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Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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06 Oct 2010, 07:11
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Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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Re: DS  Please explain
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06 Oct 2010, 07:21
agnok wrote: Is x – 3 < 7 ?
(1) x > 0 (2) x < 10 Please explain Is \(x3<7\)? Let's see for which range(s) of \(x\) this inequality holds true. One check point \(x=3\) (check point the value of \(x\) when the expression in  equals to zero), so we should check two ranges: When \(x<3\) > \(x3\) becomes \(x+3\) > \(x+3<7\) > \(4<x\) > \(4<x<3\); When \(x\geq{3}\) > \(x3\) becomes \(x3\) > \(x3<7\) > \(x<10\) > \(3\leq{x}<10\); So inequality \(x3<7\) holds true for \(4<x<10\). (1) \(x>0\). Not sufficient. (2) \(x<10\). Not sufficient. (1)+(2) \(0<x<10\) > we know that in this range inequality \(x3<7\) holds true (this range is the subset of the range we've got in the beginning). Sufficient. Answer: C.
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Re: DS  Please explain
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29 Oct 2010, 06:02
You would have read in theory of mods that mod is nothing but the distance from x = 0 on the number line. This means that if x = 4, x is a point at a distance of 4 units from 0. So x could be 4 or 4 (which suits our understanding of mods) Now, x – 3 is the distance from the point 3 on the number line. So if I say x – 3 = 7, I am looking for points which are at a distance of 7 from point 3. These points will be 10 and 4. These are the solutions of x in this equation. Coming to our question, x – 3 < 7 means we are looking for points whose distance from 3 is less than 7. There will be many such points e.g. 4, 5, 6, 2, 1 etc that satisfy our inequality as is apparent from the diagram below: Attachment:
Ques.jpg [ 5.28 KiB  Viewed 4068 times ]
Points beyond 10 on the right side of the number line and points beyond 4 on the left side of the number line will have a distance of more than 7 and hence, do not satisfy our inequality. Statement I: x > 0 There are points greater than 0 that satisfy our inequality (e.g. 1, 5, 7 etc) and there are those that do not satisfy our inequality (e.g. 11, 12, 18 etc). Hence this statement is not sufficient. Statement II: x < 10 Again, using the same logic as above, this statement is not sufficient. When we combine the two statements, we see that all the points satisfying 0 < x < 10, satisfy our inequality. Hence we can say 'Yes, x – 3 is less than 7' and we get (C) as our answer.
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Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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30 Jan 2012, 07:56
Is x – 3 < 7 ? (1) x > 0 (2) x < 10 Need explanation please. Thank you!
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Re: Is x – 3 < 7 ?
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30 Jan 2012, 09:13
First, you need to simplify the stem. Since there is an absolute value in the expression, remove the absolute value signs and setup two inequalities.
A. x3 < 7 ? x < 10 ?
B. (x3) < 7 ? x+3 < 7 ? x < 4 ? x > 4 ?
Next, combine the two inequalities: 4 < x < 10 ? In other words, the question is asking whether x is between 4 and 10.
Now, evaluate the statements.
(1) x > 0 INSUFFICIENT: because x>0, x>4. However, the statement does not prove that x<10. For example, if x = 8, the answer to the question is yes. If x = 15, the answer to the question is no.
(2) x < 10 INSUFFICIENT: this statment indicates that x<10. However, the statement does not prove that x>4. For example, if x = 8, the answer to the question is yes. If x = 10, the answer to the question is no.
Finally, combine the two statements. Combined, the two statements say: 0<x<10. If x is between 0 and 10, x must also be between 4 and 10. Therefore, the answer to the question is C.
Answer: C



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Re: Is x – 3 < 7 ?
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30 Jan 2012, 09:30



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Re: Is x – 3 < 7 ?
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30 Jan 2012, 23:44
DagwoodDeluxe wrote: First, you need to simplify the stem. Since there is an absolute value in the expression, remove the absolute value signs and setup two inequalities.
A. x3 < 7 ? x < 10 ?
B. (x3) < 7 ? x+3 < 7 ? x < 4 ? x > 4 ?
Next, combine the two inequalities: 4 < x < 10 ? In other words, the question is asking whether x is between 4 and 10.
Is x – 3 < 7 ? x3 < 7 x < 10 OR x+3 < 7 x > 4 When we consider both inequalities, question becomes  is x < 10 OR is x > 4 Isn't it wrong to combine inequalities like this 4 < x < 10 and consider two scenarios as AND scenarios?



