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What is the value of y? [#permalink]
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24 Jun 2016, 08:21
Question Stats:
29% (01:22) correct 71% (01:27) wrong based on 356 sessions
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What is the value of y? (1) \(3y1=\sqrt{(8y^24y+9)}\) (2) \(y^2–2y–8 = 0\)
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Re: What is the value of y? [#permalink]
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24 Jun 2016, 09:20
Yes the ans is A... This is a brilliant question from Magoosh... Below is the OE.. Using a tried and true DS strategy, start with the easier statement, Statement #2.
Statement #2:
(y – 4)(y + 2) = 0
y = +4 or y = –2
Since there are two values of y, this statement, alone and by itself, is not sufficient.
Statement #1:
This is an equation with a radical. The radical is already isolated, so square both sides.
(3y – 1)2 = 8y2 – 4y + 9
9y2 – 6y + 1 = 8y2 – 4y + 9
y2 – 2y – 8 = 0
Lo and behold! We have arrived at the same equation we found in Statement #2, with solutions y = +4 or y = –2. The naïve conclusion would be—this statement says exactly the same thing as the other. That's incorrect, though, because we don't know whether both of these values are valid solutions, or whether one or more is an extraneous root. We need to test this in the original equation.
Test y = +4 on equation 3y1=√(8y^24y+9) LHS=RHS
Test y = –2 on equation 3y1=√(8y^24y+9)
The LHS and RHS are not equal, so this does not check! This value, y = –2, is an extraneous root.
(NB: it's often the case that an extraneous root will make the two sides equal to values equal in absolute value and opposite in sign.)
Thus, the equation given in Statement #1 has only one solution, y = 4, so this equation provides a definitive answer to the prompt question. This statement, alone and by itself, is sufficient.
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Re: What is the value of y? [#permalink]
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24 Jun 2016, 21:02
anurag16 wrote: Yes the ans is A... This is a brilliant question from Magoosh... Below is the OE.. Using a tried and true DS strategy, start with the easier statement, Statement #2.
Statement #2:
(y – 4)(y + 2) = 0
y = +4 or y = –2
Since there are two values of y, this statement, alone and by itself, is not sufficient.
Statement #1:
This is an equation with a radical. The radical is already isolated, so square both sides.
(3y – 1)2 = 8y2 – 4y + 9
9y2 – 6y + 1 = 8y2 – 4y + 9
y2 – 2y – 8 = 0
Lo and behold! We have arrived at the same equation we found in Statement #2, with solutions y = +4 or y = –2. The naïve conclusion would be—this statement says exactly the same thing as the other. That's incorrect, though, because we don't know whether both of these values are valid solutions, or whether one or more is an extraneous root. We need to test this in the original equation.
Test y = +4 on equation 3y1=√(8y^24y+9) LHS=RHS
Test y = –2 on equation 3y1=√(8y^24y+9)
The LHS and RHS are not equal, so this does not check! This value, y = –2, is an extraneous root.
(NB: it's often the case that an extraneous root will make the two sides equal to values equal in absolute value and opposite in sign.)
Thus, the equation given in Statement #1 has only one solution, y = 4, so this equation provides a definitive answer to the prompt question. This statement, alone and by itself, is sufficient. Hi , Given : y=2 placing the values you get : 7 = sqrt(49) , this is possible y = 4 you get 11 = sqrt(121) So how can statement A be sufficient ??
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Re: What is the value of y? [#permalink]
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24 Jun 2016, 21:50
anurag16 wrote: Yes the ans is A... This is a brilliant question from Magoosh... Below is the OE.. Using a tried and true DS strategy, start with the easier statement, Statement #2.
Statement #2:
(y – 4)(y + 2) = 0
y = +4 or y = –2
Since there are two values of y, this statement, alone and by itself, is not sufficient.
Statement #1:
This is an equation with a radical. The radical is already isolated, so square both sides.
(3y – 1)2 = 8y2 – 4y + 9
9y2 – 6y + 1 = 8y2 – 4y + 9
y2 – 2y – 8 = 0
Lo and behold! We have arrived at the same equation we found in Statement #2, with solutions y = +4 or y = –2. The naïve conclusion would be—this statement says exactly the same thing as the other. That's incorrect, though, because we don't know whether both of these values are valid solutions, or whether one or more is an extraneous root. We need to test this in the original equation.
Test y = +4 on equation 3y1=√(8y^24y+9) LHS=RHS
Test y = –2 on equation 3y1=√(8y^24y+9)
The LHS and RHS are not equal, so this does not check! This value, y = –2, is an extraneous root.
(NB: it's often the case that an extraneous root will make the two sides equal to values equal in absolute value and opposite in sign.)
Thus, the equation given in Statement #1 has only one solution, y = 4, so this equation provides a definitive answer to the prompt question. This statement, alone and by itself, is sufficient. How can you say that for value y=4 11 = √121 since the value can be +11 or 11 for √121 Moreover there are other values for y which satisfy the equation like 7 = √ 49. So how can value for y be uniquely determined by both the equations put together hence E. Both statements are not sufficient. Sent from my A114 using GMAT Club Forum mobile app



