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

Question

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

chetan2u · Accepted Answer

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 SIGN So -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

HKD1710 · Answer

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.

ScottTargetTestPrep · Answer

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

stonecold · Answer

Great Question this one.

Here is what i did =>

=>1-A/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.

yezz · Answer

B not 0 and a/b <-2, means a, b has different signs and absolute value of a > that of b.

Clearly C

Sent from my iPhone using GMAT Club Forum

hellosanthosh2k2 · Answer

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)

nav1995 · Answer

1-a/b>3 =>-a/b>2 => a/b<(-2) This means that a>0 AND b<0 OR a<0 AND b>0 Also, i addition, since a/b<-2 (which is not between -1 and 1), therefore, lal>lbl Going by options: I -a>2b, putting modulus, lal>2lbl (May or may not true) II a<0 (Also, may or may not true) III a^3/b^3<0 (Definitely TRUE) Therefore, Ans.(c)

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

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