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M12-32

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Bunuel
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M12-32 [#permalink] New post  16 Sep 2014, 00:48
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36% (01:32) correct 64% (01:48) wrong based on 146 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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Bunuel
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Re M12-32 [#permalink] New post  16 Sep 2014, 00:48
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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.


Answer: E
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Senthil7
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Re: M12-32 [#permalink] New post  04 Aug 2016, 05:12
I think this is a high-quality question and I agree with explanation.
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Re: M12-32 [#permalink] New post  15 Aug 2016, 05:12
I think this is a high-quality question and I agree with explanation. good question
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Re: M12-32 [#permalink] New post  30 Aug 2016, 07:21
great question, so tricky
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Re: M12-32 [#permalink] New post  09 Sep 2016, 06:26
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.


Answer: E


Thanks for the explanation, Banuel. Do you happen to know the source of the question?
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RodrigoMi
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Re: M12-32 [#permalink] New post  09 Sep 2016, 07:30
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.


Answer: E


Hi Bunuel! could you please expand your explanation? I don't understand why A and B are not sufficient alone.
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Re: M12-32 [#permalink] New post  09 Sep 2016, 07:53
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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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Re: M12-32 [#permalink] New post  06 Oct 2016, 13:40
Can anyone show the insufficiency for Statement A and B individually?
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Re: M12-32 [#permalink] New post  07 Oct 2016, 00:42
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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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Re: M12-32 [#permalink] New post  08 Nov 2016, 04:39
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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Re: M12-32 [#permalink] New post  08 Nov 2016, 04:50
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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Re: M12-32 [#permalink] New post  08 Nov 2016, 06:40
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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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Re: M12-32 [#permalink] New post  03 Jan 2017, 11:03
How do you determine that x is 5 and y is 2? Trial and error?
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Re: M12-32 [#permalink] New post  04 Jan 2017, 01:19
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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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Re: M12-32 [#permalink] New post  05 Jan 2017, 10:37
Great Question!!
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Re: M12-32 [#permalink] New post  07 May 2017, 10:34
Great question
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Re: M12-32 [#permalink] New post  11 Jun 2017, 02:15
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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Re: M12-32 [#permalink] New post  12 Jun 2017, 04:29
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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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Re: M12-32 [#permalink] New post  14 Jun 2017, 21:02
Superb question!
Easy to forget that 2 and -2 both have to be considered.
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