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If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 08:00
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If \(cb < ab < 0\), is \(c  a = c  a\)? (1) \(c > a\) (2) \(b < 0\)
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Re: If cb < ab < 0, is c  a = c  a?
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19 Jul 2019, 02:01
Bunuel wrote: If \(cb < ab < 0\), is \(c  a = c  a\)? (1) \(c > a\) (2) \(b < 0\)
OFFICIAL EXPLANATION: FROM CRACK VERBAL: Statement I is sufficient If c > a and cb < ab then b is negative and c > a > 0 Since c and a both are positive and c > a then c  a will be equal to c  a and c  a will also be equal to c  a Statement II is sufficient If b is negative then c > a > 0 Since c and a both are positive and c > a then c  a will be equal to c  a and c  a will also be equal to c – a Answer: D
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Re: If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 10:36
cb<ab<0  given
so now 2 cases: 1. b>0 2. b<0
taking 1 : b>0: cbab<0 > b(ca)<0 b>0 so ca should be <0. So c<a also since ab<0 and b>0 so a<0. Similarly c<0 taking 2 : b<0 here ca>0, so c>a also since b<0 and ab<0, so a>0 and similarly c>0 To check if ca=ca
lets take statement 1: c>a means case 2 from above. This case gives a,c>0 and c>a. So for all values ca=ca is true. 1 is sufficient.
statement 2: b<0: again case 2. SO sufficient:
Hence Ans D




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If cb < ab < 0, is c  a = c  a?
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Updated on: 02 Jul 2019, 10:16
Given, Case 1: If b is positive, a & c both negative and c<a. Or Case 2: If b is negative, both a& c positive & c>a. Question says: are a&c in SAME DIRECTION? Statement 1: c>a that means second case & a&c both positive. Sufficient.
Statement 2: b is negative that means second case & a&c both positive. Sufficient.
My answer:D
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DECODING THE MAIN QUESTION:is c  a = c  a? In my opinion, Such type of ABSOLUTE VALUE question (mentioned in main question) ask u a simple thing I.e. the two variables are in same directions or not.
TWO TYPES of SUCH QUESTION: (i) {c+a} is either EQUAL or GREATER than {c+a}. When the two numbers (c & a) are in SAME DIRECTION (both positive or both negatives or both zero), both expressions [(c+a) & c+a] are EQUAL.
When the two numbers (c & a) are in OPPOSITE DIRECTION (one positive and another one negative), (c+a) is GREATER than c+a.
(ii) {ca} is either EQUAL or LESS than {ca}. When the two numbers (c & a) are in SAME DIRECTION (both positive or both negatives or both zero) & c has greater ABSOLUTE value, both expressions [(ca) & ca] are EQUAL.
When the two numbers (c & a) are in OPPOSITE DIRECTION (one positive and another one negative), (ca) is LESS than ca.



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If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 08:29
We are told that cb<ab<0 i.e. both cb and ab are negative. So either 1) b is positive which would mean that a and c are negative; or 2) b is negative and thus a and c are positive.
for c−ato be equal toc−a we need to meet one of these two conditions: A) if c>a then both a and c have to be positive; or B) if c<a then both have to be negative. So if the statements individually or collectively confirm either of these two sets of conditions we would have our answer.
St1: c>a: which leads us to condition A and both a and c have to be positive for this to work and b thus has to be negative (as bc<ac<0). But we do not know that. So insufficient. St2: b<0: this tells us that b<0 and thus both a and c are positive, but consider situation where a=5 and c=3, in this case LHS=2 but RHS=2. Not sufficient.
Taken together we can clearly see that this is condition A where c>a>0 (and thus b<0). Sufficient.



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Re: If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 08:30
as cb<ab, so c<a
and ca would be equal to c  a only when c>a and result of RHS is positive. So option A states exactly that, so option 1 is correct.
Option 2 is not required , so it is of no use.
Finally, Option A is correct as only option 1 is sufficient.



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Re: If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 08:32
i) Insufficient, Not sure on the sign of a,c, and b. ii)B<0, means c and a are positive for ab, bc to be less than zero; C > A as only then will CB<AB. Sufficient (gives yes to the stem)
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Re: If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 08:34
It's given that cb<ab<0. So both cb and ab are negative. For this to be possible, there are only two scenarios. C<a and b>0 Or C>a and b< 0. In the question, both the statements imply the same and point to scenario 2. Which implies c>a and that implies the given statement will always never be true. Ca is always positive whereas c  a will equal (ca). Therefore both statements alone are sufficient and hence option D. Posted from my mobile device
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Re: If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 08:35
cb<ab<0. Means the sign of the products cb and ab are opposite. From S1: c>a. Let c and a be positive. c = 5, a = 2. And b is negative. ca = 3 = ca = 3. Satisfies. If b is positive. c and a are negative. Then c = 2 and a = 4. ca = 2 = ca = 2. Not satisfies. INSUFFICIENT. From S2: b is negative. So c and a are positive. And the ca = ca. SUFFICIENT. B is the answer
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If cb < ab < 0, is c  a = c  a?
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Updated on: 01 Jul 2019, 08:40
(1) b can take +ve or ve values. but only ve value of b can satisfy both cb<ab & c>a .
So both c & a are positive, Which can answer the asked question. (if both c,a are of the same sign then only given equality will hold)
(2) b<0 here directly we can say that c>0, a>0. (2) can also answer the asked question.
Answer: D
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Originally posted by Rohan007 on 01 Jul 2019, 08:39.
Last edited by Rohan007 on 01 Jul 2019, 08:40, edited 1 time in total.



