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If x=3/4 and y=1/5, what is the value of sqrt(x^2 + 6x + 9) [#permalink]
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24 Jul 2007, 22:46
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If x=3/4 and y=1/5, what is the value of sqrt(x^2 + 6x + 9)  sqrt(y^2  2y + 1) ?
(a)91/20
(b)59/20
(c)47/20
(d)15/4
(e)14/5
So sorry, I had to edit my Question. Please support your answers with explanations.
Last edited by ajay_gmat on 25 Jul 2007, 02:52, edited 1 time in total.



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Re: Deceptive algebra Q [#permalink]
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24 Jul 2007, 23:26
ajay_gmat wrote: If x=3/4 and y=1/5, what is the value of sqrt(x^2 + 6x + 9)  sqrt(y^2  2y + 1) ?
(a)89/20 (b)59/20 (c)47/20 (d)15/4 (e)14/5
Answer B
first sqrt solves to sqrt (x+3)^2, second sqrt solves to sqrt (y1)^2
Plug in values of x and y to get 15/44/5 which is equal to 59/20



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Re: Deceptive algebra Q [#permalink]
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25 Jul 2007, 01:38
GK_Gmat wrote: ajay_gmat wrote: If x=3/4 and y=1/5, what is the value of sqrt(x^2 + 6x + 9)  sqrt(y^2  2y + 1) ?
(a)89/20 (b)59/20 (c)47/20 (d)15/4 (e)14/5 Answer B first sqrt solves to sqrt (x+3)^2, second sqrt solves to sqrt (y1)^2 Plug in values of x and y to get 15/44/5 which is equal to 59/20
I think A
But
x + 3  (y1) = x y + 4 = 4.55
15/4 (4/5) =
75 + 16

5
But my problem is 4.55 is not a choice there... even 89/20 is only 4.45 if I am right.
Am I missing something?



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I get it
sqrt can be +/
3.75 [ (y1)] is also a possible answer.
So 59/20 makes sense.



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59/20
Got to be careful with squares and roots ..
i was about to select 91/20 and when u mentioned be careful
thought twice about the answer.



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got A
sqrt [x^2+6x+9] = sqrt[(x+3)(x+3)] = x+3 = (3/4)+3 or 15/4
sqrt[y^22y+1] = sqrt[(y1)(y1)] = y1 = (1/5)1 or 4/5
so (15/4)  ((4/5)) = (15/4) + (4/5) = (75/20) + (16/20) =91/20.
what am i missing that people are getting (59/20)?
what's the OA?



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I get B. 59/20
Plugging in values I get 15/4  4/5 which equals to 59/20
I think the trick is knowing that sqrt(y1)^2 must be solved inside the parentheses first, before squaring the inside, then taking its square root. If you just have the powers cancel first, you would get 15/4  (4/5), thus equaling 91/20 the wrong answer.



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emoryhopeful wrote: I get B. 59/20
Plugging in values I get 15/4  4/5 which equals to 59/20
I think the trick is knowing that sqrt(y1)^2 must be solved inside the parentheses first, before squaring the inside, then taking its square root. If you just have the powers cancel first, you would get 15/4  (4/5), thus equaling 91/20 the wrong answer.
Btw, I dont think 91/20 is a wrong answer... Its just not one of the answer choices here. So we were left to find one of more possible right answers.



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after reading it, I worked it out and got A, little fuzzy on how folks are getting B.
isn't it 75/20  (16/20) ?



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zakk wrote: after reading it, I worked it out and got A, little fuzzy on how folks are getting B.
isn't it 75/20  (16/20) ?
I guess they are saying that you can't have a negative root.
What's the source of this question?



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Hayabusa wrote: zakk wrote: after reading it, I worked it out and got A, little fuzzy on how folks are getting B.
isn't it 75/20  (16/20) ? I guess they are saying that you can't have a negative root. What's the source of this question?
Right. But if we have handled the sqrt by eliminating the ^2 (they cancel don't they or am I really off!?) doesn't it come a moot point?



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ahhhh, it clicked.
It's because you are plugging in the numbers for the variables and squaring them BEFORE taking the square root.
That makes sense, I get it and am now a believer in option B.
Good question.
Can we confirm the OA???



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Other approaches here :
http://www.gmatclub.com/phpbb/viewtopic.php?t=49388
The OA is indeed B
(ajay_gmat : pls, do not post 2 times the same question... thx )



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Hayabusa wrote: zakk wrote: after reading it, I worked it out and got A, little fuzzy on how folks are getting B.
isn't it 75/20  (16/20) ? I guess they are saying that you can't have a negative root. What's the source of this question?
I remember reading something in Manhattan GMAT that said that for GMAT purposes, the square root is always the positive square root.










