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# M12-32

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:48
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Difficulty:

95% (hard)

Question Stats:

34% (01:10) correct 66% (01:16) wrong based on 144 sessions

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If $$x^3*y^4 = 2000$$, what is $$y$$?

(1) $$x$$ is an integer.

(2) $$y$$ is an integer.

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15 Sep 2014, 23:48
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Official Solution:

Each statement alone is insufficient. When considering them together we have: $$x^3*y^4 = 5^3*2^4=2000$$, but since $$y$$ is in even power, it can be 2 as well as -2. Not sufficient.

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04 Aug 2016, 04:12
I think this is a high-quality question and I agree with explanation.
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15 Aug 2016, 04:12
I think this is a high-quality question and I agree with explanation. good question
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30 Aug 2016, 06:21
great question, so tricky
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09 Sep 2016, 05:26
Bunuel wrote:
Official Solution:

Each statement alone is insufficient. When considering them together we have: $$x^3*y^4 = 5^3*2^4=2000$$, but since $$y$$ is in even power, it can be 2 as well as -2. Not sufficient.

Thanks for the explanation, Banuel. Do you happen to know the source of the question?
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09 Sep 2016, 06:30
Bunuel wrote:
Official Solution:

Each statement alone is insufficient. When considering them together we have: $$x^3*y^4 = 5^3*2^4=2000$$, but since $$y$$ is in even power, it can be 2 as well as -2. Not sufficient.

Hi Bunuel! could you please expand your explanation? I don't understand why A and B are not sufficient alone.
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09 Sep 2016, 06:53
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No matter what x is, y could be positive or negative. Unless we get more information on y's sign, we can't know the answer. y being an integer doesn't tell us its sign.
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06 Oct 2016, 12:40
Can anyone show the insufficiency for Statement A and B individually?
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06 Oct 2016, 23:42
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Keats wrote:
Can anyone show the insufficiency for Statement A and B individually?

For (1) if x = 1, then $$y=\sqrt[4]{2000}$$ or $$y=-\sqrt[4]{2000}$$.

For (2) consider y=1 or y=-1.
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08 Nov 2016, 03:39
Hello,

In statement no. 2 ,
y^4= 2000/ x^3

Here x should be 5,

So, y^4=2^4

y should be 2 as per GMAT rules as root value is always taken as positive.

What is wrong with my analysis.
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08 Nov 2016, 03:50
Sumanth8492 wrote:
Hello,

In statement no. 2 ,
y^4= 2000/ x^3

Here x should be 5,

So, y^4=2^4

y should be 2 as per GMAT rules as root value is always taken as positive.

What is wrong with my analysis.

y^4 = 16
This means y=2 or -2 only!
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08 Nov 2016, 05:40
Sumanth8492 wrote:
Hello,

In statement no. 2 ,
y^4= 2000/ x^3

Here x should be 5,

So, y^4=2^4

y should be 2 as per GMAT rules as root value is always taken as positive.

What is wrong with my analysis.

When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt[4]{x}$$, then the only accepted answer is the positive root.

That is, $$\sqrt{16}=4$$, NOT +4 or -4. Even roots have only a positive value on the GMAT.

Odd roots have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

In contrast, the equation $$x^2=16$$ has TWO solutions, +4 and -4.
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03 Jan 2017, 10:03
How do you determine that x is 5 and y is 2? Trial and error?
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04 Jan 2017, 00:19
Cez005 wrote:
How do you determine that x is 5 and y is 2? Trial and error?

Since both x and y ate integers then from x^3*y^4 = 5^3*2^4=2000 we can get that x is 5 and y is 2 or -2 (because of even power).
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05 Jan 2017, 09:37
Great Question!!
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07 May 2017, 09:34
Great question
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11 Jun 2017, 01:15
Bunuel

Does it matter if x & y are integers or not in this type of question (not this question in particular, but this type of question).
Let's assume the question states that x & y are both positive, does it make a difference if the question does not specify that x & y are integers? Thanks!
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12 Jun 2017, 03:29
kerin wrote:
Bunuel

Does it matter if x & y are integers or not in this type of question (not this question in particular, but this type of question).
Let's assume the question states that x & y are both positive, does it make a difference if the question does not specify that x & y are integers? Thanks!

Generally it makes a HUGE difference whether a variable is an integer or not. Answers to many GMAT questions would change if alter this important detail.
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14 Jun 2017, 20:02
Superb question!
Easy to forget that 2 and -2 both have to be considered.
Re: M12-32 &nbs [#permalink] 14 Jun 2017, 20:02

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# M12-32

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