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# The length, width, and height of a rectangular box, in centimeters, ar

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The length, width, and height of a rectangular box, in centimeters, ar  [#permalink]

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26 Apr 2019, 03:25
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85% (hard)

Question Stats:

48% (02:10) correct 52% (01:54) wrong based on 115 sessions

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The length, width, and height of a rectangular box, in centimeters, are L, W, and H. If the volume of this box is V cubic centimeters and the total area of the 6 sides of this box is A square centimeters, what is the value of V/A ?

(1) At least 2 of L, W, and H are equal to 5.
(2) L, W, and H all have the same value.

DS50351.01
OG2020 NEW QUESTION

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Re: The length, width, and height of a rectangular box, in centimeters, ar  [#permalink]

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26 Apr 2019, 13:28
Using the Alternative approach, we'll try to find two different possible numeric results in order to eliminate the wrong answers.
Statement (1): if the dimensions are 5,5,5 then V=5³ and A=6x5x5. If the dimensions are 5,5,6 then V=5x5x6 and A=4x5x5+2x5x6. The former gives us 5/6 and the latter 150/160, which is not the same. Answer choices (A) and (D) are eliminated.
Statement (2): we already saw that if the dimensions are 5,5,5 then V=5³ and A=6x5x5. If the dimensions are 1,1,1 then V=1³ and A=6x1x1. While the former gives 5/6, the latter gives 1/6. Answer (B) is also eliminated.
Combining both statements gives only one option (dimensions 5,5,5), so there's only one possible value for V/A.

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Re: The length, width, and height of a rectangular box, in centimeters, ar  [#permalink]

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27 Apr 2019, 10:42
Bunuel wrote:
The length, width, and height of a rectangular box, in centimeters, are L, W, and H. If the volume of this box is V cubic centimeters and the total area of the 6 sides of this box is A square centimeters, what is the value of V/A ?

(1) At least 2 of L, W, and H are equal to 5.
(2) L, W, and H all have the same value.

DS50351.01
OG2020 NEW QUESTION

v= l*w*h
TSA= 2*(lw+wh+hl)
#1
At least 2 of L, W, and H are equal to 5.
v=25h
TSA= 2*(50+5h)
v/TSA = 25h/2*(50+5h)
h not given insufficeint
#2
L, W, and H all have the same value
v=1 or say 125 if 5
TSA= 6 at 1 and 30 when
ratio 1/6 or 125/30 ; 25/6
insufficient
combining 1 & 2
we take v=125 and tsa = 30 so ratio 25/6
IMO C
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Re: The length, width, and height of a rectangular box, in centimeters, ar  [#permalink]

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14 May 2019, 19:07
Hi All,

We're told that the length, width, and height of a rectangular box, in centimeters, are L, W, and H, respectively, the VOLUME of this box is V cubic centimeters and the TOTAL SURFACE AREA of the 6 sides of this box is A square centimeters. We're asked for the value of V/A. This question is based around some standard Geometry formulas for solids and can be solved by TESTing VALUES.

To start, Volume of a rectangular solid is V = (L)(W)(H) and Total Surface area is SA = 2(L)(W) + 2(L)(H) + 2(W)(H).

(1) At least 2 of L, W, and H are equal to 5.

Fact 1 tells us that 2 (or perhaps all 3) of the dimensions are equal to 5, but that still leads to a number of different answers to the question.
IF...
L = 5, W = 5, H = 5, then the Volume = (5)(5)(5) = 125 and Total Surface Area = (2)(5)(5) + (2)(5)(5) + (2)(5)(5) = 150... so the answer to the question is 125/150 = 5/6.
L = 5, W = 5, H = 1, then the Volume = (5)(5)(1) = 25 and Total Surface Area = (2)(5)(5) + (2)(5)(1) + (2)(5)(1) = 70... so the answer to the question is 25/70 = 5/14.
Fact 1 is INSUFFICIENT

(2) L, W, and H all have the SAME value.

Fact 2 tells us that we're actually dealing with a CUBE, but the answer to the question will still vary depending on the side length.
IF....
L = 5, W = 5, H = 5, then the Volume = (5)(5)(5) = 125 and Total Surface Area = (2)(5)(5) + (2)(5)(5) + (2)(5)(5) = 150... so the answer to the question is 125/150 = 5/6.
L = 1, W = 1, H = 1, then the Volume = (1)(1)(1) = 1 and Total Surface Area = (2)(1)(1) + (2)(1)(1) + (2)(1)(1) = 6... so the answer to the question is 1/6.
Fact 2 is INSUFFICIENT

Combined, we know...
At least 2 of L, W, and H are equal to 5.
L, W, and H all have the SAME value.

When combining the two Facts, it's clear that we're dealing with a cube with a side length of 5, so the answer to the question is 5/6.
Combined, SUFFICIENT

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Re: The length, width, and height of a rectangular box, in centimeters, ar  [#permalink]

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15 May 2019, 00:26

Solution

Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given
• The length, width, and height of a rectangular box, in centimetres, are L, W, and H.
• The volume of this box is V cubic centimetres and the total area of the 6 sides of this box is A square centimetres.

We need to determine
• The value of V/A.

As the given box is a rectangular one, we can say
• Volume V = LWH
• Total area of 6 sides = A = 2(LW + LH + WH)

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

Step 3: Analyse Statement 1
As per the information given in statement 1, at least 2 of L, W, and H are equal to 5.
• However, we do not know the exact values of each of them.
Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2
As per the information given in statement 2, L, W, and H all have the same value.
If we assume each of them is equal to ‘a’, then we can write
• V/A = a^3/(2(3a^2)) = a^3/(6a^2 ) = a/6
• Therefore, we need to know the value of ‘a’ to get the answer.

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

Step 5: Combine Both Statements Together (If Needed)
Combining information from both statements, we can say
• L = W = H = 5.
As we know the value of each of them, we can determine the value of V/A.
Hence, the correct answer is option C.

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Re: The length, width, and height of a rectangular box, in centimeters, ar  [#permalink]

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16 May 2019, 13:37
1
Bunuel wrote:
The length, width, and height of a rectangular box, in centimeters, are L, W, and H. If the volume of this box is V cubic centimeters and the total area of the 6 sides of this box is A square centimeters, what is the value of V/A ?

(1) At least 2 of L, W, and H are equal to 5.
(2) L, W, and H all have the same value.

DS50351.01
OG2020 NEW QUESTION

The original question: $$V/A=?$$

1) We know that at least two dimensions of the rectangular box have length of 5. Let $$x$$ be its unknown dimension.

$$\frac{V}{A}=\frac{5\cdot 5\cdot x}{2\cdot 5\cdot 5+2\cdot 5\cdot x+2\cdot 5\cdot x}=\frac{25}{50/x+20}$$

Since $$x$$ can be any positive real number, we can't get a unique value to answer the original question. $$\implies$$ Insufficient

2) We know that all of its dimensions have the same value, so it is a cube. Let $$a$$ be the unknown side length of this cube.

$$\frac{V}{A}=\frac{a^3}{6a^2}=\frac{a}{6}$$

Since $$a$$ can be any positive real number, we can't get a unique value to answer the original question. $$\implies$$ Insufficient

1&2) We can infer that $$a=5$$, so $$V/A=5/6$$. Thus, the answer to the original question is a unique value. $$\implies$$ Sufficient

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Re: The length, width, and height of a rectangular box, in centimeters, ar   [#permalink] 16 May 2019, 13:37
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