3/4*1/2=3/8, hence C.
Reply 54
Original post by Doppel
You are completely wrong. That is definitely not how to solve it. What you are doing, is assume that 1 mol of carbon has the same mass as 1 mol of oxygen, which is not true. Hence, your ratio is wrong.



It's not a printing mistake, I did the question just now and got 64,5%. First of all, what you do, is calculate the percentage of carbon in 1 mol of carbon dioxide, i.e. 12/(12+32)=12/44=3/11=0,27

Now, since there are 0.27% of carbon in 1 mol, it means that 0,27% of the 4.77g of CO2 is just carbon. Hence, 0.27*4,77=1.29

Finally, as the other person said earlier, the mass of carbon (and any other element) is conserved (i.e. same before & after reaction). Hence, there are 1.29g of carbon in the 2g of the carbon compound. Thus: 1.29/2 = 64.5/100=64.5%


Ah Doppel! thats actually correct, yeah assumed it wrong. thanks for clarifying.
Reply 55
Original post by Doppel
For question 20, this "The cylinder has the same internal diameter and length as the diameter of the sphere. " is absolutely crucial. What it is saying is that the height=diameter of sphere=2r and that the radius of the circular opening is also r.

Formula for volume of a cylinder: pi*r^2*h. Now, if h=2r, we get: 2pi*r^3.

We are told (and should know) that the volume of a sphere is 4/3pi*r^3.

To calculate the fraction the sphere takes up, we simply do (4/3pi*r^3)/(2pi*r^3). pi*r^3 cancels out on both sides, giving (4/3)/2=4/6=2/3. Hence, the answer is D.

-----------------------------------------------------------------------

When it comes to 26, I actually had a bit trouble with grasping the last sentence (and what I'm supposed to find) due to, in my opinion, the poor phrasing. Nevertheless, after reading it several times, it finally made sense to me.

What they are basically asking is: out of all possible compounds of CH2BrCl, which ones will have the relative molecular mass of 128? In other words, this is a probability question within chemistry.

Now, we are told to assume that the relative atomic mass of carbon and hydrogen is 12 respectively 1 (i.e. always that) which means that we can subtract 128 by 14, giving us 114.

We have two possible masses of chlorine, 35 and 37 and two possible masses of bromine, 79 and 81. If you study these numbers, you will see that the only combination which adds up to 114 is 35 respectively 79.

Now, what is the "probability" that the chlorine in the compound has a mass of 35? We are told that the abundance of Chlorine-35 is three times that of Chlorine-37, or, in other words, that the "probability" is 3/4.

The "probability" of having bromine-79 is the same as having bromine-81, i.e. 1/2.

Hence: 3/4*1/2=3/8, hence C.


Seriously dude I owe u a big tym! btw i can get the answer for q18 same paper but what is the method you are using??? mine is a bit long! any short method?
Reply 56
and wat about q11? i know the radiation is beta but half life i get 2.76!
Reply 57
Original post by Doppel
For question 20, this "The cylinder has the same internal diameter and length as the diameter of the sphere. " is absolutely crucial. What it is saying is that the height=diameter of sphere=2r and that the radius of the circular opening is also r.

Formula for volume of a cylinder: pi*r^2*h. Now, if h=2r, we get: 2pi*r^3.

We are told (and should know) that the volume of a sphere is 4/3pi*r^3.

To calculate the fraction the sphere takes up, we simply do (4/3pi*r^3)/(2pi*r^3). pi*r^3 cancels out on both sides, giving (4/3)/2=4/6=2/3. Hence, the answer is D.

-----------------------------------------------------------------------

When it comes to 26, I actually had a bit trouble with grasping the last sentence (and what I'm supposed to find) due to, in my opinion, the poor phrasing. Nevertheless, after reading it several times, it finally made sense to me.

What they are basically asking is: out of all possible compounds of CH2BrCl, which ones will have the relative molecular mass of 128? In other words, this is a probability question within chemistry.

Now, we are told to assume that the relative atomic mass of carbon and hydrogen is 12 respectively 1 (i.e. always that) which means that we can subtract 128 by 14, giving us 114.

We have two possible masses of chlorine, 35 and 37 and two possible masses of bromine, 79 and 81. If you study these numbers, you will see that the only combination which adds up to 114 is 35 respectively 79.

Now, what is the "probability" that the chlorine in the compound has a mass of 35? We are told that the abundance of Chlorine-35 is three times that of Chlorine-37, or, in other words, that the "probability" is 3/4.

The "probability" of having bromine-79 is the same as having bromine-81, i.e. 1/2.

Hence: 3/4*1/2=3/8, hence C.



I would have either guessed or left the question an leave it to chance. they only give a little time to find out such a easy but tricky concept.
Anyways, doppel guy you are true genius and i hope you get into Oxford or Cambridge, wherever you are applying. Would you mind if I ask you about your results?
Reply 58
Original post by sherazhar
and wat about q11? i know the radiation is beta but half life i get 2.76!


Unfortunately, I haven't studied physics for a long time and I'm revising it from scratch, so I can't answer that question at the moment.

As for question 18, this is how I did it:

For starters, I drew up two equations, focusing on the oxygen and the hydrogen, respectively.

If you think about it, the no. of oxygen atoms on the LHS will be 3b (3 oxygen atoms per mol) and 6a+c+2 on the RHS. In other words:

3b=6a+c+2
Now, if you look at the hydrogen atoms, you can deduce the equation 2b=c.

Using simultaneous equations we get b=6a+2

Now, if you let a=1, you get b=8.
a=2, b=14
a=3, b=20.

As you can see, the only one which corresponds to one of the alternatives is a=1 and b=8. (I stopped after a=3 as the alternatives give a maximum value of b as 18).
Reply 59
Original post by tim3
I would have either guessed or left the question an leave it to chance. they only give a little time to find out such a easy but tricky concept.
Anyways, doppel guy you are true genius and i hope you get into Oxford or Cambridge, wherever you are applying. Would you mind if I ask you about your results?


Which results?

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