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Re: What is the value of y? [#permalink]
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Updated on: 24 Jun 2016, 23:04
ashwini86 wrote: anurag16 wrote: Yes the ans is A... This is a brilliant question from Magoosh... Below is the OE.. Using a tried and true DS strategy, start with the easier statement, Statement #2.
Statement #2:
(y – 4)(y + 2) = 0
y = +4 or y = –2
Since there are two values of y, this statement, alone and by itself, is not sufficient.
Statement #1:
This is an equation with a radical. The radical is already isolated, so square both sides.
(3y – 1)2 = 8y2 – 4y + 9
9y2 – 6y + 1 = 8y2 – 4y + 9
y2 – 2y – 8 = 0
Lo and behold! We have arrived at the same equation we found in Statement #2, with solutions y = +4 or y = –2. The naïve conclusion would be—this statement says exactly the same thing as the other. That's incorrect, though, because we don't know whether both of these values are valid solutions, or whether one or more is an extraneous root. We need to test this in the original equation.
Test y = +4 on equation 3y1=√(8y^24y+9) LHS=RHS
Test y = –2 on equation 3y1=√(8y^24y+9)
The LHS and RHS are not equal, so this does not check! This value, y = –2, is an extraneous root.
(NB: it's often the case that an extraneous root will make the two sides equal to values equal in absolute value and opposite in sign.)
Thus, the equation given in Statement #1 has only one solution, y = 4, so this equation provides a definitive answer to the prompt question. This statement, alone and by itself, is sufficient. Hi , Given : y=2 placing the values you get : 7 = sqrt(49) , this is possible y = 4 you get 11 = sqrt(121) So how can statement A be sufficient ?? Hi ashwini86, y=2 will give 7 on LHS and 7 on RHS As the LHS will not be equal to RHS so 2 will not be a valid root. So it will have only one root i.e. only one value of y=4
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Originally posted by GGMU on 24 Jun 2016, 21:52.
Last edited by GGMU on 24 Jun 2016, 23:04, edited 1 time in total.