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If cb < ab < 0, is c  a = c  a?
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Updated on: 02 Jul 2019, 08:13
If cb<ab<0cb<ab<0, is c−a=c−ac−a=c−a?
(1) c>ac>a
(2) b<0
given cb<ab<0 so either of a,c or b has to be ve and c−a=c−a will hold true only when c & a are +ve so #1 c>a means b is <0 ve c=2 and a=1 then c−a=c−a ; valid
#2 b<0 it means that a & c are both +ve so c−a=c−a ; valid IMO D
Originally posted by Archit3110 on 01 Jul 2019, 08:40.
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If cb < ab < 0, is c  a = c  a?
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Updated on: 02 Jul 2019, 10:44
This is a hard question.
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Originally posted by RashedVai on 01 Jul 2019, 08:41.
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Re: If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 08:48
Either is independently sufficient. #1 c>a Let c=5 and a=2 Statement only possible when b<0 5*(1) < 2*(1), For c=2 and a=5 Statement not possible. So c−a=c−a #2 For b<0, statement is only possible iff a and c are +ve. So, c−a=c−a for and c are positives. D IMO.
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Re: If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 08:50
Let us rephrase the question
Are both c and an on same side of the number line? Given inequality may have 2 cases based on the sign of b First Case
If \(b>0\) \(c<a<0\) Second CaseIf \(b <0\) \(c>a>0\) Statement 1: c>a From the second case we know c>a only when b<0 Hence we know that \(c>a>0\) . Clearly Sufficient.Statement 2: \(b<0\) This implies second case again. So Clearly Sufficient.Hence IMO Answer is D
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Re: If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 08:52
Hi, Given cb<ab<0 and Is ca = c  a?
From looking at the question we get, either c <0 or b< 0 or a< 0.
1. c>a using this: if c =2 and a = 1 then the Answer is Yes. But if c = 1 and a = 2 then the answer is no. Insufficient.
2. b<0 from this, we can say that c>0 and a>0, only this will hold the equality true as per the condition. so, a> 0, b<0 , c> 0 is our deduction from this. But again we don`t know about the relationship between a and c. Insufficient.
3. Using both statements we can say: b<0 , c>a and c>0 , a>0 That will give the answer Yes. So the Answer is C.
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Re: If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 08:54
Given, cb<ab<0 , is c−a=c−a? Deduce: 1. ab, cb is v 2. If b is ve, then c>a (a,c are +ve) 3. If b is +ve, then a>c (a,c are ve) (1) c>a : b is ve, c=5, a=2 > 52 = 52 YES . so, AD/ BCE(2) b<0 : OR b is ve. This is same as (1). Hence we know this statement is also sufficient. So, AD The answer is D
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Re: If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 09:03
1. c>a => b<0 since cb<ab b<0<a<c c & a both are positive c = c & a = a ca = ca =c  a Statement 1 is sufficient. 2. b<0 => c>a since cb<ab b<0<a<c c & a both are positive c = c & a = a ca = ca =c  a Statement 2 is sufficient. Since each statement alone is sufficient IMO D
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Re: If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 09:05
For cb to be less than ab, either the terms c and a play a major role or its the term b. In case 1: c>a For example, c= 1 and a= 3. Let b=3 [ Since both the terms have to be negative, b has to be positive] ca = 2 and ca=2. Hence not sufficient to answer. In case 2: b<0. Therefore, c and a have to be positive for the terms cb and ab to be less than 0. If b is negative, c has to be greater than a for it to satisfy cb<ab and positive. Hence, statement 2 is enough.



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Re: If cb < ab < 0, is c  a = c  a?
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01 Jul 2019, 09:08
A very good question indeed.
From cb < ab < 0, we can tell that (1) either b is negative & a,c are positive or b is positive & a,c are negative. (2) cb > ab ==> c > a if both c and a are positive, c−a=c−a but if both c and a are negative, c−a<>c−a So, the question boils down to determine the sign for a/c.
If we know c > a, we can tell a/c are both positive. Sufficient. If we know b < 0, we can tell a/c are both positive. Sufficient.
So, the right answer is (D).



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If cb < ab < 0, is c  a = c  a?
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Updated on: 02 Jul 2019, 08:36
Given : cb<ab<0, so both cb and ab are negative. Since b is common, there can be 2 cases 
Case I  If b>0, then c < a < 0 (For example let b = 1, c = 3, a = 2)
Then c  a = 1 = c  a, True
Case II  If b<0, then c > a > 0 (For example let b = 1, c = 3, a = 2)
Then c  a = 1 = c  a, True
This is applicable for both statements 1 and 2. Hence D.
Originally posted by taransaurav on 01 Jul 2019, 09:11.
Last edited by taransaurav on 02 Jul 2019, 08:36, edited 1 time in total.




If cb < ab < 0, is c  a = c  a?
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