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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A rectangular solid has length, width, and height of L cm, W cm, and H

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Math Expert V
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A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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1
25 00:00

Difficulty:   75% (hard)

Question Stats: 49% (01:51) correct 51% (01:37) wrong based on 601 sessions

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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

DS47651.01
OG2020 NEW QUESTION

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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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9
1
Bunuel wrote:
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

Hola amigos length = $$L$$,
width = $$W$$,
height = $$H$$,

length increased by $$x$$ % = $$L(1+\frac{x}{100})$$
width increased by $$y$$ % = $$W(1+\frac{y}{100})$$
height increased by $$z$$ % = $$H(1+\frac{z}{100})$$

What is the percentage increase in the total surface area?

Total surface area before increase = $$2LW + 2WH + 2LH$$
Total surface area after increase = $$2LW(1+\frac{x}{100})(1+\frac{y}{100}) + 2WH(1+\frac{y}{100})(1+\frac{z}{100}) + 2LH(1+\frac{x}{100})(1+\frac{z}{100})$$

Percentage increase in the total surface area = $$\frac{Total surface area AFTER increase - Total surface area BEFORE increase}{Total surface area BEFORE increase}*100$$

1. $$L, W,$$ and $$H$$ are in the ratios of $$5:3:4$$.
$$L = 5k$$
$$W = 3k$$
$$H = 4k$$
We know nothing about $$x, y,$$ and $$z$$ to calculate the percentage increase in the total surface area.
Insufficient

2. $$x = 5$$, $$y = 10$$, $$z = 20$$
We know nothing about $$L, W,$$ and $$H$$ to calculate the percentage increase in the total surface area.
Insufficient

1+2. Now we have all required variables for calculation. We need to understand abovementioned formulas to exactly know at least which variables should be IDENTIFIED for the formula to work. In this case ALL of them are required. If the VOLUME were asked, knowing only $$x, y,$$ and $$z$$ would be enough and that was the trap most people fall into choosing B under time pressure.
Sufficient

##### General Discussion
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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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From S1:

Only ratios are given, Hence Insufficient.

From S2:

Only percentages are given. Hence Insufficient.

Combining both:

We cannot use ratios to calculate the percentage change, even if increased dimension percentages are given.
Insufficient.

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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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1
1
Bunuel wrote:
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

TSA ; 2(lw+wh+lh)
#1
LWH given but % variation is missing; insufficient
#2
x = 5, y = 10, z = 20
dimensions not given
insufficeint
from 1 & 2
we can determine % increase for l,w,h
sufficient
IMO C
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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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1
Bunuel wrote:
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

$$L$$, $$W$$, and $$H$$ are the dimensions of a rectangular solid, in cm. The original question: $$\Delta SA\%=?$$

1) We know the ratio of the dimensions of this rectangular solid, but no information is given about the actual percent increases of its dimensions. Thus, we can't get a unique value to answer the original question. $$\implies$$ Insufficient

2) We know the actual percent increases of the dimensions of this rectangular solid. To determine the percent increase of its surface area, we try to determine the growth factor for its surface area.

$$\frac{2(1.05\cdot1.1LW+1.05\cdot1.2LH+1.1\cdot1.2WH)}{2(LW+LH+WH)}=$$

$$=\frac{1.05\cdot1.1+1.05\cdot1.2\frac{H}{W}+1.1\cdot1.2\frac{H}{L}}{1+\frac{H}{W}+\frac{H}{L}}$$

Clearly, the above growth factor depends on the ratio of the dimensions, about which we don't have any information. Thus, we can't get a unique value to answer the original question. $$\implies$$ Insufficient

1&2) We have the information to determine the percent increase of the surface area. Thus, we could get a unique value to answer the original question. $$\implies$$ Sufficient

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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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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

GMAT assassins aren't born, they're made,
Rich
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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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Solution

Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given
• A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively.

We need to determine
• If the length, width, and height are increased by x%, y% and z% respectively, then the corresponding percentage increase in the total surface area of the solid.

The total surface area of the rectangular solid, before increase = 2(LW + LH + WH)
To increase the percentage of the total surface area, we need to know
• The values of L, W, H, before increase (or the ratio of L, W, H)
• The values of x, y, and z.

With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1
As per the information given in statement 1, L, W, and H are in the ratios of 5: 3: 4.
• However, from this statement, we cannot determine the values of x, y, and z.

Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2
As per the information given in statement 2, x = 5, y = 10, z = 20.
• However, from this statement, we cannot determine the values of L, W, and H (or their ratios).

