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If 4x12 >= x + 9, which of the following must be true
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26 Sep 2010, 09:48
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If 4x12 >= x + 9, which of the following must be true A. x > 6 B. x < 7 C. x > 7 D. x > 8 E. x < 8
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Re: MGMAT Inequalities
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26 Sep 2010, 12:53
saxenagarima wrote: Bunuel wrote: saxenagarima wrote: If 4x12 >= x + 9, which of the following must be true a) X > 6 b) X < 7 C) X > 7 D) X > 8 E) X < 8 I doubt the OA in MGMAT solutions Given: \(4x12\geq{x + 9}\) > \(3x\geq{21}\) > \(x\geq{7}\). Only A is always true, as ANY \(x\) from the TRUE range \(x\geq{7}\) will be more than 6. Answer: A. But with A) x can be 6.1, which will not satisfy the given equation..... shouldn't option C) be valid choice .... It should be other way around. We are given that \(x\geq{7}\). The question is: which of the following is true about \(x\)? \(x>6\) is true about \(x\), because as \(x\) is more than (or equal to) 7 then it's definitely more than 6. To elaborate more. Question uses the same logic as in the examples below:If \(x=5\), then which of the following must be true about \(x\):A. x=3 B. x^2=10 C. x<4 D. x=1 E. x>10 Answer is E (x>10), because as x=5 then it's more than 10. Or: If \(1<x<10\), then which of the following must be true about \(x\):A. x=3 B. x^2=10 C. x<4 D. x=1 E. x<120 Again answer is E, because ANY \(x\) from \(1<x<10\) will be less than 120 so it's always true about the number from this range to say that it's less than 120. Or: If \(1<x<0\) or \(x>1\), then which of the following must be true about \(x\):A. x>1 B. x>1 C. x<1 D. x=1 E. x^2>1 As \(1<x<0\) or \(x>1\) then ANY \(x\) from these ranges would satisfy \(x>1\). So B is always true. \(x\) could be for example 1/2, 3/4, or 10 but no matter what \(x\) actually is it's IN ANY CASE more than 1. So we can say about \(x\) that it's more than 1. On the other hand for example A is not always true as it says that \(x>1\), which is not always true as \(x\) could be 1/2 and 1/2 is not more than 1. Hope it's clear.
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Re: MGMAT Inequalities
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26 Sep 2010, 09:52



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Re: MGMAT Inequalities
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26 Sep 2010, 10:32
Bunuel wrote: saxenagarima wrote: If 4x12 >= x + 9, which of the following must be true a) X > 6 b) X < 7 C) X > 7 D) X > 8 E) X < 8 I doubt the OA in MGMAT solutions Given: \(4x12\geq{x + 9}\) > \(3x\geq{21}\) > \(x\geq{7}\). Only A is always true, as ANY \(x\) from the TRUE range \(x\geq{7}\) will be more than 6. Answer: A. But with A) x can be 6.1, which will not satisfy the given equation..... shouldn't option C) be valid choice ....



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Re: MGMAT Inequalities
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26 Sep 2010, 13:07
Thanks a lot Bunuel......



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Re: MGMAT Inequalities
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25 May 2012, 02:47
Bunuel wrote: If \(1<x<0\) or \(x>1\), then which of the following must be true about \(x\): A. x>1 B. x>1 C. x<1 D. x=1 E. x^2>1
As \(1<x<0\) or \(x>1\) then ANY \(x\) from these ranges would satisfy \(x>1\). So B is always true.
\(x\) could be for example 1/2, 3/4, or 10 but no matter what \(x\) actually is it's IN ANY CASE more than 1. So we can say about \(x\) that it's more than 1.
On the other hand for example A is not always true as it says that \(x>1\), which is not always true as \(x\) could be 1/2 and 1/2 is not more than 1.
Hope it's clear. just for the sake of learning please tell me how to evaluate option E. X^2>1 is it x>1 and x>1 if x>1 then 1 >x>1 if x>1 then how do we evaluate this part, confused here.



