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The size of diamonds is measured in carats. If the price of a diamond

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Bunuel
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The size of diamonds is measured in carats. If the price of a diamond [#permalink] New post   12 Jul 2017, 00:46
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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 three 2.5-carat diamonds
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pushpitkc
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Re: The size of diamonds is measured in carats. If the price of a diamond [#permalink] New post   12 Jul 2017, 00:53
Let the cost of a 0.5 carat diamond be x$
So, 1 carat will cost 2x$ and this repeats till 4 carat diamond which will cost 128x$

If x = 1, the cost of the 0.5 carat diamond is 1$ and the cost of a 4 carat diamond is 128$

So, Option A(One 4 carat diamond) is definitely costlier than the combination of the other diamond's costs.
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Re: The size of diamonds is measured in carats. If the price of a diamond [#permalink] New post   12 Jul 2017, 01:03
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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 three 2.5-carat diamonds



Let Price of 1 1carat diamond be x ..
according to the question, the price of a diamond doubles for every 0.5 carats

So,

Price of 1 1.5 carat diamond = 2x
Price of 1 2 carat diamond = 4x
Price of 1 2.5 carat diamond = 8x
Price of 1 3 carat diamond = 16x
Price of 1 4 carat diamond = 64x


So,

(A) One 4-carat diamond = 64x
(B) Fourteen 1-carat diamonds = 14x
(C) Four 2-carat diamonds and eight 1-carat diamonds = 4[2x] + 8x = 24x
(D) One 1-carat diamond, two 2-carat diamonds, and three 3-carat diamonds = x + 2[4x] + 3[16x] = x + 8x + 48x = 57x
(E) Three 1.5-carat diamonds and three 2.5-carat diamonds = 3[2x] + 3[8x] = 30x

So.
A is the Answer since it is the greatest...


Thanks for the Kudos I will receive.... :-D :-D :-D :-D :-D :-D
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Re: The size of diamonds is measured in carats. If the price of a diamond [#permalink] New post   06 Jun 2018, 15:05
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Bunuel wrote:
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 three 2.5-carat diamonds



Let x be the price of a 0.5 carats diamond

Therefore, since the price doubles for every 0.5 carats, we have
2x as the price of a 1 carat diamond
4x as the price of a 1.5 carat diamond
8x as the price of a 2 carat diamond
16x as the price of a 2.5 carat diamond
32x as the price of a 3 carat diamond
64x as the price of a 3.5 carat diamond
128x as the price of a 4 carat diamond

based on the above chart we can calculate the price for the answer choices.

We can then see that Answer choice A has the highest price.


Thanks,
GyM
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Varane
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Re: The size of diamonds is measured in carats. If the price of a diamond [#permalink] New post   13 Jun 2022, 03:39
Can an expert help here.

Posted from my mobile device
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Re: The size of diamonds is measured in carats. If the price of a diamond [#permalink] New post   13 Jun 2022, 05:20
Let the price of a diamond of 0.5 carats be x. Since the diamond doubles for every 0.5 carats, for 1 carat, it will be 2x.
For 2 carats, it will be 2^3x.
For 2.5 carats, it will be 2^4x.
For 3 carats, it will be 2^5x.
For 4 carats, it will be 2^7x.

Consider the option A:
The price = 2^7x = 128x

Option B:
Price = 14*2x = 28x

Option C:
Price = 4*8x + 8*2x = 32x + 16x = 68x

Option D:
Price = 2x + 2*8x + 3*32 = 18x + 96x = 114x

Option E:
Price = 3*4x + 3*16x = 60x

Thus, the highest price is for option A
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Re: The size of diamonds is measured in carats. If the price of a diamond [#permalink] New post   13 Jun 2022, 07:59
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Varane wrote:
Can an expert help here.

Posted from my mobile device


Varane

There is no variable in the question, but the instinct is to introduce one to use for the price of a 1-carat or a 0.5-carat diamond. Any time your instinct is to introduce a variable that isn't there, see if it makes sense to just use a number. Let's make a 1-carat diamond $1.

1-carat = $1
1.5-carat = $2
2 = $4
2.5 = $8
3 = $16
3.5 = $32
4 = $64

Let's look at the answer choices.
(A) One 4-carat diamond = $64
(B) Fourteen 1-carat diamonds = $14 Less than A.
(C) Four 2-carat diamonds and eight 1-carat diamonds = 4($4)+8($1) = $16+$8 Less than A.
(D) One 1-carat diamond, two 2-carat diamonds, and three 3-carat diamonds = $1+2($4)+3($16) = $1+$8+$48 Less than A.
(E) Three 1.5-carat diamonds and three 2.5-carat diamonds = 3($2)+3($8) = $6+$24 Less than A.

Answer choice A.
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Re: The size of diamonds is measured in carats. If the price of a diamond [#permalink]
13 Jun 2022, 07:59
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