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# A box measuring 11 inches by 10 inches by 7 inches is filled with soli

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A box measuring 11 inches by 10 inches by 7 inches is filled with soli  [#permalink]

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22 Feb 2017, 04:14
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Difficulty:

45% (medium)

Question Stats:

52% (01:18) correct 48% (01:46) wrong based on 63 sessions

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A box measuring 11 inches by 10 inches by 7 inches is filled with solid wooden cubical blocks, each measuring 3 inches per side. How many wooden blocks can fit into the box?

A. 18
B. 27
C. 28
D. 29
E. 54

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Re: A box measuring 11 inches by 10 inches by 7 inches is filled with soli  [#permalink]

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22 Feb 2017, 04:24
C
Integral value of (11*7*10)/(27) gives 28

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Re: A box measuring 11 inches by 10 inches by 7 inches is filled with soli  [#permalink]

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22 Feb 2017, 04:30
Option A

:Size of box - L =11, W = 10 & H =7. To be filled with wooden cubes of side 3 (l = w = h 3).

: Can start with putting cubes one over another - max number of cubes which can be put together in this pattern = 2 (total h = 3 + 3 = 6, which is constrained by the height H, of box = 7)

: Now, this set of 2 cubes (one over other) can be placed together, max number of such sets which can be put together along the length = 3 (total l of cubes = =3*3 = 9, which is constrained by the length L, of box = 11)

: Similarly, these sets can be placed along the width, max number of such sets which can be put together along the width = 3 (total w of cubes = =3*3 = 9, which is constrained by the width W, of box = 10)

Total number wooden cubes = 2*3*3 = 18
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A box measuring 11 inches by 10 inches by 7 inches is filled with soli  [#permalink]

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22 Feb 2017, 04:37

Box = 11 by 10 by 7
Cubes = 3 by 3 by 3
Number of Cubes = 3 * 3 * 2 [ (11/3) * (10/3) * (7/3) ] Only integer wholes
Number of Cubes =18
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Re: A box measuring 11 inches by 10 inches by 7 inches is filled with soli  [#permalink]

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22 Feb 2017, 04:49
Spartan85 wrote:

Box = 11 by 10 by 7
Cubes = 3 by 3 by 3
Number of Cubes = 3 * 3 * 2 [ (11/3) * (10/3) * (7/3) ] Only integer wholes
Number of Cubes =18

How did u arrive at ds??
Any formulae

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Re: A box measuring 11 inches by 10 inches by 7 inches is filled with soli  [#permalink]

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22 Feb 2017, 04:58
2
No formula. One cannot fit fractional cubes at the end (you would need to visualize). If it would have been a fluid, then Box volume divided by volume would have sufficed.
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Re: A box measuring 11 inches by 10 inches by 7 inches is filled with soli  [#permalink]

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07 Mar 2017, 17:27
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Bunuel wrote:
A box measuring 11 inches by 10 inches by 7 inches is filled with solid wooden cubical blocks, each measuring 3 inches per side. How many wooden blocks can fit into the box?

A. 18
B. 27
C. 28
D. 29
E. 54

Official solution from Veritas Prep.

This problem is tricky because you must think about it logically BEFORE you do the math. Mathematically, you can quickly calculate $$11∗10∗7=770$$. Each cube has a volume of $$3∗3∗3=27$$. This problem invites you to do the math $$\frac{770}{27}=28.5$$. And if you've done that, choices C and D are waiting for you to determine whether to round up or down.

HOWEVER, you should not do the math before logically setting up the problem. Since you have solid wooden blocks, you will not be able to fit blocks across all levels. For instance, if one side measures 7 inches, only two blocks can fit. There will be 1 inch of wasted space. You will get only three blocks on each of the two remaining sides. Consequently, you will be able to fit $$2∗3∗3=18$$ blocks inside the box.
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Re: A box measuring 11 inches by 10 inches by 7 inches is filled with soli  [#permalink]

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08 Mar 2017, 03:58
1
1
under 11 inches multiple of 3 that fits is 9
under 10 inches multiple of 3 that fits is 9
under 7 inches multiple of 3 that fits is 6

hence the volume covered by blocks = 9*9*6
volume per block = 3*3*3
therefore, number of volume = 9*9*6/3*3*3 = 3*3*2 = 18

Option A
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Re: A box measuring 11 inches by 10 inches by 7 inches is filled with soli  [#permalink]

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25 Mar 2019, 15:32
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Re: A box measuring 11 inches by 10 inches by 7 inches is filled with soli   [#permalink] 25 Mar 2019, 15:32
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