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Re: MGMAT Inequalities
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25 May 2012, 04:27
Joy111 wrote: Bunuel wrote: If \(1<x<0\) or \(x>1\), then which of the following must be true about \(x\): A. x>1 B. x>1 C. x<1 D. x=1 E. x^2>1
As \(1<x<0\) or \(x>1\) then ANY \(x\) from these ranges would satisfy \(x>1\). So B is always true.
\(x\) could be for example 1/2, 3/4, or 10 but no matter what \(x\) actually is it's IN ANY CASE more than 1. So we can say about \(x\) that it's more than 1.
On the other hand for example A is not always true as it says that \(x>1\), which is not always true as \(x\) could be 1/2 and 1/2 is not more than 1.
Hope it's clear. just for the sake of learning please tell me how to evaluate option E. X^2>1 is it x>1 and x>1 if x>1 then 1 >x>1 if x>1 then how do we evaluate this part, confused here. x^2>1 is the same as x^2>1, so it holds true for x<1 and x>1. As for x>1: it holds true for ANY value of x, because absolute value of a number is always nonnegative. Hope it helps.
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Re: MGMAT Inequalities
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25 May 2012, 05:57
Bunuel wrote: Joy111 wrote: Bunuel wrote: If \(1<x<0\) or \(x>1\), then which of the following must be true about \(x\): A. x>1 B. x>1 C. x<1 D. x=1 E. x^2>1
As \(1<x<0\) or \(x>1\) then ANY \(x\) from these ranges would satisfy \(x>1\). So B is always true.
\(x\) could be for example 1/2, 3/4, or 10 but no matter what \(x\) actually is it's IN ANY CASE more than 1. So we can say about \(x\) that it's more than 1.
On the other hand for example A is not always true as it says that \(x>1\), which is not always true as \(x\) could be 1/2 and 1/2 is not more than 1.
Hope it's clear. just for the sake of learning please tell me how to evaluate option E. X^2>1 is it x>1 and x>1 if x>1 then 1 >x>1 if x>1 then how do we evaluate this part, confused here. x^2>1 is the same as x^2>1, so it holds true for x<1 and x>1. As for x>1: it holds true for ANY value of x, because absolute value of a number is always nonnegative. Hope it helps. ok , thank you for that . Now suppose x>1 was one of the options of the question , then couldn't this have been one of the solutions . can you please show how x>1 fails to satisfy all the values of x in the equation If 1< x <0 or x >1 then which of the following must be true about x : A. x>1 B. x>1 C. x<1 D. x=1 E. x>1 now for all values of x i.e x=1/2, x=3 ,x=4, option E also is also satisfied . seems to me that both A and E ,could be the solutions? please correct me . Thank you.



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Re: MGMAT Inequalities
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25 May 2012, 06:21
Joy111 wrote: ok , thank you for that .
Now suppose x>1 was one of the options of the question , then couldn't this have been one of the solutions .
can you please show how x>1 fails to satisfy all the values of x in the equation
If 1< x <0 or x >1 then which of the following must be true about x : A. x>1 B. x>1 C. x<1 D. x=1 E. x>1
now for all values of x i.e x=1/2, x=3 ,x=4, option E also is also satisfied .
seems to me that both A and E ,could be the solutions? please correct me . Thank you. The question in my example is as follows: If \(1<x<0\) or \(x>1\), then which of the following must be true about \(x\):A. x>1 B. x>1 C. x<1 D. x=1 E. x^2>1For this question E cannot be correct since if x=1/2 then x^2>1 does not hold true. Hope it's clear.
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Re: MGMAT Inequalities
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11 Dec 2012, 20:21
Bunuel wrote: saxenagarima wrote: If 4x12 >= x + 9, which of the following must be true a) X > 6 b) X < 7 C) X>7 D) X>8 E) X < 8 I doubt the OA in MGMAT solutions Given: \(4x12\geq{x + 9}\) > \(3x\geq{21}\) > \(x\geq{7}\). Only A is always true, as ANY \(x\) from the TRUE range \(x\geq{7}\) will be more than 6. Answer: A. Bunuel, I must be reading the question incorrectly because I feel that after you get x>=7 you think 7=7 and 8>7 so the answer of x could 7 or 8 but since it is asking which is always greater than the answer would be D. 8. I don't see why we would look at it as x>6 when we solved the equation and got x>=7. How would the question need to be worded for that to be the case because I am really confused. I don't feel that in other OG questions we we replaced the x with a number smaller when it is asking what number is greater than or equal to a number larger. If that's the case, that means C, D, and E were the trap answers? I'd appreciate your help. Thanks!
If , then which of the following must be true about : A. x=3 B. x^2=10 C. x<4 D. x=1 E. x>10
Answer is E (x>10), because as x=5 then it's more than 10.
And for this one I know it can't be AD, but for E, x could be 9 which wouldn't necessarily mean that it is greater than 5? Would you choose it anyways?



