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

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

Answer: C

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

Final Answer:

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

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.
The correct answer is (C).

Posted from my mobile device

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

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.


_________________

LWH/(2(LW + WH + HL) = ?

1) Suppose L = W = 5

5*5*H/(2(5*5 + 5H + 5H)) = 25H/(2(25+10H) => Not Sufficient

2) L^3/(2(L^2 + L^2 + L^2) = L^3/(6L^2) = L/6 => Not Sufficient

1+2)
L = 6
Therefore, L/6 = 5/6 => Sufficient

ANSWER: C

Why this question is tagged under 700 level. Can anybody explain?

Answer: Option C

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Tamalmallick13

40% takers of this question have got wrong answer which is enough reason to tag it 700 level.

I am sure you are good and therefore you are finding it unworthy of 700.

This question seems ambiguous, 2 of l, w and h ?

I mean they should retire this question for this reason alone. 2 of l can been 2 * l

This can be interpreted as either 2l or 2w = 5 or 2w and 2h =5

or it could be interpreted as 2l 2w and 2h =5 or 3l 3w and 3h =5

one of the worst questions i've ever seen, and this is coming from GMAC.

The volume of Rectangular Solid = LHW
Area of 6 sides is = 2LH +2WH+2WL

1) We need to know all sides of the rectangle [ Insufficient]

2) L= W=H
So, this is a cube but we don't know any value for the variables. Insufficient.

V/A = 8/64 = 1/8


Considering both the options that this is cube and each side has unique value . Sufficient.

Ans. C.

Solution:

Question Stem Analysis:

We need to determine the value of V/A. Notice that V = LWH and A = 2(LW + LH + WH).

Statement One Alone:

Without loss of generality, we can let L and W be 5. So, in terms of H, we have V = LWH = 5 x 5 x H = 25H, and A = 2(LW + LH + WH) = 2(5 x 5 + 5H + 5H) = 10(5 + 2H). Therefore, V/A = 25H/[10(5 + 2H)] = 5H/[2(5 + 2H)]. Notice that the value of the ratio changes as the value of H changes. For example, if H = 1, V/A = 5/14. However, if H = 2, V/A = 10/18 = 5/9. Statement one alone is not sufficient.

Statement Two Alone:

We can let L = W = H = s. So, in terms of s, we have V = LWH = s x s x s = s^3, and A = 2(LW + LH + WH) = 2(s x s + s x s + s x s) = 6s^2. Therefore, V/A = s^3 / 6s^2 = s/6. Notice again that the value of the ratio changes as the value of s changes. For example, if s = 1, V/A = 1/6. However, if s = 2, V/A = s/6 = 1/3. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we see that L = W = H = 5. From statement two, we have V/A = s/6. Therefore, s = 5 yields V/A = 5/6. Both statements together are sufficient.

Answer: C
_________________

Answer: Option C

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Do not kill your time
we know
V= LWH
A= 2(LW+LH+WH)
1) given 2 sides = 5 but no information about third so insufficient (AD out)
2) all sides are equal but value is not given so insufficient (B also out)
Combine
L= W= H=5 NOW all information are given we can determine value
And (c)

Posted from my mobile device

V=LWH, A = 2(LH+WH+LW) | V/A = LWH/2(LH+WH+LW) = ?

1. 2 of L, W, H is 5.
either of the two is 5. Can't be solved. (Insufficient)

2. all are same, say x
putting values in V/A = x/6. (Insufficient)

Combining 1 and 2, we get 5/6. And C.