Interesting PS-related GMAT question! See if you can solve =)

[rockzilla]

So, I''m studying for the GMAT (ugh!) and I come across this question that makes me smile. See if you can solve it for yourself:

The size of diamonds is measured in carats. If the price of a diamond doubles for every 0.5 carats, which of the following is worth the most?

A) one 4-carat diamond
B) fourteen 1-carat diamonds
C) four 2-carat diamonds and eight 1-carat diamonds
D) one 1-carat diamond, two 2-carat diamonds, and three 3-carat diamonds
E) three 1.5-carat diamonds and 3 2.5-carat diamonds


Now you know what I am going through....I was like...the answer should be F) Not enough information to tell! (You assume everything else is equal, i suppose)

 

[FrekeChild]

Ooooo....A!

 

[VRBeauty]

I''ll take A!

 

[heb1976]

I came up with D....

 

[VRBeauty]

Date: 7/10/2008 1:51:23 AM
Author: heb1976
I came up with D....

I''ll trade you my A for your D, if....you''ll make it two 2.5 ct stones instead of two 2 ct stones.

 

[goldenstar]

Ugh, math.... That's why I went to law school.

Best of luck with the GMAT! It's always nice to come across a question that makes you smile.

 

[Beacon]

I did a pretty sloppy job, but I think it''s A. It is a weird question though, cause in reality, a 3.5 carat stone would never be double the price of a 3 carater.

 

[heb1976]

Date: 7/10/2008 2:04:07 AM
Author: MINIMS

Date: 7/10/2008 1:51:23 AM
Author: heb1976
I came up with D....

I''ll trade you my A for your D, if....you''ll make it two 2.5 ct stones instead of two 2 ct stones.

LOL! I forgot to hit = for the A equation. DUHHHH!

What can I say, it''s 2:30 in the morning!

Now, if someone were offering me a choice I would take D anyday!

That''s earrings, a three stone ring and a pendant!

 

[choro72]

Date: 7/10/2008 2:18:19 AM
Author: goldenstar
Ugh, math.... That''s why I went to law school.

Don''t you need a pretty math oriented mind to go through law school? Logic and all that.

My question is, what do you mean by "worth the most"? Price only? Or taking into account of your desires and what YOU think is worth paying for?

Anyway, I got that B will be the cheapest. I wonder what I''m doing wrong...

 

[brooklyngirl]

A is the winner, costing 128 times the half carat. D comes in a close second at 114.

 

[NoID]

OK - for those of us who have no idea where to even start (aka math dunce

) can you post how you guys solved it?

 

[VRBeauty]

I made up a quick cheat sheet on how much diamonds from one to four carats would be worth if a 1 carat stone was equal to 1. It looks like this, with the stone size on the left and the value on the right:

1 = 1
1.5 = 2
2 = 4
2.5 = 8

etc.

Using the cheat sheet, it's easy to calculate the relative value of each option.

I'm sure there's a more elegant way to do it though, and I hope someone will share it with us!

BTW, heb1976 -- those are going to be some killer earrings!

 

[goldenstar]

Date: 7/10/2008 3:09:44 AM
Author: choro72

Date: 7/10/2008 2:18:19 AM

Author: goldenstar

Ugh, math.... That''s why I went to law school.

Don''t you need a pretty math oriented mind to go through law school? Logic and all that.

Well, yes and no. You need strong logical reasoning skills for law school, but working with numbers and working with facts is very different.

For example, I can put two facts together and make inferences but if you give me long division I''ll

.

A poor example that I just made up: Cows are the only animals that eat grass + This animal is eating grass= This animal is a cow

I can''t work with numbers well, but I''m good with words.

 

[brooklyngirl]

Here''s how I solved it:

Consider the .5 carat number as a unit (cu), so 0.5 carats = 1cu, 1 carat = 2cu, 1.5 carats = 3cu.

Total units (tcu) = carat weight/0.5 = carat weight * 2

Cost of diamond = 2^(tcu-1). (Here, the cost a .5 carat diamond is 2^0 =1, 1 carat diamond is 2^1=2)

A: One 4 carat diamond --> 1*2^(4*2-1) = 128
B: Fourteen 1-carat diamonds --> 14*2^(1*2-1) = 28
C: Four 2-carat and eight 1 carat --> 4*2^(2*2-1) + 8*2^(1*2-1)= 48
D: one 1-carat diamond, two 2-carat diamonds, and three 3-carat diamonds --> 1*2^(1*2-1) + 2 *^(2*2-1)+ 3*^(3*2-1) = 114
E: three 1.5-carat diamonds and 3 2.5-carat diamonds --> 3*2^(1.5*2-1) + 3*2^(2.5*2-1) = 60

 

[princesss]

Date: 7/10/2008 4:38:39 AM
Author: brooklyngirl
Here''s how I solved it:

Consider the .5 carat number as a unit (cu), so 0.5 carats = 1cu, 1 carat = 2cu, 1.5 carats = 3cu.

