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655-705 Level|   Geometry|               
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A rectangular solid has length, width, and height of L cm, W cm, and H 20 Dec 2020, 11:24
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Ryanh7788
Can someone explain why the ratio part 1 is even needed? to solve for Part 2?

Even if you use L = X, W = Y, H = Z
Does it matter?

i.e. Original SA: 2(xy + xz + yz)
example increase for each length, width height = 150%

2[(1.5x)(1.5y) + (1.5x)(1.5z) + (1.5y)(1.5z)] - 2xy + 2xz + 2yz
____________________________________________________

2xy + 2xz + 2yz


= Reduce:

2.5 (xy + xz + yz)
_______________
2 (xy + xz + yz)

Answer: 2.5/2 = 5/4 = 1.25 = 125% increase


I still don't understand
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Hi Ryanh7788,

In your example, you chose to increase each dimension by 50% of its original value (which is fine) - and you ended up with a specific result (a 125% increase in Total Surface Area). What happens IF you increase each dimension by something OTHER than 50% though? What happens if you increase each of the three dimensions by a different percent? Will you still end up with a 125% overall increase in Total Surface Area?

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A rectangular solid has length, width, and height of L cm, W cm, and H 21 Dec 2020, 02:24
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Ryanh7788
Can someone explain why the ratio part 1 is even needed? to solve for Part 2?

Even if you use L = X, W = Y, H = Z
Does it matter?

i.e. Original SA: 2(xy + xz + yz)
example increase for each length, width height = 150%

2[(1.5x)(1.5y) + (1.5x)(1.5z) + (1.5y)(1.5z)] - 2xy + 2xz + 2yz
____________________________________________________

2xy + 2xz + 2yz


= Reduce:

2.5 (xy + xz + yz)
_______________
2 (xy + xz + yz)

Answer: 2.5/2 = 5/4 = 1.25 = 125% increase


I still don't understand

Hi Ryanh7788,

In your example, you chose to increase each dimension by 50% of its original value (which is fine) - and you ended up with a specific result (a 125% increase in Total Surface Area). What happens IF you increase each dimension by something OTHER than 50% though? What happens if you increase each of the three dimensions by a different percent? Will you still end up with a 125% overall increase in Total Surface Area?

GMAT assassins aren't born, they're made,
Rich
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Hello EMPOWERGmat,

That's precisely my point. 150% was for the purpose of the calculation to make it possible to find the end overall increase in total surface area.

With (2) x = 5, y = 10, z = 20
The answer is sufficient without (1)

Therefore the answer is B?
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A rectangular solid has length, width, and height of L cm, W cm, and H 21 Dec 2020, 14:52
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Hi Ryanh7788,

In DS questions, a Fact is only SUFFICIENT if the answer to the given question (in this case: "what is the percentage increase in the total surface area of the solid?") stays the SAME. If the answer to the question changes, then the information in the Fact is INSUFFICIENT.

With the information in Fact 2, you know the percent increase of each side, but you do not know the exact 'base values' of what you are increasing. Here's a simple example of how the results can change:

With the information in Fact 2, what if the Length = 1, Width = 1 and Height = 100.... what would the percentage increase in the total surface area be? Now, what if you made the Length = 100 and the Height = 1 instead?

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A rectangular solid has length, width, and height of L cm, W cm, and H 14 May 2021, 07:02
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Bunuel
A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively. If these dimensions are increased by x%, y%, and z%, respectively, what is the percentage increase in the total surface area of the solid?

(1) L, W, and H are in the ratios of 5:3:4.
(2) x = 5, y = 10, z = 20

DS47651.01
OG2020 NEW QUESTION
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Solution:

Question Stem Analysis:

We need to determine the percentage increase in the total surface area of the solid given that the length, width, and height of the solid are L cm, W cm, and H cm, respectively and these dimensions are increased by x%, y%, and z%, respectively,

Statement One Alone:

Without knowing the values of x, y, and z, we can’t determine the percentage increase in the total surface area of the solid. Statement one alone are not sufficient.

Statement Two Alone:

Without knowing the values of L, W, and H, we can’t determine the percentage increase in the total surface area of the solid. Statement two alone are not sufficient.

Statements One and Two Together:

Although we don’t know the exact values of L, W, and H, we can let them be 5s, 3s, and 4s, respectively since their ratio is 5:3:4. Therefore, the original surface area of the solid is 2(5s * 3s + 5s * 4s + 3s * 4s) = 2(47s) = 94s.

