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GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a

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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   13 Jul 2022, 09:31
If you solve the given question, it basically asks us if c > b?

Using statement 1, we can clearly arrive at the answer easily since it's stated.

Using statement 2, we just know that a > -b. We don't really know anything about c here.

So, option A is the best bet imo
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   13 Jul 2022, 10:58
Bunuel wrote:
If \(|a| > |b| > |c|\), is \(a*b^3*c^3 > a*b^4*c^2\) ?

(1) \(a > b > c\)
(2) \(a + b > 0\)



 


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for the GMAT Club World Cup Competition

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\(a*b^3*c^3 > a*b^4*c^2\)
\(a*b*(c-b) > 0\)

(1) \(a > b > c\)
\(|a| > |b| > |c|\)
\(a*b*(c-b) < 0\) --- Sufficient

(2) \(a + b > 0\)
Nothing is known about relationship of b and c. ---- InSufficient

Ans A
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   13 Jul 2022, 19:27
Bunuel wrote:
If \(|a| > |b| > |c|\), is \(a*b^3*c^3 > a*b^4*c^2\) ?

(1) \(a > b > c\)
(2) \(a + b > 0\)


The correct Answer is Choice E.

given that mod A > mod B> mod C
Hence we are not sure of the signs of the A, B, and C respectively.
it can be mod (-10) > mod (4) > mod (-1)
or mod (10) > mod (-5) > mod(0) etc

we want to find out if \(a*b^3*c^3 > a*b^4*c^2\) ?


statement 1 : (1) \(a > b > c\)

Insufficient
considering a = 10 , b =5 and c =0
we will have 10 * 5^3 * 0^3 > 10* 5^4 * 0^2
i.e. 0 > 0 - Answer is No

considering a=10, b =5, c = 2
the answer is yes

Hence Statement 1 is insufficient

(2) \(a + b > 0\)

here we dont have any information about the sign of C, it can be positive or negative as mod a> mod b > moc c and given a+b >0
Hence statement 2 is insufficient


combining statement 1 and 2, we still dont have the value of C and hence it is insufficient

Hence Choice E.


 


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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   13 Jul 2022, 21:34
Set inequality to one side and factor for:
ab^3c^2(c-b)>0 ??
ab* b^2c^2 * (c-b)>0 ?? left side becomes 0 if any of a,b,c, or c-b = 0

Statement (1) tells you that a and b both (+), c is closer to 0 than B is. also --> (c-b) is negative
ab (+) * (bc)^2 * (c-b) (-) cannot be (+)
Sufficient

Statement (2) tells you a>b and a is (+) Insufficient

Choice A is the answer.
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   13 Jul 2022, 22:39
We know mods are in the given inequality form however we do not know their signs.
We can also figure that a and b can't be 0 since their mods are both more than |c| and no number is less than 0 :)
1) a>b>c
If a, b and c are all positive, then RHS>LHS because a higher exponent is associated with the higher variable
If c= 0, then a and b can only take positive values. Here RHS=LHS. NS

2) a+b>0
a is positive and |b|<|a| thus b can be positive or negative. We do not know anything about c. If c is 0, they will equal otherwsie they won't. Same two scenarios as above can play out here. NS

1 and 2:
We still do not know value of c and the same 2 scenarios can take place again. NS

Ans E
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   14 Jul 2022, 00:34
Bunuel wrote:
If \(|a| > |b| > |c|\), is \(a*b^3*c^3 > a*b^4*c^2\) ?

(1) \(a > b > c\)
(2) \(a + b > 0\)



(1) \(a > b > c\)
If \( a > b > c > 0\)
\(=> a*b^3*c^3 < a*b^4*c^2\)
If \( a > b > c = 0\)
\(=> a*b^3*c^3 = a*b^4*c^2 = 0\)

=> Insuff

(2) \(a + b > 0\)
\(=> a > 0\)
* Case \(b>0\)
If \( c<0 => a*b^3*c^3 < a*b^4*c^2\)
If \( c>0 => a*b^3*c^3 > a*b^4*c^2\)
\(=> a*b^3*c^3 > a*b^4*c^2\)
=> Insuff

(1) & (2)
Same as (1). We don't know whether \(c = 0\) or not. => Insuff
=> Choice E
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   14 Jul 2022, 02:31
If |a|>|b|>|c|, is a∗b3∗c3>a∗b4∗c2 ?

