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# For all positive numbers x, Δx is defined as the cube root of x, and ∇

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Math Expert
Joined: 02 Sep 2009
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For all positive numbers x, Δx is defined as the cube root of x, and ∇  [#permalink]

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22 Aug 2018, 03:12
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:20) correct 24% (01:59) wrong based on 49 sessions

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For all positive numbers x, Δx is defined as the cube root of x, and ∇x is defined as the square root of x. If ∇(Δk)=m^2 , then k =

A. m^(12/5)

B. m^6

C. m^12

D. m^36

E. m^64

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For all positive numbers x, Δx is defined as the cube root of x, and ∇  [#permalink]

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22 Aug 2018, 03:18
1
Bunuel wrote:
For all positive numbers x, Δx is defined as the cube root of x, and ∇x is defined as the square root of x. If ∇(Δk)=m^2 , then k =

A. m^(12/5)

B. m^6

C. m^12

D. m^36

E. m^64

Best way to go about doing this problem is to substitute a value for $$m$$. Let $$m = 2$$

Therefore, we have to find the value of ∇(Δk) = $$m^2$$ or 4

$$4(2^2)$$ is the cube root of $$4*4*4 = 64(2^6)$$, which the square root of $$64*64 = 4096(2^{12})$$

Substituting the values in the answer options, we arrive at the value of k which is $$m^{12}$$ (Option C)
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For all positive numbers x, Δx is defined as the cube root of x, and ∇  [#permalink]

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22 Aug 2018, 03:23
1
Bunuel wrote:
For all positive numbers x, Δx is defined as the cube root of x, and ∇x is defined as the square root of x. If ∇(Δk)=m^2 , then k =

A. m^(12/5)

B. m^6

C. m^12

D. m^36

E. m^64

$$∇(Δk)=m^2$$
Or,$$∇(k^{\frac{1}{3}})=m^2$$
Or, $$(k^{\frac{1}{3}})^{\frac{1}{2}}=m^2$$
Or, $$k^{\frac{1}{2}*\frac{1}{3}}=m^2$$
Or, $$k^{\frac{1}{6}}=m^2$$
Or,$$k=(m^2)^6=m^{12}$$

Ans. (C)
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For all positive numbers x, Δx is defined as the cube root of x, and ∇ &nbs [#permalink] 22 Aug 2018, 03:23
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