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If b ≠ 0, and 1 – a/b > 3, which of the following must be true? [#permalink]
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24 Apr 2017, 04:20
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Re: If b ≠ 0, and 1 – a/b > 3, which of the following must be true? [#permalink]
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24 Apr 2017, 08:13
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Bunuel wrote: If b ≠ 0, and 1 – a/b > 3, which of the following must be true?
I. –a > 2b II. a < 0 III. a^3/b^3 < 0 A. I only B. II only C. III only D. II and III only E. I, II, and III Hi.... Easy to error in inequalities with '' sign.. \(1\frac{a}{b}>3\).... \(\frac{a}{b}<2\).. Let's see the equations.. I. –a > 2b Do not cross multiply if you are not aware of SIGNSo a/b>2 does not MEAN a>2b always. Will depend on sign of b.. MUST be true  NO II. a < 0 Nothing that can tell us this.. MUST be true III. a^3/b^3 < 0 We know a/b<2 so a/b<0.. So \(\frac{a^3}{b^3}<0\).. Always TRUE.. Only III.. C
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Re: If b ≠ 0, and 1 – a/b > 3, which of the following must be true? [#permalink]
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24 Apr 2017, 12:02
Bunuel wrote: If b ≠ 0, and 1 – a/b > 3, which of the following must be true?
I. –a > 2b II. a < 0 III. a^3/b^3 < 0 A. I only B. II only C. III only D. II and III only E. I, II, and III 1  a/b > 3. This can only be true when a and b have different sign. a > 2b a + 2b < 0 here both a and b can be ve i.e. same sign or different as well. a < 0 we can have a > 0 and b < 0 and the given condition would still be true. so a < 0 is not MUST BE true. a^3/b^3 < 0 this can only happen if a and b have different sign. hence this is a must be true condition for 1 – a/b > 3. C should be the answer.
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Re: If b ≠ 0, and 1 – a/b > 3, which of the following must be true? [#permalink]
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27 Apr 2017, 17:12
Bunuel wrote: If b ≠ 0, and 1 – a/b > 3, which of the following must be true?
I. –a > 2b II. a < 0 III. a^3/b^3 < 0 A. I only B. II only C. III only D. II and III only E. I, II, and III We are given that 1  a/b > 3, so a/b > 2 or a/b < 2. Since a/b is less than 2, either a is negative and b is positive OR a is positive and b is negative. Let’s analyze our Roman numerals: I. –a > 2b If we multiply both sides of a/b > 2 by b, then a > 2b if b is positive OR a < 2b if b is negative. However, since we don’t know whether b is positive or negative, we can’t determine whether a > 2b. II. a < 0 Since we’ve mentioned a could be either positive or negative, we can’t determine whether a < 0. III. a^3/b^3 < 0 Since a/b < 2, a/b is negative. Since a/b is negative, a^3/b^3 = (a/b)^3 is also negative. Answer: C
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Re: If b ≠ 0, and 1 – a/b > 3, which of the following must be true? [#permalink]
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27 Apr 2017, 22:56
Great Question this one.
Here is what i did =>
=>1A/B >3 =>A/B >2
We are asked as to which of the following must be true. Option 1 => If B>0 => A>2B If B<0 => A<2B
REJECTED.
Option 2 => Let A=100 and B=2
REJECTED.
Option 3 => As A/B <0 => A^3/B^3 will be negative too. This is always True.
Hence III is always True.
SMASH THAT C.
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If b ≠ 0, and 1 – a/b > 3, which of the following must be true? [#permalink]
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02 Oct 2017, 12:18
B not 0 and a/b <2, means a, b has different signs and absolute value of a > that of b.
Clearly C
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Re: If b ≠ 0, and 1 – a/b > 3, which of the following must be true? [#permalink]
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27 Jan 2018, 02:03
Given: 1  (a/b) > 3 0 > 2 + (a/b) (a + 2b)/b < 0
case 1 if b < 0, then to hold above inequality, a + 2b > 0 => a > 2b => a < 2b => since b is negative, RHS is negative, a can't be negative, if it were, then a > 2b. so if b < 0, then a > 0
case 2 if b > 0, then to hold above inequality, a + 2b < 0 => a < 2b => a > 2b => since b is +ve, RHS is positive, a can't be positive, if it were, then a < 2b so if b > 0, then a < 0
Let us the see options: (1) a > 2b (case 2), but this need not be true always, there is possibility of case 1 (2) a < 0(case 2), need not be true, there is possibility of case 2 (3) a^3/b^3 < 0 => a, b are of opposite sign => this is always true in both the cases
(C)




Re: If b ≠ 0, and 1 – a/b > 3, which of the following must be true?
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