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Re: MGMAT Inequalities
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12 Dec 2012, 01:23
dcastan2 wrote: Bunuel wrote: saxenagarima wrote: If 4x12 >= x + 9, which of the following must be true a) X > 6 b) X < 7 C) X>7 D) X>8 E) X < 8 I doubt the OA in MGMAT solutions Given: \(4x12\geq{x + 9}\) > \(3x\geq{21}\) > \(x\geq{7}\). Only A is always true, as ANY \(x\) from the TRUE range \(x\geq{7}\) will be more than 6. Answer: A. Bunuel, I must be reading the question incorrectly because I feel that after you get x>=7 you think 7=7 and 8>7 so the answer of x could 7 or 8 but since it is asking which is always greater than the answer would be D. 8. I don't see why we would look at it as x>6 when we solved the equation and got x>=7. How would the question need to be worded for that to be the case because I am really confused. I don't feel that in other OG questions we we replaced the x with a number smaller when it is asking what number is greater than or equal to a number larger. If that's the case, that means C, D, and E were the trap answers? I'd appreciate your help. Thanks! If , then which of the following must be true about : A. x=3 B. x^2=10 C. x<4 D. x=1 E. x>10 Answer is E (x>10), because as x=5 then it's more than 10. And for this one I know it can't be AD, but for E, x could be 9 which wouldn't necessarily mean that it is greater than 5? Would you choose it anyways? I think you are confused about what is given and what is asked. Given that \(x\geq{7}\), so \(x\) is some number which is more than or equal to 7. Now, the question asks, what must be true about \(x\) (which we know is more than or equal to 7). If \(x\) is more than or equal to 7, then it must be true that \(x\) is greater than 6, thus A must be true. The same with another example in your post: given that \(x=5\). The question asks, what must be true about \(x\). Since, \(x=5\), thus it's true to say that it's greater than 10. Hope it's clear.
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Re: MGMAT Inequalities
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12 Dec 2012, 12:03
Yes, thank you Bunuel!



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Re: If 4x12 >= x + 9, which of the following must be true
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13 Dec 2012, 15:02
Hi Bunuel, I am not quite satisfied with the OA. Since the question is not clear if x is an integer, for example x = 6.5 <7 => then it is not true. So the correct choice answer should be C
What do you think?



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Re: If 4x12 >= x + 9, which of the following must be true
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Re: If 4x12 >= x + 9, which of the following must be true
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Re: If 4x12 >= x + 9, which of the following must be true
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14 Jan 2014, 05:47
I fell for D. It says which of the following must be true. x>8 holds good for all values.
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Re: If 4x12 >= x + 9, which of the following must be true
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30 Jun 2015, 17:31
Good question and great comments. The questions asks, not what x is, but what must be true for the "if" statement. If statement reduces to, \(x\geq{7}\)
So, the answer must fit the form, "if [answer choice], then \(xgeq\{7}\).
A) x>6 if x>6, then \(x\geq{7}\). True. B) x<7 if x<7, then \(x\geq{7}\) is not true since x could equal 4. C) x>7 if x>7, then \(x\geq{7}\) is not true since x cannot equal 7. D) x>8 if x>8, then \(x\geq{7}\) is not true since x cannot equal 7 . E) x<8 if x<8, then \(x\geq{7}\) is not true since x cannot equal something like 10.
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Re: If 4x  12 > x + 9, which of the following must be true
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12 Oct 2015, 23:11
arhumsid wrote: If \(4x  12 > x + 9\), which o f the following must be true?
A. \(x > 6\) B. \(x < 7\) C. \(x > 7\) D. \(x > 8\) E. \(x < 8\)
Im confused with the 'must be true' part. Once you choose an answer, please explain why others cant be correct. Solving \(4x  12 > x + 9\) i.e. \(4x  x > 12 + 9\) i.e. \(3x > 21\) i.e. \(x > 7\) Answer: option C A. \(x > 6\) is Incorrect because as per this option x may be 6.5 whereas x must be Essentially Greater than 7 B. \(x < 7\) is Completely Incorrect because x must be Essentially Greater than 7 C. \(x > 7\) is CORRECT (Exactly what we have derived) D. \(x > 8\) is Incorrect because as per this option x can NOT be 7.5 whereas x must be Essentially Greater than 7 which can be 7.5 as well E. \(x < 8\) is Incorrect because as per this option x can NOT be 8.5 whereas x must be Essentially Greater than 7 and can be anything greater than 8 as well I hope this helps and clears your doubt!
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Re: If 4x12 >= x + 9, which of the following must be true
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06 Feb 2017, 09:26
Bunuel wrote: saxenagarima wrote: If 4x12 >= x + 9, which of the following must be true a) X > 6 b) X < 7 C) X>7 D) X>8 E) X < 8 I doubt the OA in MGMAT solutions Given: \(4x12\geq{x + 9}\) > \(3x\geq{21}\) > \(x\geq{7}\). Only A is always true, as ANY \(x\) from the TRUE range \(x\geq{7}\) will be more than 6. Answer: A. Similar question to practice: http://gmatclub.com/forum/ifitistrue ... 29093.htmlJust wanted to let you know your post made me realize and go OHHHHHHHHHHHH! I get it now. Thanks B



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Re: If 4x12 >= x + 9, which of the following must be true
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08 Feb 2017, 18:55
saxenagarima wrote: If 4x12 >= x + 9, which of the following must be true
A. x > 6 B. x < 7 C. x > 7 D. x > 8 E. x < 8 Let’s solve the given inequality: 4x  12 ≥ x + 9 3x ≥ 21 x ≥ 7 Thus, x must be greater than 6. Answer: A
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