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Which of the following inequalities has a solution set that, when [#permalink]
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03 Jan 2011, 07:06
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Which of the following inequalities has a solution set that, when graphed on the number line, is a single line segment of finite length? A. \(x^4 \geq 1\) B. \(x^3 \leq 27\) C. \(x^2\geq 16\) D. \(2 \leq x \leq 5\) E. \(2 \leq 3x+4 \leq 6\)
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Which of the following inequalities has a solution set that, when [#permalink]
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03 Jan 2011, 07:41
Which of the following inequalities has a solution set that, when graphed on the number line, is a single line segment of finite length? A. \(x^4 \geq 1\) B. \(x^3 \leq 27\) C. \(x^2\geq 16\) D. \(2 \leq x \leq 5\) E. \(2 \leq 3x+4 \leq 6\) The key words in the stem are: " a single line segment of finite length" Now, answer choices A, B, and C cannot be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus cannot be finite (x can go to + or infinity for A and C and x can got to infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other. Answer: E. Just to demonstrate:A. \(x^4 \geq 1\) > \(x\leq{1}\) or \(x\geq{1}\): two infinite ranges; B. \(x^3 \leq 27\) > \(x\leq{3}\): one infinite range; C. \(x^2\geq 16\) > \(x\leq{4}\) or \(x\geq{4}\): two infinite ranges; D. \(2 \leq x \leq 5\) > \(5\leq{x}\leq{2}\) or \(2\leq{x}\leq{5}\): two finite ranges; E. \(2 \leq 3x+4 \leq 6\) > \(2\leq{3x}\leq{2}\) > \(\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range. Answer: E. Hope it's clear.
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Re: Which of the following inequalities has a solution set that, when [#permalink]
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11 Jun 2011, 22:36
It is good question, It was obvious that A,B , C are incorrect as these are exponent of X but I couldn't figure out which one between d & e is better, so attempted D on GMAT Prep test Later, During review of the question I found that X was actually X  absolute value , Hence two lines, So correct is E



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Re: Which of the following inequalities has a solution set that, when [#permalink]
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13 Jul 2014, 08:34
Bunuel wrote: anilnandyala wrote: which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length? Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length? The key words in the stem are: " a single line segment of finite length" Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or infinity for A and C and x can got to infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other. Answer: E. Just to demonstrate: A. x^4 >= 1 > \(x\leq{1}\) or \(x\geq{1}\): two infinite ranges; B. x^3 <= 27 > \(x\leq{3}\): one infinite range;C. x^2 >= 16 > \(x\leq{4}\) or \(x\geq{4}\): two infinite ranges; D. 2 <= x <= 5 > \(5\leq{x}\leq{2}\) or \(2\leq{x}\leq{5}\): two finite ranges; E. 2 <= 3x+4 <= 6 > \(2\leq{3x}\leq{2}\) > \(\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range. Answer: E. Hope it's clear. Hi Bunuel, for option B, why isn't it a finite range? x^3<=27 3<=x<=3



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Re: Which of the following inequalities has a solution set that, when [#permalink]
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13 Jul 2014, 08:36
russ9 wrote: Bunuel wrote: anilnandyala wrote: which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length? Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length? The key words in the stem are: " a single line segment of finite length" Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or infinity for A and C and x can got to infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other. Answer: E. Just to demonstrate: A. x^4 >= 1 > \(x\leq{1}\) or \(x\geq{1}\): two infinite ranges; B. x^3 <= 27 > \(x\leq{3}\): one infinite range;C. x^2 >= 16 > \(x\leq{4}\) or \(x\geq{4}\): two infinite ranges; D. 2 <= x <= 5 > \(5\leq{x}\leq{2}\) or \(2\leq{x}\leq{5}\): two finite ranges; E. 2 <= 3x+4 <= 6 > \(2\leq{3x}\leq{2}\) > \(\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range. Answer: E. Hope it's clear. Hi Bunuel, for option B, why isn't it a finite range? x^3<=27 3<=x<=3x^3<=27 > \(x\leq{3}\).
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Re: Which of the following inequalities has a solution set that, when [#permalink]
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18 Feb 2015, 05:35
Bunuel wrote: anilnandyala wrote: which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length? Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length? The key words in the stem are: " a single line segment of finite length" Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or infinity for A and C and x can got to infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other. Answer: E. Just to demonstrate: A. x^4 >= 1 > \(x\leq{1}\) or \(x\geq{1}\): two infinite ranges; B. x^3 <= 27 > \(x\leq{3}\): one infinite range; C. x^2 >= 16 > \(x\leq{4}\) or \(x\geq{4}\): two infinite ranges; D. 2 <= x <= 5 > \(5\leq{x}\leq{2}\) or \(2\leq{x}\leq{5}\): two finite ranges; E. 2 <= 3x+4 <= 6 > \(2\leq{3x}\leq{2}\) > \(\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range. Answer: E. Hope it's clear. Could someone explain Option A in detail? I understand upon taking 4th root on both sides it becomes: x>= +1 But, I don't understand how it gets simplified further as its been explained as: x^4 >= 1 > \(x\leq{1}\) or \(x\geq{1}\)



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Re: Which of the following inequalities has a solution set that, when [#permalink]
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18 Feb 2015, 05:40
connectvinoth wrote: Bunuel wrote: anilnandyala wrote: which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length? Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length? The key words in the stem are: " a single line segment of finite length" Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or infinity for A and C and x can got to infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other. Answer: E. Just to demonstrate: A. x^4 >= 1 > \(x\leq{1}\) or \(x\geq{1}\): two infinite ranges; B. x^3 <= 27 > \(x\leq{3}\): one infinite range; C. x^2 >= 16 > \(x\leq{4}\) or \(x\geq{4}\): two infinite ranges; D. 2 <= x <= 5 > \(5\leq{x}\leq{2}\) or \(2\leq{x}\leq{5}\): two finite ranges; E. 2 <= 3x+4 <= 6 > \(2\leq{3x}\leq{2}\) > \(\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range. Answer: E. Hope it's clear. Could someone explain Option A in detail? I understand upon taking 4th root on both sides it becomes: x>= +1 But, I don't understand how it gets simplified further as its been explained as: x^4 >= 1 > \(x\leq{1}\) or \(x\geq{1}\)x >= +/ 1 does not make any sense. When taking 4th root from both sides we'll get \(x \geq{1}\), which is the same as \(x\leq{1}\) or \(x\geq{1}\).
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Re: Which of the following inequalities has a solution set that, when [#permalink]
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18 Apr 2015, 09:52
Bunuel , Could you please elaborate on how to solve 2 <= x <= 5 > −5≤x≤−2 or 2≤x≤5 in steps..?



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Re: Which of the following inequalities has a solution set that, when [#permalink]
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05 Sep 2016, 18:23
Ralphcuisak wrote: Bunuel , Could you please elaborate on how to solve 2 <= x <= 5 > −5≤x≤−2 or 2≤x≤5
in steps..? The absolute value of X is between 2 and 5. X = 2 through 5 X = 2 through 5 On the number line in bold:  0   250 25 2 separate finite line segments.



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Re: Which of the following inequalities has a solution set that, when [#permalink]
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09 Aug 2017, 11:32
Bunuel wrote: anilnandyala wrote: which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length? Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length? The key words in the stem are: " a single line segment of finite length" Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or infinity for A and C and x can got to infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other. Answer: E. Just to demonstrate: A. x^4 >= 1 > \(x\leq{1}\) or \(x\geq{1}\): two infinite ranges; B. x^3 <= 27 > \(x\leq{3}\): one infinite range; C. x^2 >= 16 > \(x\leq{4}\) or \(x\geq{4}\): two infinite ranges; D. 2 <= x <= 5 > \(5\leq{x}\leq{2}\) or \(2\leq{x}\leq{5}\): two finite ranges; E. 2 <= 3x+4 <= 6 > \(2\leq{3x}\leq{2}\) > \(\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range. Answer: E. Hope it's clear. Hi, I think I am unable to understand the question here. I was between B and E and chose B because it gave one value which is 3. I failed to understand what "a single line segment of finite length" means. Can you explain this and what we actually need to find here?



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Re: Which of the following inequalities has a solution set that, when [#permalink]
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09 Aug 2017, 23:31
pra1785 wrote: Bunuel wrote: anilnandyala wrote: which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length? Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length? The key words in the stem are: " a single line segment of finite length" Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or infinity for A and C and x can got to infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other. Answer: E. Just to demonstrate: A. x^4 >= 1 > \(x\leq{1}\) or \(x\geq{1}\): two infinite ranges; B. x^3 <= 27 > \(x\leq{3}\): one infinite range; C. x^2 >= 16 > \(x\leq{4}\) or \(x\geq{4}\): two infinite ranges; D. 2 <= x <= 5 > \(5\leq{x}\leq{2}\) or \(2\leq{x}\leq{5}\): two finite ranges; E. 2 <= 3x+4 <= 6 > \(2\leq{3x}\leq{2}\) > \(\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range. Answer: E. Hope it's clear. Hi, I think I am unable to understand the question here. I was between B and E and chose B because it gave one value which is 3. I failed to understand what "a single line segment of finite length" means. Can you explain this and what we actually need to find here? \(x^3 \leq 27\) gives \(x\leq{3}\), not x = 3. Maybe images could help: A. x^4 >= 1 > \(x\leq{1}\) or \(x\geq{1}\): two infinite ranges; B. x^3 <= 27 > \(x\leq{3}\): one infinite range; C. x^2 >= 16 > \(x\leq{4}\) or \(x\geq{4}\): two infinite ranges; D. 2 <= x <= 5 > \(5\leq{x}\leq{2}\) or \(2\leq{x}\leq{5}\): two finite ranges; E. 2 <= 3x+4 <= 6 > \(2\leq{3x}\leq{2}\) > \(\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range. Similar questions: https://gmatclub.com/forum/whichofthe ... 27820.html (GMAT Prep). https://gmatclub.com/forum/whichofthe ... 30666.html (Knewton). Attachment:
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Re: Which of the following inequalities has a solution set that, when [#permalink]
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15 Aug 2017, 11:00
anilnandyala wrote: Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?
A. x^4 >= 1 B. x^3 <= 27 C. x^2 >= 16 D. 2 <= x <= 5 E. 2 <= 3x+4 <= 6 We must determine from our answer choices which inequality is a single line segment of finite length when graphed on the number line. A) x^4 ≥ 1 ∜(x^4) ≥ ∜1 x ≥ 1 x ≥ 1 or x ≤ 1 Since the solution set from answer choice A produces two rays of infinite length, answer choice A is not correct. B) x^3 ≤ 27 ∛(x^3) ≤ ∛27 x ≤ 3 Since the solution set from answer choice B produces one ray of infinite length, answer choice B is not correct. C) x^4 ≥ 16 ∜(x^4) ≥ ∜16 x ≥ 2 x ≥ 2 or x ≤ 2 Since the solution set from answer choice C produces two rays of infinite length, answer choice C is not correct. D) 2 ≤ x ≤ 5 We must solve for when x is positive and for when x is negative. When x is positive: 2 ≤ x ≤ 5 When x is negative: 2 ≤ x ≤ 5 1(2 ≤ x ≤ 5) 2 ≥ x ≥ 5 Since the solution set from answer choice D produces two line segments of finite length, answer choice D is not correct. Since answers A, B, C, and D are not correct, E must be the correct answer. However, for practice, we can solve it anyway. E) 2 ≤ 3x + 4 ≤ 6 2 ≤ 3x ≤ 2 2/3 ≤ x ≤ 2/3 Since the solution set from answer choice E produces one line segment of finite length, answer choice E is correct. Answer: E
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Re: Which of the following inequalities has a solution set that, when [#permalink]
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15 Aug 2017, 13:34
Hi, Since question is saying single line of finite length, Graph is going to be a straight line is equation is a linear equation. Linear equation is equation with highest power of variable being one. For higher powers, graph is going to be a curve. Option A has highest power of x as 4, so it is curve Option B has highest power of x as 3, so it is also curve Option C has highest power of x as 2, so it is also curve Option D has absolute function. An absolute function is combination of two functions, so it is going to give two lines. Thus option E
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Re: Which of the following inequalities has a solution set that, when [#permalink]
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06 Feb 2018, 15:35
anilnandyala wrote: Which of the following inequalities has a solution set that, when graphed on the number line, is a single line segment of finite length? A. \(x^4 \geq 1\) B. \(x^3 \leq 27\) C. \(x^2\geq 16\) D. \(2 \leq x \leq 5\) E. \(2 \leq 3x+4 \leq 6\) IMPORTANT This is one of those questions that require us to check/test the answer choices. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top. E) 2 ≤ 3x + 4 ≤ 6 Subtract 4 from all sides to get: 2 ≤ 3x ≤ 2 Divide all sides by 3 to get: 2/3 ≤ x ≤ 2/3 So, x can have any value from 2/3 to 2/3 So, if we were to graph the possible values of x, the line segment would have a FINITE length. Answer: E Cheers, Brent
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Re: Which of the following inequalities has a solution set that, when [#permalink]
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17 Mar 2018, 12:43
Hi All, The equations in this question can be physically drawn or handled as a Number Property concept: Note that the question asks for a SINGLE SEGMENT of FINITE LENGTH. This means that the group of numbers that make up the solution set would be consecutive and limited (as opposed to nonconsecutive and/or infinite). Here are the Number Properties: A: X^4 >= 1 X can be 1, 2, 3, etc. or 1, 2, 3, etc. This group of answers is infinite and nonconsecutive. Eliminate A. B: X^3 <= 27 X can be 3, 2, 1, 0, 1, etc. This group is infinite. Eliminate B. C: X^2 >= 16 X can be 4, 5, 6, etc. or 4, 5, 6, etc. This group is infinite and nonconsecutive. Eliminate C. D: 2 <= X <= 5 X can be 2, 3, 4, 5 or 2, 3, 4, 5, This group is finite BUT nonconsecutive. Eliminate D. E: 2 <= 3X + 4 <= 6 Let's simplify with algebra… 2 <= 3X <= 2 2/3 <= X <= 2/3 X is a finite set of answers and the answers are consecutive. This is a MATCH to what we're looking for. Final Answer: GMAT assassins aren't born, they're made, Rich
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