CRE 2 - Maximum / Minimum cuts | LR - Cubes

Answer: 7

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Explanation :

When a certain number of pieces are obtained by cutting a cube:

We would have maximum cuts when all the cuts are made along the same axis, and

Minimum cuts when cuts are made as equally as possible along the three axes.

Here, we have 8 smaller pieces,

∴ maximum cuts would be obtained when we have all cuts along same axis.

∴ maximum number of cuts will be (8 – 1) = 7 cuts.

Hence, 7.

Answer: 3

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Explanation :

When a certain number of pieces are obtained by cutting a cube:

We would have maximum cuts when all the cuts are made along the same axis, and

Minimum cuts when cuts are made as equally as possible along the three axes.

Here, we have 8 smaller pieces,

∴ minimum cuts would be obtained when we have equal number of pieces along all 3 axes.

∴ 8 = 2 × 2 × 2.

⇒ 2 pieces along each axis.

⇒ 1 cut along each axis

∴ 3 cuts total.

Hence, 3.

Answer: 6

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Explanation :

Here, we have 27 smaller pieces,

∴ Minimum cuts would be obtained when we have equal number of pieces along all 3 axes.

∴ 27 = 3 × 3 × 3

⇒ 3 pieces along each axis.

⇒ 2 cuts along each axis

∴ 6 cuts total.

Hence, 6.

Answer: 9

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Explanation :

Here, we have 64 smaller pieces,

∴ Minimum cuts would be obtained when we have equal number of pieces along all 3 axes.

∴ 64 = 4 × 4 × 4

⇒ 4 pieces along each axis.

⇒ 3 cuts along each axis

∴ 9 cuts total.

Hence, 9.

Answer: 21

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Explanation :

Here, we have 512 smaller pieces,

∴ Minimum cuts would be obtained when we have equal number of pieces along all 3 axes.

∴ 512 = 8 × 8 × 8

⇒ 8 pieces along each axis.

⇒ 7 cuts along each axis

∴ 21 cuts total.

Hence, 21.

Answer: 11

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Explanation :

Here, we have 100 smaller pieces,

∴ Minimum cuts would be obtained when we have pieces distributed as equally as possible along all 3 axes.

∴ 100 = 5 × 5 × 4

⇒ 5, 5, and 4 pieces along the three axes.

⇒ 4, 4 and 3 cuts along the three axes.

∴ 11 cuts total.

Hence, 11.

Answer: 27

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Explanation :

Here, we have 990 smaller pieces,

∴ Minimum cuts would be obtained when we have pieces distributed as equally as possible along all 3 axes.

∴ 990 = 9 × 10 × 11

⇒ 9, 10, and 11 piece along the three axes.

⇒ 8, 9 and 10 cuts along the three axes.

∴ 27 cuts total.

Hence, 27.

Answer: 72

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Explanation :

Here, we have 73 smaller pieces,

∴ Minimum cuts would be obtained when we have pieces distributed as equally as possible along all 3 axes.

∴ 73 = 73 × 1 × 1

⇒ 73, 1, and 1 piece along the three axes.

⇒ 72, 0 and 0 cuts along the three axes.

∴ 72 cuts total.

Note: There is only 1 way you can cut a cube to get 73 pieces, i.e., make 72 cuts along the same axis.

Hence, 72.

Answer: 18

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Explanation :

Here, we have 73 smaller cubes.

Since the smaller pieces are also cubes, this is possible only when equal number of pieces are obtained along each axis.

∴ 343 = 7 × 7 × 7

⇒ 7, 7, and 7 pieces along the three axes.

⇒ 6, 6 and 6 cuts along the three axes.

∴ 18 cuts total.

Hence, 18.

Answer: Option D

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Explanation :

Here, we have 180 smaller cubes.

Since the smaller pieces are also cubes, this is possible only when equal number of pieces are obtained along each axis.

∴ 180 is not a perfect cube hence, such a case is not possible.

Hence, option (d).