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If 0 < a < b < c, which of the following statements must be true?
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14 Jun 2016, 14:08
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If 0 < a < b < c, which of the following statements must be true? I. 2a > b + c II. c – a > b  a III. \(\frac{c}{a}\) < \(\frac{b}{a}\) A) I only B) II only C) III only D) I and II E) II and III OG 2017 New Question
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If 0 < a < b < c, which of the following statements must be true?
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Updated on: 03 Mar 2018, 14:51
AbdurRakib wrote: If 0 < a < b < c, which of the following statements must be true? I. 2a > b + c II. c – a > b  a III. \(\frac{c}{a}\) < \(\frac{b}{a}\) A) I only B) II only C) III only D) I and II E) II and III OG 2017 New Question I. 2a > b + c Consider this scenario: a = 1, b = 2 and c = 3. This meets the given condition that 0 < a < b < c. HOWEVER, if we plug these values into statement I, we see that it is NOT the case that 2a > b + c So, statement I NEED NOT BE TRUE II. c – a > b  a It's already given that c > b If we subtract ANY VALUE (such as a) from both sides, the inequality remains valid. So, statement II MUST BE TRUE III. c/a < b/a Consider this scenario: a = 1, b = 2 and c = 3. This meets the given condition that 0 < a < b < c. HOWEVER, if we plug these values into statement III, we see that it is NOT the case that c/a < b/a So, statement III NEED NOT BE TRUE Answer: B Cheers, Brent
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Re: If 0 < a < b < c, which of the following statements must be true?
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16 Jun 2016, 04:39
I. obvously we cannot say that it "must" be true.
II. c – a > b  a Cancelling a on both sides c > b Definitely true as per question.
III. c/a < b/a Multiply both sides by "a" (positive) c < b Definitely "not" true as per question.
So, only II is correct.



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Re: If 0 < a < b < c, which of the following statements must be true?
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24 Jun 2016, 13:21
Hey,
For (1), 0<a<b<c, can't we write it as a<b....i a<c...ii
adding i and ii
2a<b+c ???? (addition property of inequalities)
Or Is it like this property holds true only when abcd are different numbers??
Appreciate a clarification!
TIA.



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Re: If 0 < a < b < c, which of the following statements must be true?
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26 Jun 2016, 01:31
Nothing indicates what a may be greater than, so I is wrong. III is always wrong because the order should be reversed. II is correct. Answer choice B is correct.
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Re: If 0 < a < b < c, which of the following statements must be true?
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05 Dec 2016, 17:29
AbdurRakib wrote: If 0 < a < b < c, which of the following statements must be true?
I. 2a > b + c II. c – a > b  a III. \(\frac{c}{a}\) < \(\frac{b}{a}\)
A) I only B) II only C) III only D) I and II E) II and III We are given that 0 < a < b < c and need to determine which statements are true. Let’s analyze each Roman numeral. I. 2a > b + c 2a cannot be greater than the sum of b and c. Since a + a = 2a, a < b, and a < c, a + a < b + c, or 2a < b + c. Statement I is FALSE. II. c – a > b  a We can simplify the inequality to c > b. Since we are given that c is greater than b in the stem, c – a is greater than b  a. Statement II is TRUE. III. c/a < b/a We can multiply both sides by a and we have c < b (note: we don’t need to switch the inequality sign because a is positive). However, we are given that c is greater than b, so c/a can’t be less than b/a. Statement III is FALSE. Thus, only Roman numeral II is true. Answer: B
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Re: If 0 < a < b < c, which of the following statements must be true?
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26 Feb 2018, 15:00
A simple and quick approach is to assume values for a, b, c If a=2, b=3, c=4 I. 2a > b + c = 4 > 7; this is wrong II. c – a > b  a = 2 > 1; this is correct III. c/a <b/a = 2 < 1.5; this is wrong
Therefore, II only is correct. Answer is B



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Re: If 0 < a < b < c, which of the following statements must be true?
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09 Mar 2019, 07:40
[1] Assign Test Values
Must follow rule: 0 < a < b < c,
a = 2 b = 3 c = 4
[2] Plug In & Calculate
\(I. 2a > b + c \rightarrow 2(2) > 3 + 4 \rightarrow 4 > 7 \space (FALSE)\)
\(II. c – a > b  a \rightarrow 4  2 > 3  2 \rightarrow 2 > 1 \space (TRUE)\)
\(III. \frac{c}{a} < \frac{b}{a} \rightarrow \frac{4}{2} < \frac{3}{2} \rightarrow 2 < 1.5 \space (FALSE)\)
Answer: II ONLY (B)



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Re: If 0 < a < b < c, which of the following statements must be true?
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16 Apr 2019, 06:33
Shouldn't the question say a,b,c are integers?



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Re: If 0 < a < b < c, which of the following statements must be true?
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11 May 2019, 22:57
AbdurRakib wrote: If 0 < a < b < c, which of the following statements must be true? I. 2a > b + c II. c – a > b  a III. \(\frac{c}{a}\) < \(\frac{b}{a}\) A) I only B) II only C) III only D) I and II E) II and III OG 2017 New Question We can let smart numbers a=2 so,b=3 c=4 Now, we'll apply on each options given☺ And we get option B() only matches Answer is B Posted from my mobile device



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Re: If 0 < a < b < c, which of the following statements must be true?
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04 Mar 2020, 07:12
AbdurRakib wrote: If 0 < a < b < c, which of the following statements must be true? I. 2a > b + c II. c – a > b  a III. \(\frac{c}{a}\) < \(\frac{b}{a}\) A) I only B) II only C) III only D) I and II E) II and III OG 2017 New Question I. 2a > b + c Taking numbers a = 1, b = 2 and c = 3 this is not trueII. c – a > b  a In 0 < a < b < c, subtracting a from each 0  a < a  a < b  a < c  a Hence c  a > b  a TrueIII. \(\frac{c}{a}\) < \(\frac{b}{a}\) As b < c dividing by 'a' which is positive doesn't impact inequality Hence \(\frac{b}{a} < \frac{c}{a}\) not trueAnswer B.
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Re: If 0 < a < b < c, which of the following statements must be true?
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04 Mar 2020, 07:12