The new values of L, W, and H, in terms of s, are 5.25s, 3.3s, and 4.8s. Therefore, the new surface area of the solid is 2(5.25s * 3.3s + 5.25s * 4.8s + 3.3s * 4.8s) = 2(58.365s) = 116.73s.

Therefore, the percent increase in surface area is (116.73s - 94s) / (94s) * 100%. We see that variable s will cancel out, leaving us a unique value for the percent increase. Both statements together are sufficient.

Answer: C
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A rectangular solid has length, width, and height of L cm, W cm, and H 23 May 2021, 07:50
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A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively. If these dimensions are increased by x%, y%, and z%, respectively, what is the percentage increase in the total surface area of the solid?

(1) L, W, and H are in the ratios of 5:3:4.
(2) x = 5, y = 10, z = 20
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Answer: Option C

Video solution by GMATinsight

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A rectangular solid has length, width, and height of L cm, W cm, and H 24 Jul 2021, 04:58
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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A rectangular solid has length, width, and height of L cm, W cm, and H 22 Aug 2021, 13:34
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EMPOWERgmatRichC
Hi All,

We're told that a rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively. We're asked if these dimensions are increased by X%, Y%, and Z%, respectively, what would be the PERCENTAGE INCREASE in the total SURFACE AREA of the solid. This question is based around a couple of specific math formulas and can be solved with a mix of Arithmetic and TESTing VALUES. There are clearly a lot of variables in this question, so we'll need a lot of information to define the percentage increase in the total surface area.

To start, Total Surface area is SA = 2(L)(W) + 2(L)(H) + 2(W)(H) and the Percentage Change Formula = (New - Old)/(Old) = (Difference)/(Original).

(1) L, W, and H are in the ratios of 5:3:4

Fact 1 defines the relationships between the three dimensions (for example, the width is 3/4 of the height), but tells us nothing about the percent increase in any of the 3 dimensions, so there's clearly no way to define the percentage increase in surface area.
Fact 1 is INSUFFICIENT

(2) X = 5, Y = 10, Z = 20

Fact 2 gives us the exact percent increase in each dimension, but without any information on the original dimensions of the rectangular solid, we have no way to define the 'impact' that each increase would have on the total surface area.
Fact 2 is INSUFFICIENT

Combined, we know...
L, W, and H are in the ratios of 5:3:4
X = 5, Y = 10, Z = 20

With the ratio in Fact 1, we can refer to the three dimensions as Length = 5X, Width = 3X and Height = 4X, so whatever "X" actually is, the increase or decrease in the side lengths will be proportional. This means that the impact on the Original Surface Area and New Surface Area will always be the same in the above calculation and we will ALWAYS end up with the exact same answer (the math would look a bit 'ugly', so I'm going to refrain from presenting it here).
Combined, SUFFICIENT

Final Answer:
Show Spoiler
C


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Thank you for your explanation! What confused me about the problem was if the starting l, w, and h could be different values as long as they were in the proportion of 5:3:4. For instance, if I assume the l, w, and h are just 5,3,4, then the original SA is 94 and the SA post the increase is ~117, yielding a % increase of over 11,000%. If I change the values for the sides (while keeping them in proportion to 5:3:4), I get a different difference. For instance if I let l=5, w=6, and w=8, then my SA is 376. Once I increase the values by the specifications in the directions, the new SA is ~467, yielding a % increase of over 46,000%. I am so sorry for the long question, but what am I missing here that prevents you from multiplying the original surface area by a different factor (while maintaining the 5:3:4 ratio)? Essentially, I tested cases and had different values (don't worry I did this math in Excel after to make sure I understood the problem). Many thanks in advance :)
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A rectangular solid has length, width, and height of L cm, W cm, and H 22 Aug 2021, 19:21
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Hi woohoo921,

Based on what you described in your post, I think there are either some 'typos' in what you wrote OR you made some math mistakes in your work.

Remember that the ratio of the sides MUST be 5:3:4... so your example of 5, 6 and 8 does NOT fit (you 'doubled' both the 3 and the 4, but you left the 5 the same). That having been said, with side lengths of 10, 6 and 8, you would have a Total Surface area that is DOUBLE that of the SA when the sides are 5, 3 and 4 (and that would be a Total Surface Area of 188.... NOT 376).

When you increase the 10, 6 and 8 by the percentages mentioned in Fact 2 - and perform the rest of the Percentage Change math that's involved, you'll find that you end up with the SAME result that you did when you worked through side lengths of 5, 3 and 4.

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A rectangular solid has length, width, and height of L cm, W cm, and H 07 Sep 2023, 20:12
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