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
C
Source: Official Guide 2020
A rectangular solid has length, width, and height of L cm
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 394
- Joined: Sun Jul 02, 2017 10:59 am
- Thanked: 1 times
- Followed by:5 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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: C
GMAT assassins aren't born, they're made,
Rich
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: C
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Solution:AbeNeedsAnswers wrote: ↑Fri May 03, 2019 4:08 pmA 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
C
Source: Official Guide 2020
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
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews