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If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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03 Jul 2020, 00:59
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Competition Mode Question If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2) a < 0
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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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03 Jul 2020, 01:36
Quote: If ab  2b = (4  a)b, what is the value of b?
(1) a^2  9 ≤ 0 (2) a < 0 ab  2b = 4b ab 2ab  6b = 0 2b (a  3) = 0 statement 1: a^2  9 ≤ 0 a^2  9 = 0 a can be +3 or 3 when a = 3, b can be anything. when a= 3, b has to be 0. not sufficient statement 2: a < 0 a \(\ne 0\) b has to be 0. ans: B



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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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03 Jul 2020, 02:05
ab  2b = (4  a)b 6b = 2ab 3b = ab b(3a) = 0 St. 1:a^2  9 <= 0 a^2  9 <= 0; when a^2  9 <= 0 i.e; a > [3,3]..........(i) a^2  9 >=0; when a^2  9 >= 0 i.e; a > (infinity,  3] U [3, inifnity)..........(ii) From (i): if a = 3, b = any value if a = 2, b = 0 if a = 1, b = 0 St. 1 is insufficientSt. 2:a < 0 => a != 3 => a  3 != 0 => b = 0 St. 2 is sufficientAnswer: B
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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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03 Jul 2020, 03:04
Solution Step 1: Analyse Question Stem • We have, \( ab2b = (4a)b\) • We need to find the value of b.
• Now, \( ab2b = (4a)b\)
\( ⟹ b(a2) – b(4a) = 0 \) \( ⟹ b( a 2 – 4 + a)= 0 \) \( ⟹ b(2a – 6)= 0 \) \( ⟹ 2b(a3)= 0 …….Eq.(i) \)
So, if \(a ≠ 3\), in that case b must be 0. And, if \(a = 3\), in that case b can take any real number value. • So, if we can determine that \(a ≠ 3\), we can find the unique value of b. Now, let’s analyse the statements. Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE Statement 1: \(a^2 – 9 ≤ 0\) • We know that absolute values cannot be less than 0
o This, means, \(a^2 – 9 = 0\) \(⟹ a = 3,\) or \(3\)
If a = 3, in that case b = 0, unique solution However, if a = 3, in that cases b can take any real number value. Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D. Statement 2: \(a< 0\) • From this statement, we can be sure that \(a ≠ 3\).
Hence, statement 2 is sufficient. Thus, the correct answer is Option B.
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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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03 Jul 2020, 03:24
from question: ab2b=4bab 2ab=6b
statement 1: tells us either a=<3, 3 or 3, 3<=a, nothing about B, hence Insuff statement 2: tells us nothing about b, hence insuff together: nothing about b.. hence IMO ans: E



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If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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Updated on: 06 Jul 2020, 04:54
If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2) a < 0 ab  2b = 4b  ab 2ab = 6b 2ab  6b = 0 b(a  3) = 0 So, either b = 0 and a  3 ≠ 0 OR b ≠ 0 and a  3 = 0 OR b = 0 and a  3 = 0 (1) a^2  9 ≤ 0 Since mod ≥ 0 a^2  9 = 0 only a^2  9 = 0 a = 3 => b can take any value OR 3 => b = 0 However, b can take any value. INSUFFICIENT. (2) a < 0 Here, since a < 3 so b can take only one value i.e. b = 0, so that b(a  3) = 0 SUFFICIENT. Answer B.
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Originally posted by unraveled on 03 Jul 2020, 04:11.
Last edited by unraveled on 06 Jul 2020, 04:54, edited 1 time in total.



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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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03 Jul 2020, 05:03
Given: ab  2b = (4  a)b which upon simplification becomes b(3a)=0. Thus, either b = 0 or a = 3 or both.
Statement 1: a^2  9 ≤ 0, as absolute (modulus) values are either 0 or Positive Numbers. Therefore a^2 = 9. We get a = 3 or a = 3. Thus we cannot be sure about the value of 'b'. Insufficient
Statement 2: a < 0, thus a≠3. Therefore, b = 0. Sufficient.
Choice B is the correct answer.