Hence, statement 2 is not sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)
Combining information from both statements, we get
• L: W: H = 5: 3: 4 and x = 5, y = 10, z = 20.

As we have all the necessary information to calculate the percentage increase, we can say the correct answer is option C.

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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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again this problem is abit tough to tackle it in 2 mins
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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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Hi gmatjindi,

Your goal when dealing with any individual Quant question should NOT be to try to answer it in under 2 minutes (that is bad advice that will likely cost you some points on Test Day) - a number of the questions that you will face are designed to take up to 3 minutes to solve (and that's if you know what you are doing). Your actual goal is to be 'efficient' with your work, meaning that you don't waste time and you choose the most efficient method for answering that question that's in front of you. Most GMAT questions are actually written so that you can approach them in more than one way - so as you continue to study, you might consider reviewing more than just the questions that you got wrong. There might be much faster ways to deal with questions that you have correctly answered (and you have to learn and practice those methods if you want to properly take advantage of them on Test Day).

GMAT assassins aren't born, they're made,
Rich
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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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I dont think that GMAT exam tests such a heavy calculation requiring question. There must be easier way of solving this one.
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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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shrivatipryanik wrote:
I dont think that GMAT exam tests such a heavy calculation requiring question. There must be easier way of solving this one.

Some gmat questions require about 3 mins. To have enough time for them you need to solve easier questions faster or under 2 mins.
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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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EMPOWERgmatRichC wrote:
Hi gmatjindi,

Your goal when dealing with any individual Quant question should NOT be to try to answer it in under 2 minutes (that is bad advice that will likely cost you some points on Test Day) - a number of the questions that you will face are designed to take up to 3 minutes to solve (and that's if you know what you are doing). Your actual goal is to be 'efficient' with your work, meaning that you don't waste time and you choose the most efficient method for answering that question that's in front of you. Most GMAT questions are actually written so that you can approach them in more than one way - so as you continue to study, you might consider reviewing more than just the questions that you got wrong. There might be much faster ways to deal with questions that you have correctly answered (and you have to learn and practice those methods if you want to properly take advantage of them on Test Day).

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

Hi Rich,

Thank you very much for your time to post, that was a great advice.
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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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Still not very clear why B is wrong .Thanks for the clarification
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A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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Can someone explain why not knowing the L,W,H in statement 2 is insufficient? It seems like as long as you know that L,W,H is being increased by the respective %, the overall increase will always be the same, regardless of the actual dimensions.

ie. if L,W,H = 1,1,1 or 2,3,5, and we know the % increase is 5%,10%,20%, the resulting increase from original to new will always be the same.

Can someone show it with actual examples? I figure I must be performing the question wrong.
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Re: A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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Hi cchen679,

Fact 2 doesn't define any of the original dimensions - and increasing different measurements by 5%, 10% or 20% will lead to different overall increases in overall surface areas (try a couple of different examples and you'll see).

GMAT assassins aren't born, they're made,
Rich
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A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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EMPOWERgmatRichC wrote:
Hi cchen679,

Fact 2 doesn't define any of the original dimensions - and increasing different measurements by 5%, 10% or 20% will lead to different overall increases in overall surface areas (try a couple of different examples and you'll see).

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

Thanks for the quick reply, but this is what confuses me. When I try different examples, I'm getting the same results

Example1:
L= 2
W= 3
H= 4
original surface area = 24(2*3*4)

new L,W,H after increasing by %
L= 2.1
W= 3.3
H= 4.8
new surface area = 33.264(2.1*3.3*4.8)

old SA/ new SA
24/33.264 = .7215

Example2:
L= 3
W= 5
H= 2
original surface area = 30(3*5*2)

new L,W,H after increasing by %
L= 3.15
W= 5.5
H= 2.4
new surface area = 41.58(3.15*5.5*2.4)

old SA/ new SA
30/41.58 = .7215
EMPOWERgmat Instructor V
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A rectangular solid has length, width, and height of L cm, W cm, and H  [#permalink]

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1
Hi cchen679,

In your examples, you're calculating the volume of the solid - you're supposed to be calculating the SURFACE AREA though.

Surface Area = (2)(L)(W) + (2)(L)(H) + (2)(W)(H)

You'll find that the answer varies when you change the initial Surface Area.

GMAT assassins aren't born, they're made,
Rich
_________________ A rectangular solid has length, width, and height of L cm, W cm, and H   [#permalink] 08 Jul 2019, 06:42
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