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Re: What is the value of y? [#permalink]
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24 Jun 2016, 22:55
anurag16 wrote: ashwini86 wrote: anurag16 wrote: Yes the ans is A... This is a brilliant question from Magoosh... Below is the OE.. Using a tried and true DS strategy, start with the easier statement, Statement #2.
Statement #2:
(y – 4)(y + 2) = 0
y = +4 or y = –2
Since there are two values of y, this statement, alone and by itself, is not sufficient.
Statement #1:
This is an equation with a radical. The radical is already isolated, so square both sides.
(3y – 1)2 = 8y2 – 4y + 9
9y2 – 6y + 1 = 8y2 – 4y + 9
y2 – 2y – 8 = 0
Lo and behold! We have arrived at the same equation we found in Statement #2, with solutions y = +4 or y = –2. The naïve conclusion would be—this statement says exactly the same thing as the other. That's incorrect, though, because we don't know whether both of these values are valid solutions, or whether one or more is an extraneous root. We need to test this in the original equation.
Test y = +4 on equation 3y1=√(8y^24y+9) LHS=RHS
Test y = –2 on equation 3y1=√(8y^24y+9)
The LHS and RHS are not equal, so this does not check! This value, y = –2, is an extraneous root.
(NB: it's often the case that an extraneous root will make the two sides equal to values equal in absolute value and opposite in sign.)
Thus, the equation given in Statement #1 has only one solution, y = 4, so this equation provides a definitive answer to the prompt question. This statement, alone and by itself, is sufficient. Hi , Given : y=2 placing the values you get : 7 = sqrt(49) , this is possible y = 4 you get 11 = sqrt(121) So how can statement A be sufficient ?? Hi ashwini86, y=2 will give 7 on LHS and 7 on RHS As the LHS will not be equal to RHS so 2 will not be a valid root. So it will have only one root i.e. only one value of y=4 Hi anurag 16, Is the sqrt of a perfect square treated as positive value by default? If yes then A can be the solution ashwini86 wrote: anurag16 wrote: Yes the ans is A... This is a brilliant question from Magoosh... Below is the OE.. Using a tried and true DS strategy, start with the easier statement, Statement #2.
Statement #2:
(y – 4)(y + 2) = 0
y = +4 or y = –2
Since there are two values of y, this statement, alone and by itself, is not sufficient.
Statement #1:
This is an equation with a radical. The radical is already isolated, so square both sides.
(3y – 1)2 = 8y2 – 4y + 9
9y2 – 6y + 1 = 8y2 – 4y + 9
y2 – 2y – 8 = 0
Lo and behold! We have arrived at the same equation we found in Statement #2, with solutions y = +4 or y = –2. The naïve conclusion would be—this statement says exactly the same thing as the other. That's incorrect, though, because we don't know whether both of these values are valid solutions, or whether one or more is an extraneous root. We need to test this in the original equation.
Test y = +4 on equation 3y1=√(8y^24y+9) LHS=RHS
Test y = –2 on equation 3y1=√(8y^24y+9)
The LHS and RHS are not equal, so this does not check! This value, y = –2, is an extraneous root.
(NB: it's often the case that an extraneous root will make the two sides equal to values equal in absolute value and opposite in sign.)
Thus, the equation given in Statement #1 has only one solution, y = 4, so this equation provides a definitive answer to the prompt question. This statement, alone and by itself, is sufficient. Hi , Given : y=2 placing the values you get : 7 = sqrt(49) , this is possible y = 4 you get 11 = sqrt(121) So how can statement A be sufficient ?? Sent from my A114 using GMAT Club Forum mobile app



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Re: What is the value of y? [#permalink]
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24 Jun 2016, 23:01
Hi ShreyasCM Suppose we have x^2=49 we will have two roots +7 and 7 because both these values will satisfy the equation. However, if we talk about only sqrt49 as an individual identity we will only get +7 as the solution. I hope it's clear now why we A option is sufficient.
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Re: What is the value of y? [#permalink]
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07 Sep 2017, 01:02
well, there is a trap of y >= 1/3, right?



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Re: What is the value of y? [#permalink]
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07 Sep 2017, 01:20
1) (3y1)= √(8y^24y+9) squaring both sides 9y^2+16y = 8y^24y+9 y^22y8=0 (y4)(y+2) =0 y=4 or y=2 but y= 2 not possible as RHS √ (8y^24y+9) will always be positive, but y=2 makes LHS negative so single deifinite ans y=4. so A or D 2) y^22y8=0 (y4)(y+2) =0 y=4 or y=2 Multiple Ans => D eliminated A is the Ans
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Re: What is the value of y? [#permalink]
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07 Sep 2017, 02:02



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Re: What is the value of y? [#permalink]
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07 Sep 2017, 05:10
chesstitans wrote: well, there is a trap of y >= 1/3, right? chesstitansYou can see my solution, No need to assume y>=1/3 just whatever value of y you calculate should make LHS positive. Hope you find this useful.
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Re: What is the value of y? [#permalink]
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04 Oct 2017, 10:53
sahilvijay wrote: 1) (3y1)= √(8y^24y+9) squaring both sides 9y^2+16y = 8y^24y+9 y^22y8=0 (y4)(y+2) =0 y=4 or y=2 but y= 2 not possible as RHS √ (8y^24y+9) will always be positive, but y=2 makes LHS negative so single deifinite ans y=4. so A or D
2) y^22y8=0 (y4)(y+2) =0 y=4 or y=2 Multiple Ans => D eliminated
A is the Ans can you explain why the RHS will always be positive ?



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Re: What is the value of y? [#permalink]
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04 Oct 2017, 11:31
Kunal  RHS HAS A square root which is always positive Posted from my mobile device
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Re: What is the value of y?
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