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The size of diamonds is measured in karats. If the price of

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Senior Manager
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The size of diamonds is measured in karats. If the price of  [#permalink]

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New post 14 Oct 2005, 19:36
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The size of diamonds is measured in karats. If the price of a diamond doubles for every.5karats, which of the following is worth the most?

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


I can't seem to find the shortucut. Please explain your answer. I will post OA on Sunday 9/16.

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New post 14 Oct 2005, 19:48
C

The price is max where there are max 0.5 karats.

a) 1*4*2 = 8 k
b) 1*14*2 = 28 k
c) 4*2*2 + 8*1*2 = 32 k
d) 1*1*2 + 2*2*2 + 3*3*2 = 28 k
e) 1.5*3*2 + 3*2.5*2 = 24k
Senior Manager
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New post 14 Oct 2005, 20:01
The price doubles every .5 k. Assume price is x, then

.5k = x
1k = 2x
1.5k = 4x
2k = 8x and so on

1. 2^8 = 256x
2. 14 * 2^2 = 56x
3. 4*2^4 + 8*2^2 = 96x
4. 2^2 + 2*2^4 + 3*2^6 = 228x
5. 3*2^3 + 3*2^5 = 88x

Hence answer is A
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Re: PS - Number Properties/Arithmetic  [#permalink]

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New post 14 Oct 2005, 21:02
desiguy wrote:
The size of diamonds is measured in karats. If the price of a diamond doubles for every.5karats, which of the following is worth the most?

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


I can't seem to find the shortucut. Please explain your answer. I will post OA on Sunday 9/16.


Assume:
.5k = 1
1k = 2
1.5k = 4
2k = 8 so on & so forth

A = 128
B = 28
C = 48
D = 114
E = 60

Ans: A ( Yeah, I'll be interested in the shortcut as well)
Senior Manager
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New post 14 Oct 2005, 22:32
sudhagar wrote:
The price doubles every .5 k. Assume price is x, then

.5k = x
1k = 2x
1.5k = 4x
2k = 8x and so on

1. 2^8 = 256x
2. 14 * 2^2 = 56x
3. 4*2^4 + 8*2^2 = 96x
4. 2^2 + 2*2^4 + 3*2^6 = 228x
5. 3*2^3 + 3*2^5 = 88x

Hence answer is A


I did a mistake in the above one. I took .5k as 2^1 during calculation. It should be 2^0. Hence all the answers should be divided by 2, which would still yield A :-)
Senior Manager
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New post 16 Oct 2005, 18:41
Answer is A, but I still don't see the shortcut.

I guess this is one of those problems, that will take the full two minutes...

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Re: The size of diamonds is measured in karats. If the price of  [#permalink]

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New post 12 Jan 2019, 15:53
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Re: The size of diamonds is measured in karats. If the price of &nbs [#permalink] 12 Jan 2019, 15:53
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