Total units (tcu) = carat weight/0.5 = carat weight * 2

Cost of diamond = 2^(tcu-1). (Here, the cost a .5 carat diamond is 2^0 =1, 1 carat diamond is 2^1=2)

A: One 4 carat diamond --> 1*2^(4*2-1) = 128
B: Fourteen 1-carat diamonds --> 14*2^(1*2-1) = 28
C: Four 2-carat and eight 1 carat --> 4*2^(2*2-1) + 8*2^(1*2-1)= 48
D: one 1-carat diamond, two 2-carat diamonds, and three 3-carat diamonds --> 1*2^(1*2-1) + 2 *^(2*2-1)+ 3*^(3*2-1) = 114
E: three 1.5-carat diamonds and 3 2.5-carat diamonds --> 3*2^(1.5*2-1) + 3*2^(2.5*2-1) = 60

Okay, technically I did the same thing to solve it. But seeing it written out like this is confusing, lol. Basically, to solve it I made a chart (.5 = 1, 1=2, 1.5=4, 2=8, 2.5=16, 3=32, 3.5=64, 4=12 and then added things up, inserting these values for carat weight. So the exact same thing as brooklyngirl, just less confusing on my paper.

 

[Anna0499]

Date: 7/10/2008 3:53:11 AM
Author: goldenstar

Date: 7/10/2008 3:09:44 AM
Author: choro72

Date: 7/10/2008 2:18:19 AM

Author: goldenstar

Ugh, math.... That''s why I went to law school.

Don''t you need a pretty math oriented mind to go through law school? Logic and all that.

Well, yes and no. You need strong logical reasoning skills for law school, but working with numbers and working with facts is very different.

For example, I can put two facts together and make inferences but if you give me long division I''ll

.

A poor example that I just made up: Cows are the only animals that eat grass + This animal is eating grass= This animal is a cow

I can''t work with numbers well, but I''m good with words.

My law professors always *ugh* when any sort of math comes up in a case...it is well-known, at least in my school, that law students don''t like math! That''s what law firm accountants are for!

 

[dockman3]

Date: 7/10/2008 4:38:39 AM
Author: brooklyngirl
Here''s how I solved it:


Consider the .5 carat number as a unit (cu), so 0.5 carats = 1cu, 1 carat = 2cu, 1.5 carats = 3cu.


Total units (tcu) = carat weight/0.5 = carat weight * 2


Cost of diamond = 2^(tcu-1). (Here, the cost a .5 carat diamond is 2^0 =1, 1 carat diamond is 2^1=2)


A: One 4 carat diamond --> 1*2^(4*2-1) = 128

B: Fourteen 1-carat diamonds --> 14*2^(1*2-1) = 28

C: Four 2-carat and eight 1 carat --> 4*2^(2*2-1) + 8*2^(1*2-1)= 48

D: one 1-carat diamond, two 2-carat diamonds, and three 3-carat diamonds --> 1*2^(1*2-1) + 2 *^(2*2-1)+ 3*^(3*2-1) = 114

E: three 1.5-carat diamonds and 3 2.5-carat diamonds --> 3*2^(1.5*2-1) + 3*2^(2.5*2-1) = 60

This is pretty much how I did it, except I didn''t subtract one from the exponent. I just said that at 4ct=2^8, 1ct=2^2 and so on. Came up with the same answer though, A is the most expensive. Sometimes I love being a math geek!

 

[Bia]

Math is my nemesis...ugh. I failed College Algebra, its that bad! Who fails algebra???

I pick A because it seems like the best choice...that and most everyone seems to agree.

 

[Delster]

Date: 7/10/2008 9:44:31 AM
Author: IndyGirl22

Date: 7/10/2008 3:53:11 AM
Author: goldenstar

Date: 7/10/2008 3:09:44 AM
Author: choro72

Date: 7/10/2008 2:18:19 AM

Author: goldenstar

Ugh, math.... That''s why I went to law school.

Don''t you need a pretty math oriented mind to go through law school? Logic and all that.

Well, yes and no. You need strong logical reasoning skills for law school, but working with numbers and working with facts is very different.

For example, I can put two facts together and make inferences but if you give me long division I''ll

.

A poor example that I just made up: Cows are the only animals that eat grass + This animal is eating grass= This animal is a cow

I can''t work with numbers well, but I''m good with words.

My law professors always *ugh* when any sort of math comes up in a case...it is well-known, at least in my school, that law students don''t like math! That''s what law firm accountants are for!

Oh yup. FI swears blind that sudoku is just ''logic'' and so with a law degree then I should looooove it. Eh, there are numbers in there!!!

But I can argue the definition of a ''charge having an equivalent effect'' or ''intoxication'' till the, um, grass eating animals come home