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# If x is an integer greater than 1, is x equal to the 12th

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Manager
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Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]

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13 Dec 2016, 11:28
can the answer not be as simple as - to be the 12th power of an integer, x would need to be the 3rd power and 4th power as well. Since individually the statements do not tell us this information, if we combine we get that x= m^12. Experts could you please let me know if this approach is wrong.

Thanks.

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Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]

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23 Feb 2017, 06:01
Prompt Analysis
x is an integer.

Superset
The answer to this question will be either yes or no.

Translation
In order to know if x = p^12, we need:
1# exact value of p or x
2# any property or equation to infer the statement.

Statement analysis

St 1: x =a^3. Insufficient as a may or may not be the form of b^4. Hence option a, d eliminated.
St 2: x = c^4. Insufficient as a may or may not be the form of d^4. Hence b is eliminated.

St 1 & St 2: LCM of 4 and 3 is 12. Hence x is an integer to the power 12. Option C.

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Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]

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08 Nov 2017, 09:32
Hi, I need some help.

I follow the above posts on (i) and (ii) as not sufficient. However, I am struggling with a case where, if true, leads to the answer E, not C:

If $$x=m^3=n^4$$, where $$m=2^8$$ and $$n=2^6$$, then

$$x=(2^8)^3=(2^6)^4=2^{24}$$ which does NOT equal $$2^{12}$$; NOT SUFFICIENT

But where where $$m=2^4$$ and $$n=2^3$$, then

$$x=(2^4)^3=(2^3)^4=2^{12}$$, SUFFICIENT

How is my thinking flawed here?

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Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]

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08 Nov 2017, 09:44
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Expert's post
DanielAustin wrote:
Hi, I need some help.

I follow the above posts on (i) and (ii) as not sufficient. However, I am struggling with a case where, if true, leads to the answer E, not C:

If $$x=m^3=n^4$$, where $$m=2^8$$ and $$n=2^6$$, then

$$x=(2^8)^3=(2^6)^4=2^{24}$$ which does NOT equal $$2^{12}$$; NOT SUFFICIENT

But where where $$m=2^4$$ and $$n=2^3$$, then

$$x=(2^4)^3=(2^3)^4=2^{12}$$, SUFFICIENT

How is my thinking flawed here?

If $$x=2^{24}$$ it's still is the 12th power of an integer: $$x=2^{24}=4^{12}$$
_________________

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Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]

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12 Nov 2017, 08:42
bhupi wrote:
If x is an integer greater than 1, is x equal to the 12th power of an integer ?

(1) x is equal to the 3rd Power of an integer

(2) x is equal to the 4th Power of an integer.

We are given that x is an integer greater than 1 and must determine whether x is equal to the 12th power of an integer.

Statement One Alone:

x is equal to the 3rd power of an integer.

Using the information in statement one, we cannot determine whether x is equal to the 12th power of an integer. For example, if x = 8 = 2^3, then it’s not equal to the 12th power of an integer. However, if x = (2^4)^3 = 2^12, then it is equal to the 12th power of an integer. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x is equal to the 4th power of an integer

Using the information in statement two, we cannot determine whether x is equal to the 12th power of an integer. For example, if x = 16 = 2^4, then it’s not equal to the 12th power of an integer. However, if x = (2^3)^4 = 2^12, then it is equal to the 12th power of an integer. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the information from statements one and two, we know that x is equal to the 3rd power of an integer and that x is also equal to the 4th power of some other integer. Let’s represent x as a^3 where a is an integer > 1. Since a^3 is also a 4th power, the 4th root of a^3 is an integer. The only way this could happen is if a is also the 4th power of an integer; in other words, a by itself is a 4th power, say a = b^4 where b is an integer > 1.

Thus, x = a^3 = (b^4)^3 = b^12. Therefore, x is equal to the 12th power of an integer.

_________________

Jeffery Miller

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Re: If x is an integer greater than 1, is x equal to the 12th   [#permalink] 12 Nov 2017, 08:42

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