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Re: Is x – 3 < 7 ?
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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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31 Jan 2012, 12:48
In the post below we considered two scenarios as OR scenarios and in this question we are considering them as AND scenarios. I understand the distance approach but still little confused. How is this question different from one below? Please help! http://gmatclub.com/forum/dsinequalities126369.htmlIn the question below we considered two cases separately and didn't combine i.e. didn't do y + 3 <= x <= 3  y If y >= 0, What is the value of x? (1) x3 >= y (2) x3 <= y 1) x3 >= y x 3 >=y x >= y + 3 OR 3  x >=y x <= 3  y Posted from my mobile device



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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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31 Jan 2012, 21:18



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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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31 Jan 2012, 21:56
Thanks Bunuel. I think i understand now.
So in the first example we can combine ranges because it's a continuous range but in the second example the range is not continuous so we can't combine.



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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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31 Jan 2012, 22:37
if X>0 , then from 1  9 , the inequality is correct and if X>10 it doesnt hold correct  1 Not sufficient if X<10, then from 9  (3) , the inequality is correct and for X< 3 it doent hold correct  2 Not sufficient 1 n 2 togethe 0<X<10 for all the values in this range the inequality holds good. +1 kudos if U like this....
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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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09 May 2016, 13:58
Hi Bunuel Question is asking about whether 4<x<10 so Sts. 1+2 give us 0<x>10 so how we consider it is true. it is not asking whether x is positive and < 10. I need to get the missing point please.



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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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18 May 2016, 11:25
DesecratoR wrote: Is x – 3 < 7 ?
(1) x > 0 (2) x < 10
Need explanation please. Thank you! we have to find the value of lx3l<7 simplify this statement 7<(x3)<7 on solving this equation we get 4<x<10 so basically we have to find whether the of x lies betwee 4 and 10 Statement 1 x>0 so from this we can say the value of x is greater than 0 and can be any positive value fro example 50 so A is not possible Statement 2 x<10 similarly from this we only know value of x< 10 and can even 50 so B is also not possible on combining both statement we can conclude 0<x<10 and after combining we get that the vaue of x is in between 4<x<10 So C is ans
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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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18 May 2016, 11:33
DesecratoR wrote: Is x – 3 < 7 ?
(1) x > 0 (2) x < 10
Need explanation please. Thank you! we have to find the value of lx3l<7 simplify this statement 7<(x3)<7 on solving this equation we get 4<x<10 so basically we have to find whether the of x lies betwee 4 and 10
Statement 1 x>0 so from this we can say the value of x is greater than 0 and can be any positive value fro example 50 so A is not possible Statement 2 x<10 similarly from this we only know value of x< 10 and can even 50 so B is also not possible
on combining both statement we can conclude 0<x<10 and after combining we get that the vaue of x is in between 4<x<10 So C is ans
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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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03 Feb 2017, 02:09
DesecratoR wrote: Is x – 3 < 7 ?
(1) x > 0 (2) x < 10
Need explanation please. Thank you! Hi Bunuel and bbThis question is also seen in another thread. Can you merge this topics, please? Here is link of another thread... https://gmatclub.com/forum/isx371x ... fl=similar
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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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03 Feb 2017, 02:28
agnok wrote: Is x – 3 < 7 ?
(1) x > 0 (2) x < 10 The question stem says: Is 4<x<10? In number line, it is green part. <(5)(4)(3)(2)(1)01234567891011> Statement 1: x>0 here, x may be any positive values. This may be in the green part or may be next after the green part. So, insufficient. Statement 2: x<10 Here, x may be into the green part or it may be in the red part. So, the answer may be YES or NO. So, insufficient. Statement 1+2: It combined says: 0<x<10 So, sufficient from the number line. The correct choice is C.
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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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Re: Is x – 3 < 7 ? (1) x > 0 (2) x < 10
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