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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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03 Jul 2020, 10:17
If ab  2b = (4  a)b, what is the value of b?
(1) a^2  9 ≤ 0 (2) a < 0
Given, b (a2) = b (4 a), so, when b =0, a can assume any value. If b is not 0, a will be 3.
1) a^2  9 =0, as the absolute value cannot be less than 0. so, a is either 3 or +3. Both of the values will satisfy the equation given b is 0 or not. not sufficient.
2) no information about b. not sufficient.
Together, a can assume only the value 3. so b is 0. Sufficient.
C is the answer.



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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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03 Jul 2020, 12:58
(a  2)b = (4  a)b Either a=3 or b=0
Q. what is the value of b?
(1) a^2  9 ≤ 0 a=3 > b=0 a=3 > b can be any NOT SUFFICIENT
(2) a < 0 a=3 > b=0 Any other a > b=0 SUFFICIENT
Ans (B)
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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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03 Jul 2020, 16:16
E  Neither sufficient
ab  2b = (4  a)b ==> ab  2b = 4b  ab ==> 2ab = 6b. ==> a = 3
then 3b  2b = (43)b ===> b=b
So whatever value we chose for B, will give us B and since neither statement 1 or 2 talk about option B we can conclude the answer is E



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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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03 Jul 2020, 22:20
If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2) a < 0 This is a question in which the question stem gives more information than we usually give it credit for! ab  2b = 4b  ab => 2ab  6b = 0 => (a3)b = 0 So either a = 3 or b = 0 st1) From the inequality equation, it is clear that \(a\neq{3} \), so b has to be equal to 0 (SUFFICIENT) st2) clearly tells us that \(a\neq{3}\) , so b = 0 (SUFFICIENT) So, the answer should be D



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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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03 Jul 2020, 22:43
IMO B.
ab2b = 4bab
2ab = 4b + 2b
2ab =6b
ab =3b
ab3b = 0 b(a3) = 0
either a=3 or b= 0 or both
Stmt 1 suggests that a^2 = 9 since it is absolute a = 3
(a = 3 does not hold true after we simplify the question stem.)
3b = 3b
we get b = b We dont get value so insuff.
Stmt 2 says a is negative. Since this condition is false after we simplify the question stem. so b has to be 0. Suff.
B it is
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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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03 Jul 2020, 22:51
From statement 1 a =3, so b can take up 0 or any other value Not sufficient From statement 2 a is less than 0 that means b can only be 0. Sufficient Answer is B option.
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If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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Updated on: 09 Jul 2020, 03:39
We have \(ab2b=(4a)b\)
\((a2)b=(4a)b\) \(ab2b=4bab\) \(2ab6b=0\) \(ab3b=0\) \(b(a3)=0\)
From the above we can infer the following two cases  (i) if \(a=3\), \(b\) can be any real number (ii) if \(a\neq{3}\), \(b\) = 0
From Statement (1) we have, \(a^2  9\leq{0}\) We know that a modulus function always gives a positive number as it's output. Hence \(a^2  9\) cannot be negative and can only be equal to 0 at the best.
\(a^29=0\) \(a^2=9\) \(a=3\) or \(a=3\)
Unique value of b cannot be arrived at by either value of a. Hence Options (A) and (D) may be eliminated.
From Statement (2) we have, \(a<0\)
If \(a<0\) then \(a\neq{3}\). Then b should be equal to 0 as we have found in (ii) above. Since we have a unique value of b in this case, (B) is the answer.
Originally posted by Pran1990 on 04 Jul 2020, 05:05.
Last edited by Pran1990 on 09 Jul 2020, 03:39, edited 1 time in total.



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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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05 Jul 2020, 10:02
And C
With statement A You get two values of a= 3, 3 This is not sufficient to find b
With statement 2 A<0 We are not clear what A is and what can be possible value for b. So this is insufficient
1+2 it is clear that A= 3, as A<0, with this find B from given equation 3B 2B = 5B = 7B So B=0
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Re: If ab  2b = (4  a)b, what is the value of b? (1) a^2  9 ≤ 0 (2)
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