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Which of the following is satisfied with x4+x3<2?
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Updated on: 30 Jan 2016, 06:21
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Which of the following is satisfied with x4+x3<2? A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5 D. 2.5<x<4 E. 3<x<4
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Originally posted by MathRevolution on 27 Jan 2016, 17:24.
Last edited by chetan2u on 30 Jan 2016, 06:21, edited 3 times in total.
Reformatted the question.




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Re: Which of the following is satisfied with x4+x3<2?
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30 Jan 2016, 05:15
Which of the following is satisfied with x4+x3<2? A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5 D. 2.5<x<4 E. 3<x<4 > If there is addition when there are 2 absolute values, you can just ignore the middle. That is, x4+x3<2 > x4+x3<2 > 2x7<2, 2<2x7<2, 5<2x<9, 5/2<x<9/2 > 2.5<x<4.5 Therefore, the answer is C.
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Re: Which of the following is satisfied with x4+x3<2?
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27 Jan 2016, 18:01
MathRevolution wrote: Which of the following is satisfied with x4+x3<2? A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5 D. 2.5<x<4 E. 3<x<4
* A solution will be posted in two days. Remember that xa represents distance of x from 'a'. As mentioned in the question, x4+x3<2 simply means that you need to find the range of 'x' such that distance of x from 4 + distance of x from 3 < 2. Refer to the attached image, you realize that the distance 'y' when it is in between 3 and 4 will always be <2. For regions x<3 or x>4, the sum of the distances of 'y' from 3 and 4 will be <2 only when y+1+y<2 > 2y+1<2 > y<0.5 or in other words, range of x is > 2.5 < x < 4.5 Attachment:
20160127_205035.jpg [ 6.25 KiB  Viewed 7371 times ]
C is thus the correct answer. Alternate solution: using POE to arrive at the correct answer.Once you know that the sum of the distances of x from 3 and 4 must be < 2, A. 1<x<5 . Try with x=1.5. Clearly the distance of 1.5 from 3 and 4 will be >2. Eliminate.B. 2<x<5 . Take x=2.1. Again, the distances of 2.1 from 3 and 4 (=0.9 and 1.9 respectively) will sum to > 2. Hence Eliminate.C. 2.5<x<4.5. Works for all possible values. Keep.D. 2.5<x<4. Take x=4.2. The distances of 4.2 from 3 and 4 (=1.2 and 0.2 respectively) will sum to < 2 but this value is NOT in the given range, thus incomplete range. Hence Eliminate.E. 3<x<4. Take x=2.6. It works for the given sums of the distances < 2 but is not in the given range, thus incomplete range. Hence eliminate.C is thus the correct answer. Hope this helps.
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Re: Which of the following is satisfied with x4+x3<2?
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27 Jan 2016, 17:55
If we put x=2.51 , 2.501 ... x4+x3 = 1.98 , 1.998 ..... just below 2 Again if we put x= 4.49,4.499..... x4+x3=1.98,1.998 ... just below 2 So Range should be 2.5<x<4.5 Answer (C)
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Re: Which of the following is satisfied with x4+x3<2?
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13 Feb 2016, 05:00
Given the modules x4 and x3, we have 2 key points (4 and 3) which give us 3 cases:
1. x<3 x+4x+3<2 > \(x<\frac{5}{2}\) >2.5<x<3 Solution is valid.
2. 3\(\leq{x}\)<4
x+4+x3<2 > 1<2 Solution is valid.
3. 4\(\leq{x}\)
x4+x3<2 > x\(\leq\frac{9}{2}\) > x\(\leq4.5\) Solution is valid.
Therefore x must belong to the interval 2.5<x\(\leq{4.5}\) to satisfy the given inequation.



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Re: Which of the following is satisfied with x4+x3<2?
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15 May 2017, 04:31
A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5 D. 2.5<x<4 E. 3<x<4



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Re: Which of the following is satisfied with x4+x3<2?
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20 Sep 2018, 02:28
FelixM wrote: Given the modules x4 and x3, we have 2 key points (4 and 3) which give us 3 cases:
1. x<3 x+4x+3<2 > \(x<\frac{5}{2}\) >2.5<x<3 Solution is valid.
2. 3\(\leq{x}\)<4
x+4+x3<2 > 1<2 Solution is valid.
3. 4\(\leq{x}\)
x4+x3<2 > x\(\leq\frac{9}{2}\) > x\(\leq4.5\) Solution is valid.
Therefore x must belong to the interval 2.5<x\(\leq{4.5}\) to satisfy the given inequation. Hi.... I need to learn this key point method......can you send some links please? regards



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Re: Which of the following is satisfied with x4+x3<2?
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20 Oct 2018, 04:55
MathRevolution wrote: Which of the following is satisfied with x4+x3<2?
A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5 D. 2.5<x<4 E. 3<x<4
> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, x4+x3<2 > x4+x3<2 > 2x7<2, 2<2x7<2, 5<2x<9, 5/2<x<9/2 > 2.5<x<4.5 Therefore, the answer is C. Hello MathRevolution , If there is addition when there are 2 absolute values, you can just ignore the middleIs this because lal+lbl>=la+bl ?



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Re: Which of the following is satisfied with x4+x3<2?
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12 Apr 2020, 02:46
Hi Bunuel! Can you please help with this problem? I am trying to solve it using the critical method, however, my answer does not match with the OA Thanks! Aakriti




Re: Which of the following is satisfied with x4+x3<2?
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12 Apr 2020, 02:46




