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705-805 (Hard)|   Geometry|      
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EgmatQuantExpert
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In the rectangular solid above, if each dimension of the solid is an Updated on: 03 Jun 2019, 01:08
Originally posted by EgmatQuantExpert on 28 Feb 2017, 03:52.
Last edited by Bunuel on 03 Jun 2019, 01:08, edited 2 times in total.
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In the rectangular solid above, if each dimension of the solid is an integer, what is the volume of the solid?

    (1) The area of two sides of the rectangular solid is 4 and 20 respectively
    (2) The area of two sides of the rectangular solid is 4 and 5 respectively.


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In the rectangular solid above, if each dimension of the solid is an Updated on: 19 Mar 2017, 06:46
Originally posted by EgmatQuantExpert on 28 Feb 2017, 03:54.
Last edited by EgmatQuantExpert on 19 Mar 2017, 06:46, edited 1 time in total.
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The official solution has been posted. Looking forward to a healthy discussion..:)
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Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
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In the rectangular solid above, if each dimension of the solid is an 01 Mar 2017, 06:42
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(1) ab = 4; bc = 20
Different options are feasible, thus the volume of solid in all cases would be different, i.e.
a=1;b=4;c=5 V= 20
a=2;b=2;c=10 V= 40
Hence, insuff.
(2) ab=4; ac=5
Since question stem tells us that dims of all sides of solid are integers, then only one option satisfies both this requirement and (2):
a=1;b=4;c=5 V=20
Sufficient.

I suppose that it is the so-called "c-trap" problem as from the first sight it is really tempting to pick C and save time on reasoning, however that would be incorrect.
MathRevolution described GMAT's common traps in one of the topics related to quant score improvement, here is the link, I personally learned a lot from it, hope it would be useful for anybody.
https://gmatclub.com/forum/the-ultimate ... 09801.html



Answer B.
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In the rectangular solid above, if each dimension of the solid is an 19 Mar 2017, 06:45
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Official Solution




Steps 1 & 2: Understand Question and Draw Inferences



Let the length, breadth, and height of the rectangular solid be L, B and H respectively.

We are given that L, B, H are integers.

We need to find the volume of the solid, that is, the value of the product LBH.


Step 3: Analyze Statement 1 independently



Statement 1 states that "The area of two sides of the rectangular solid is 4 and 20 respectively
    Let the two sides whose area is 4 be B and L, and the two sides whose area is 20 be B and H.
    So, we can write: B*L = 4
    In how many ways can 4 be expressed as a product of 2 numbers?
    We can write 4 = 1*4 or 2*2
    This means (B,L) are either (1,4) or (2,2)

Let’s now analyze the second piece of information given in St. 1
    B*H = 20 = 1*20 = 2*10 = 4*5
    This means (B,H) are either (1,20) or (2,10) or (4,5)

Note that the pairs of sides (B,L) and (B,H) share one dimension – B.
Applying this constraint on the possible values of (B,L) and (B,H) deduced above, we get:
    (B,L,H) = (1,4,20) and Volume = 1 * 4 * 20 = 80
    OR
    (B,L,H) = (2,2,10) and Volume = 2 * 2* 10 = 40
    OR
    (B,L,H) = (4,1,5) and Volume - 4 * 1 * 5 =20

Since we’ve not been able to determine a unique value of the volume, Statement 1 alone is not sufficient.



Step 4: Analyze Statement 2 independently



Statement 2 states that: The area of two sides of the rectangular solid is 4 and 5 respectively.

    Let the two sides whose area is 4 be B and L, and the two sides whose area is 5 be L and H.
    So, we can write: L*B = 4 = 1*4 = 2*2
      This means (L,B) is either (1,4) or (2,2)
    Also, L*H = 5 = 1*5
    Since 5 is a prime number, it can only be expressed as a product of 1 and 5 itself.
      This means (L, H) = (1,5)
    Now, the pairs of sides (L,B) and (L,H) share one dimension – L
    Applying this constraint on the possible values of (L,B) and (H,L) deduced above, we get:
      L = 1, H = 5 and B = 4
      Therefore, LBH = 1*4*5 = 20

Since Statement 2 leads us to a unique value of the volume of the solid, it is sufficient.

Hence the correct answer is Option B .

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Saquib
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