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If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:00
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46% (01:31) correct 54% (01:32) wrong based on 435 sessions
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If \(x  3 > 1\) then which of the following must be true? I. \(x > 4\) II. \(x^2 > 16\) III. \(x > 4\) A. I only B. II only C. III only D. I, II and III E. None
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If x  3 > 1 then which of the following must be true?
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19 Jul 2019, 02:31
Bunuel wrote: If \(x  3 > 1\) then which of the following must be true? I. \(x > 4\) II. \(x^2 > 16\) III. \(x > 4\) A. I only B. II only C. III only D. I, II and III E. None
SOLUTION: \(x  3 > 1\) means that: \(x  3 > 1\) > \(x > 4\) \((x  3) > 1\) > \(x < 2\) So, we are given that \(x < 2\) or \(x > 4\). I. \(x > 4\). Not necessarily true. Consider x = 0. II. \(x^2 > 16\). Not necessarily true. Consider x = 0. III. \(x > 4\). Not necessarily true. Consider x = 0. Answer: E. To understand the underline concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.
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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:10
Answer should be none. As x=1 satisfies the exuation x3>1 But does not satisfy any of the options.



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If x  3 > 1 then which of the following must be true?
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Updated on: 04 Jul 2019, 11:06
Refer attached Image. Ans. E
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Originally posted by MayankSingh on 04 Jul 2019, 08:22.
Last edited by MayankSingh on 04 Jul 2019, 11:06, edited 1 time in total.



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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:24
x3>1
Then we should consider two cases: x3>1 >> x>4 x3<1 >> x<2
So the solution is : (∞;2) to (4;+∞)
I. x>4 then x>4; x<4 Must be true
II. x^2>16 x>4; x<4 the same as the 1st case Must be true
III. x>4 Must be true
Answer: D. I, II and III



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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:25
Easy. What x−3>1 depicts is that x is at a distance of more than 1 from 3 on the number line, and thus, x>4 OR x<2
For x=1, x−3>1, 13 = 2 = 2 and 2>1 and hence, x=1 satisfies the inequality
Now quickly looking at all the options, x=1 does not fit in any of the three, and hence <1 min., you can arrive at your answer, i.e. (E) None



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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:28
As explained in the attached picture, x<2 & x>4 All the given choices CAN BE TRUE, but not MUST BE TRUE. Hence Ans should be (E)
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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:28
Given x3>1 Which implies x<2 or x>4 Now go thru the given statements: I. x>4 implies x<4 or x>4. DISCARD II. x^2>16 implies x>4 which again implies x<4 or x>4. DISCARD III. x>4 matches with the interval given in the question stem .KEEP Ans. (C)
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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:28
x3>1 i.e. x3>1 or (x3)<1 x>4 or x <4 i.e. x>4 imo A.
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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:31
Lets solve the equation
x3>1 ,gives : x>4 and x3<1 gives : x<2
all three equation satisfies.
Option D



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If x  3 > 1 then which of the following must be true?
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Updated on: 22 Jul 2019, 23:35
If x−3>1 then which of the following must be true? I. x>4 II. x^2>16 III. x>4 A. I only B. II only C. III only D. I, II and III E. None x3>1 x>4 or x<2 I. x>4 Take for example x =1 => x3 = 13 = 2>1 satisfies the equation. But 1 is not >4. NOT NECESSARILY TRUE. II. x^2>16 Take for example x =1 => x3 = 13 = 2>1 satisfies the equation. But 1^2 is not >16. NOT NECESSARILY TRUE. III. x>4 Take for example x =1 => x3 = 13 = 2>1 satisfies the equation. But 1 is not > 4. NOT NECESSARILY TRUE. IMO E
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Originally posted by Kinshook on 04 Jul 2019, 08:33.
Last edited by Kinshook on 22 Jul 2019, 23:35, edited 1 time in total.



