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What inequality represents the condition 1<x<9? [#permalink]
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24 May 2010, 18:21
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What inequality represents the condition 1 (A) x<3 (B) x+5<4 (C) x1<9 (D) 5+x<4 (E) 3+x<5
OPEN DISCUSSION OF THE QUESTION IS HERE: http://gmatclub.com/forum/whichofthe ... 26845.html
Solution: 10sec. Traditional 3steps method is too timeconsume technique. First of all we find length (91)=8 and center (1+8/2=5) of the segment represented by 1 Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner
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Re: Abs value [#permalink]
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24 May 2010, 19:13
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1<x<9 represents segment with length: 91 = 8 center: (9+1)/2 = 5 For any xa<b a is a center and b is a half of length. So, x5<8/2 represents our inequality (answer D) Problems in our app are the most difficult problems from GMAT Club's Tests. Maybe it would be useful for you to take a look at mathabsolutevaluemodulus86462.html
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Re: Abs value [#permalink]
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24 May 2010, 19:29
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Jinglander wrote: This is copied from the clubs iPhone app
Problem: 1 A. x<3 B. x+5<4 C. x1<9 D. 5+x<4 E. 3+x<5 Solution: 10sec. Traditional 3steps method is too timeconsume technique. First of all we find length (91)=8 and center (1+8/2=5) of the segment represented by 1 Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner
Posted from my mobile device You can also think of this the way manhattan suggest. Think of D on a number line. For l x5 l the a center point of the line is at positive 5. The difference from this point must be less than 4. so the x would have to be between 1 and 9. When you look at B it has a center point at negative 5. The difference from this point must be less than 4. So you know x would be between 9 and 1
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Re: Abs value [#permalink]
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24 May 2010, 22:06
walker wrote: 1<x<9 represents segment with length: 91 = 8 center: (9+1)/2 = 5
For any xa<b a is a center and b is a half of length. So, x5<8/2 represents our inequality (answer D)
Problems in our app are the most difficult problems from GMAT Club's Tests. Maybe it would be useful for you to take a look at Can you explain the logic of why a is the center and b half the length?



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Re: Abs value [#permalink]
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24 May 2010, 22:13
Detran wrote: Jinglander wrote: This is copied from the clubs iPhone app
Problem: 1<x<9. What inequality represents this condition?
A. x<3 B. x+5<4 C. x1<9 D. 5+x<4 E. 3+x<5 Solution: 10sec. Traditional 3steps method is too timeconsume technique. First of all we find length (91)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.
Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner
[size=80]Posted from my mobile device
You can also think of this the way manhattan suggest. Think of D on a number line. For l x5 l the a center point of the line is at positive 5. The difference from this point must be less than 4. so the x would have to be between 1 and 9.
When you look at B it has a center point at negative 5. The difference from this point must be less than 4. So you know x would be between 9 and 1 I am understanding why all points must be 4 away, but why is the center point the one that sets the left side to zero. Ie 5



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Re: Abs value [#permalink]
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24 May 2010, 22:40
imagine if you had the inequality l x l = y . Your graph would start at 0,0 and be a v shape. Now imagine you had the graph at l x  2 l = y. The graph is now shifted over 2 units to the right because now you have to have 2 more units of x to get the same y value. For example F(4) for the first equation is l 4 l = 4 . For the second equation, you would need F(6) = l (4+2) 2 l = 4 to get the same y value. The answers above follow the same principle because now you have to compensate by more points to get the same values. The centers is 5 for l x5l because you now have to have 5 more x's to get the same y value. In relation to l xl. The same logic works for l x + 5l You now have compensate by moving 5 units back
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Re: Abs value [#permalink]
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08 Jun 2010, 08:41
one thing i don't understand is that we can get the answer by simply solving the ineqs which takes less than a minute. Why are we trying to make it more complicated? or am i missing something here?



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Re: Abs value [#permalink]
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08 Jun 2010, 08:59
We are all different and it's always better to know another way to solve a problem. For example, I can't solve 5 inequalities for less than 1 minute but the approach described above allows me to solve the problem over 10sec. It works for me but it doesn't work for you and that's ok.
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Re: Abs value [#permalink]
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08 Jun 2010, 18:43
Hey, I was just trying to find out the plus point of using the alternative method. That is the reason why i wrote " i don't understand........am i missing sth here....." We're all different and have different point of views therefore, we're here to learn from each other. I didn't know we could solve the problem in that way...i'll use that method from now on. thx.



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Re: Abs value [#permalink]
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09 Jun 2010, 07:25
Sorry Bibha, I misunderstood you. Yeah, the more ways to solve a problem we know the better. At the same time not all ways work for everybody. For example, I love graphic approach to inequities, but there is a lot of people who find it more difficult in use. Best, Walker
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Re: Abs value [#permalink]
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09 Jan 2014, 06:50
Jinglander wrote: Problem: 1<x<9. What inequality represents this condition?
A. x<3 B. x+5<4 C. x1<9 D. 5+x<4 E. 3+x<5 Solution: 10sec. Traditional 3steps method is too timeconsume technique. First of all we find length (91)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.
Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner
me too, because there is no condition where answer C is insufficient or wrong. especially since x is between 2 and 8



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Re: Abs value [#permalink]
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09 Jan 2014, 07:03
TroyfontaineMacon wrote: Jinglander wrote: Problem: 1<x<9. What inequality represents this condition?
A. x<3 B. x+5<4 C. x1<9 D. 5+x<4 E. 3+x<5 Solution: 10sec. Traditional 3steps method is too timeconsume technique. First of all we find length (91)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.
Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner
me too, because there is no condition where answer C is insufficient or wrong. especially since x is between 2 and 8Here is another topic discussing the same question: whichofthefollowingrepresents1x126845.html There is conceptual approach in Mike's post and plugin method in my post. Hope it helps.
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