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Updated on: 18 Oct 2015, 13:02
Originally posted by harish1986 on 14 Oct 2015, 10:22.
Last edited by Bunuel on 18 Oct 2015, 13:02, edited 3 times in total.
Last edited by Bunuel on 18 Oct 2015, 13:02, edited 3 times in total.
Edited the OA.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
73% (01:34) correct
27%
(01:15)
wrong
based on 182
sessions
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14 Oct 2015, 10:33
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harish1986
What is the value of X?
1) 3x² - 8x - 35 = 0
2) x² - 3x = 7x - 25
Target question: What is the value of x?1) 3x² - 8x - 35 = 0
2) x² - 3x = 7x - 25
Statement 1: 3x² - 8x - 35 = 0
Factor to get: (3x + 7)(x - 5) = 0
So, 3x + 7 = 0 OR x - 5 = 0
This means x = -7/3 OR x = 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x² - 3x = 7x - 25
Rewrite as: x² - 10x + 25 = 0
Factor to get: (x - 5)(x - 5) = 0
So, x - 5 = 0 OR x - 5 = 0 [same for each - great!]
This means x = 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
14 Oct 2015, 10:40
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Hi Harish,
at a first glance it might be tempting to choose C, since in principle quadratic equations give you two possible solutions, and therefore one answer choice would not be sufficient.
Let's first take a look statement (1):
(1) If you factorize the quadratic expression (see here for a good explanation of factoring quadratics: https://www.purplemath.com/modules/factquad.htm), you get:
\(3x^2-8x-35=(x-5)(3x+7)\)
from this, it follows: \(x=5\) OR \(\frac{7}{3}\), therefore (1) is NOT SUFFICIENT
A logical approach now, but it would be misleading, would be to check whether statement (2) leads you to any of the two solutions you just found. To do this we just have to plug in \(5\) and \(x=-\frac{7}{3}\) and see if the result is zero. If we do this, we find that \(5\) does in fact work, and we could be tempted to choose C. #FAIL!!!!
This is a good example of why it's important to look at each statement separately. If we solve the quadratic expression from statement (2), we'll quickly see that this equation has a unique (double) solution, which is 5. Therefore B is the right answer!!
Hope this helps!
Cheers.
paula
at a first glance it might be tempting to choose C, since in principle quadratic equations give you two possible solutions, and therefore one answer choice would not be sufficient.
Let's first take a look statement (1):
(1) If you factorize the quadratic expression (see here for a good explanation of factoring quadratics: https://www.purplemath.com/modules/factquad.htm), you get:
\(3x^2-8x-35=(x-5)(3x+7)\)
from this, it follows: \(x=5\) OR \(\frac{7}{3}\), therefore (1) is NOT SUFFICIENT
A logical approach now, but it would be misleading, would be to check whether statement (2) leads you to any of the two solutions you just found. To do this we just have to plug in \(5\) and \(x=-\frac{7}{3}\) and see if the result is zero. If we do this, we find that \(5\) does in fact work, and we could be tempted to choose C. #FAIL!!!!
This is a good example of why it's important to look at each statement separately. If we solve the quadratic expression from statement (2), we'll quickly see that this equation has a unique (double) solution, which is 5. Therefore B is the right answer!!
Hope this helps!
Cheers.
paula