(1) a>b>ca>b>c
(2) a+b>0

We have 1, a>b>c so a and b must be positive. Cause a<0, a>b => |a|<|b|. Similar with b. But we are not sure about c. For example, a=6,b=4, c=2 or c=-2, both cases satisfy conditions in the question. => insuf

2. a+b>0, still no information about c => insuf

=> E
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   14 Jul 2022, 02:37
My answer is A

A>B>C it means A b and C are positive because mode of (A>B>C) ,So A B and C must be positive
And from this condition we can answer the question given in the Stem
So statement A is Sufficient

Statement B is not sufficient as we don't know anything about C and also about the sign of value B
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   14 Jul 2022, 04:28
Answer: A

Given |a|>|b>|c|
when all three are +ve, then a>b>c
when all three are -ve, then a<b<c

We need to find
if a*b^3*c^3 > a*b^4*c^2
i.e. a*b^3*c^3 - a*b^4*c^2 > 0
i.e. a*b^3*c^2*(c-b) > 0
i.e. a*b^3*(c-b) > 0 .......c^2 will always be positive
when a, b, c are all +ve, then if c > b ?
when a and b are -ve, then if c > b ?
when a is -ve and b is +ve, then if |c| < |b| ?
when a is +ve and b is -ve, then if |c| < |b| ?

If we can find the relationship between b and c then answer to the question can be found.

When any of the value is 0 then the answer will be No.

(1) a>b>c
with given condition, this means a, b, c are all +ve
in this case, answer will be No.
a*b^3*c^3 will not be > a*b^4*c^2
Sufficient.

(2) a+b>0
With the given condition, there is no possibility to find relationship between b and c.
Hence, insufficient.
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   14 Jul 2022, 05:32
Bunuel wrote:
If \(|a| > |b| > |c|\), is \(a*b^3*c^3 > a*b^4*c^2\) ?

(1) \(a > b > c\)
(2) \(a + b > 0\)

 


This question was provided by GMAT Club
for the GMAT Club World Cup Competition

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\(a*b^3*c^3 > a*b^4*c^2\)
Dividing by \(b^2*c^2\) on both sides we get
=> \(a*b*c > a*b^2\)
=> \(a*b*c - a*b^2 > 0\)
=> \(a*b(c - b) > 0\) --> We have to check if this holds true

Statement (1)
Here we have a > b > c. We already know \(|a| > |b| > |c|\)
Choosing two sets of values we get
(i) a = -1, b = 2, c = 3, we get \(a*b(c - b) > 0\) = -2
(ii) a = 1, b = 2, c = 3, we get \(a*b(c - b) > 0\) = 2
Different values hence insufficient

Statement (2)
\(a + b > 0\)
Both the above examples (i) and (ii) from statement 1 are applicable to statement 2 hence this is also insufficient

Since both the examples (i) and (ii) are valid for both the equations, and both the statements cannot provide the solution individually or together, we would have to choose option E

IMHO Option E
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   14 Jul 2022, 05:44
We know that If |a|>|b|>|c| and asked whether a∗b^3∗c^3>a∗b^4∗c^2 (*)

(1) a>b>c
This statement means that a, b, c are positive,
then for (*) to be correct : a∗b^3∗c^3>a∗b^4∗c^2=>c>b which is not correct because b>c, so a∗b^3∗c^3<a∗b^4∗c^2

So 1st statement is sufficiant

(2) a+b>0
this means that,
a>0 and b>=0, but taking into account that |a|>|b|
OR, a>0 and b=<0 but taking into account that |a|>|b|

If b=0then (*) is not true because a∗b^3∗c^3=a∗b^4∗c^2 (same reasoniing for c)

if a>0 and b>0
then a∗b^4∗c^2>0 (no matter c is >or<0) and a∗b^3∗c^3 could be <0 (case where c<0) or could be >0 (case where c>0)
So we couldn't decide,
2nd statement is not sufficiant,

Answer is A
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   14 Jul 2022, 07:11
If |a|>|b|>|c||a|>|b|>|c|, is a∗b3∗c3>a∗b4∗c2 ?

(1) a>b>c
(2) a+b>0

statement 1 says that (a,b) are positive so the question becomes
is c3> bc2
or c3 - bc2 > 0
c2 * ( c - b) > 0
is c>b
given c< b ans is no
SUfficient


statement 2 clearly it is not sufficient
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   14 Jul 2022, 09:59
|a| > |b| > |c|, 2 conclusion can be drawn from this: (A). a>b>c , (B). -c>-b>-a

Question Stem a∗b3∗c3>a∗b4∗c2; ab3c2(c-b) > 0.

Statement 1: a>b>c, From A, it is sufficient

Statement 2: a+b>0, It's only satisfy A, so no ambiguity (for B, -b-a<0 not >0) Sufficient.

hence D is the answer
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink] New post   21 Oct 2023, 15:40
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Re: GMAT Club World Cup 2022 (DAY 3): If |a| > |b| > |c|, is a*b^3*c^3 > a [#permalink]
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