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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:33
If x−3>1 then which of the following must be true?
=>x−3>1 => x−3>1 & x−3 < 1 => x > 4 & x < 2 > so x is in this range, the it must be true
<oo> <24>
I. x>4 > must be true : x>4 & x < 4 : <44> is subset of <24> II. x^2>16 > must be true: x^2>16 => x>4 same as I III. x>4 > must be true:4> is subset of <24>
A. I only B. II only C. III only D. I, II and III > correct E. None



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If x  3 > 1 then which of the following must be true?
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Updated on: 21 Jul 2019, 05:51
x−3>1
if x>3 x3>1 x>4
If x<3 x3<1 (multiply by 1) x<2
So we have x in the range (x<2) and (x>4)
Now lets check the options
1)x > 4 x>4 for x>0 x<4 for x<0 AND for x > 0 x>4
So this falls in the range.
2)x^2 > 16 sqrt of both side gives x > 4 This is same as 1) above so again this is also fine.
3)x>4 again falls in the range.
So all the above falls in the range.
I would chose D as OA.
Originally posted by prabsahi on 04 Jul 2019, 08:37.
Last edited by prabsahi on 21 Jul 2019, 05:51, edited 1 time in total.



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If x  3 > 1 then which of the following must be true?
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Updated on: 05 Jul 2019, 08:34
solving lx3l>1 gives x>4 or x<2 so out of given options IMO E is only valid If x−3>1x−3>1 then which of the following must be true? I. x>4x>4 II. x2>16x2>16 III. x>4x>4 A. I only B. II only C. III only D. I, II and III E. None
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Originally posted by Archit3110 on 04 Jul 2019, 08:38.
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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:38
x3>1
Either (x3)>1 or (x3)<1
Either x>4 or x<2
IMO, Answer is (E) All three statements only take x>4 into consideration but we also have x<2
So none of the statements MUST BE true



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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:44
If x−3>1 then which of the following must be true?
I. x>4 II. \(x^2>16\) III. \(x>4\)
Given x−3>1 thus either x3>1 hence x>4 or x3<1 or x<2
thus take x =1 I. 1>4 not true II. \(1^2>16\) not true III. \(1>4\) not true
Thus None E



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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:44
Two ways to solve : Method 1) Find a counter example (easiest), X=1 will satisfy the stem I. x>4  since x = 1 will satisfy this is not true II. x^2>16  since x = 1 will satisfy this is not true III. x>4  since x = 1 will satisfy this is not true IMO E NoneMethod 2: solve using modulus properties to arrive at X cannot lie from 2 to 4. it can take any other value.
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If x  3 > 1 then which of the following must be true?
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Updated on: 04 Jul 2019, 22:40
x3>1 => x3>1 or 3x > 1 => x>4 or x<2 I. x > 4 implies x > 4 or x < 4 =>definitely true based on the solution above II. x^2 > 16 implies x>4 or x<4 => same as above and is true III. x>4 => true All statements are true. Option D should be the answer. Posted from my mobile device
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Originally posted by prashanths on 04 Jul 2019, 08:44.
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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:56
Given x  3 > 1 Solving for x; x  3 > 1 x > 1 + 3 x > 4 Also, negating the right side of the original equation x  3 > 1 x > 1 + 3 x > 2 From the options available, only III fulfilled the condition, hence answer choice "C" Posted from my mobile device
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Re: If x  3 > 1 then which of the following must be true?
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04 Jul 2019, 08:56
Hi, Given x3 > 1 => (x3) < 1 or (x3) > 1 => x < 4 or x > 4 so possible range or values are => (infinte , 4) or (4, +infinite)
Now the question: 1. x > 4 for all the possible values this will always be true. take x = 5 or x = +5
2. \(x^2\)> 16 for all possible values, this will always be true.
3. x > 4 this comes by solving the inequality.
So Answer is D.
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Re: If x  3 > 1 then which of the following must be true?
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