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Manager
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Question Stats:
71% (01:40) correct
28% (00:38) wrong based on 121 sessions
a , b , and c are integers. Is abc = 0 ? 1. a^2 = 2a2. \frac{b}{c} = \frac{(a+b)^2}{a^2+2ab+b^2} - 1 ( a \ne -b and c \ne 0 ) Source: GMAT Club Tests - hardest GMAT questions REVISED VERSION OF THIS QUESTION IS HERE: m03-70290.html#p1228282
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CIO
Joined: 02 Oct 2007
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Hi. From S1 we see that a is either 0 or 2. Insufficient. S2. You have to notice that we need to simplify the fraction in S2: \frac{b}{c} = \frac{(a+b)^2}{a^2+2ab+b^2} - 1\frac{b}{c} = \frac{(a+b)^2}{(a+b)^2} - 1\frac{b}{c} = 1 - 1 = 0b = 0Hope this helps.
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Manager
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dzyubam wrote: Hi.
From S1 we see that a is either 0 or 2. Insufficient.
S2. You have to notice that we need to simplify the fraction in S2:
\frac{b}{c} = \frac{(a+b)^2}{a^2+2ab+b^2} - 1
\frac{b}{c} = \frac{(a+b)^2}{(a+b)^2} - 1
\frac{b}{c} = 1 - 1 = 0
b = 0
Hope this helps. he is missing -1 in S2. otherwise good one dzyubam
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Intern
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nshah12 wrote: Can some one explain Statement 1? Thanks! Statement one is saying that the square of A is equal to 2 x A. So this can be 2 or 0. 0 squared = 0 * 0 = 0 2 * 0 = 0 AND 2 squared = 2 * 2 = 4 2 * 2 = 4 So statement implies that A is either 0 or 2, therefore we can't tell if ABC = 0. Hope that helps.
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Manager
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this is how I approached it:
1) First condition gives us 2 possible values of a => a=0 or 2
2) Second condition comes as [b][/c] = 1-1=0
since "c" is not = 0, "b" is zero to make the result "0". hence B is the answer!
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Intern
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Question: Is abc = 0? Solution 1: a^2 = 2a => a . (a-2) = 0 => a = 0 or a = 2 When a = 0 => abc = 0 When a = 2 => abc may or may not be zeros depending on the values of b and c. Thus, solution 1 does not give a clear yes or no answer and is not sufficient. Solution 2: Solving the given equation: a^2 + 2ab + b^2 = (a + b)^2 Thus, b/c = 1 - 1 = 0 => b = 0 When b = 0 => abc = 0 Thus, Solution 2 gives a clear answer that, yes, abc = 0. Therefore, the correct answer choice is B. Award me with Kudos+1, if this helps!! Cheers!!!
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Director
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Enough solution has been given from the previous posts. (1) a= 0 or 2...insufficient (2) b=0...sufficient to answer whether abc = 0 (yes). B, off course is the answer.
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Manager
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A is insufficient as a=2 and B & C values are not given
B is sufficient because b/c = 1-1 => 0
Since c cannot be zero, b = 0 ==> abc=0
Therefore answer is B
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Director
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1. Not sufficient As a can be 0 or 2,abc may or may not be 0. 2.Sufficient b/c = 1-1 = 0. => b=0=> abc=0 Answer is B. Posted from my mobile device 
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jjhko wrote: a , b , and c are integers. Is abc = 0 ? 1. a^2 = 2a2. \frac{b}{c} = \frac{(a+b)^2}{a^2+2ab+b^2} - 1 ( a \ne -b and c \ne 0 ) Source: GMAT Club Tests - hardest GMAT questions Can't seem to figure out the explanation that I saw on the test. Thanks, John. I think the answer is B as st 2 gives us b=0 because C \ne 0. so abc = 0.
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AM
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\frac{b}{c} = \frac{(a+b)^2}{a^2+2ab+b^2} - 1 ( a \ne -b and c \ne 0 ) (a+b)^2=a^2+2ab+b^2 therefore frac{(a+b)^2}{a^2+2ab+b^2}=1 \frac{(a+b)^2}{a^2+2ab+b^2} - 1 =0 so 2 is sufficient so Answer=B
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1) A = 0 or 2 therefore insuff 2) B is sufficient since b/c = 1-1 => 0 and C != 0, therefore B = 0 B
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Intern
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Interpretation:
Statement: a=0 or b=0 or c=0
all three a,b,c =0?
option 1: insufficient since a=0 or a=2
option 2: sufficient since b=0
Ans: B
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Manager
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I missed the - 1 in the question ... It gets mixed with conditions given at the side of question... Anyways B is correct
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As we know a^2 + 2ab +b^2 is(a+b)^2
Therefore the expression (a+b)^2/(a^2 +2ab + b^2) can be reduced to 1
So substituting this in our equation we get
b/c=1 - 1 =0
which implies b=0, which satisfies our condition
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jjhko wrote: a , b , and c are integers. Is abc = 0 ? 1. a^2 = 2a2. \frac{b}{c} = \frac{(a+b)^2}{a^2+2ab+b^2} - 1 ( a \ne -b and c \ne 0 ) Source: GMAT Club Tests - hardest GMAT questions Can't seem to figure out the explanation that I saw on the test. Thanks, John. BELOW IS REVISED VERSION OF THIS QUESTION:Is abc = 0 ?In order abc = 0 to be true at least one of the unknowns must be zero. (1) a^2 = 2a --> a^2-2a=0 --> a(a-2)=0 --> a=0 or a=2. If a=0 then the answer is YES but if a=2 then abc may not be equal to zero (for example consider: a=2, b=3 and c=4). Not sufficient. (2) b= \frac{(a*\sqrt{c}+b*\sqrt{c})^2}{a^2+2ab+b^2} - c --> b= \frac{c*(a+b)^2}{(a+b)^2} - c --> b=c-c --> b=0. Sufficient. Answer: B.
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(A)a(a-2) = 0
a = 0 or a =2
In sufficient
b/c = ((a+b)^2 - (a+b)^2)/(a+b)^2
b/c=0
b=0
Sufficient
Ans:B
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guptasulabh7 wrote: (A)a(a-2) = 0
a = 0 or a =2
In sufficient
b/c = ((a+b)^2 - (a+b)^2)/(a+b)^2
b/c=0
b=0
Sufficient
Ans:B Is this the right simplification for statement 1:- I got only 1 value for a i.e. a=2 a square = 2a a * a = 2a a = 2 if its not correct simplification please explain, why?
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crackgmat2013 wrote: guptasulabh7 wrote: (A)a(a-2) = 0
a = 0 or a =2
In sufficient
b/c = ((a+b)^2 - (a+b)^2)/(a+b)^2
b/c=0
b=0
Sufficient
Ans:B Is this the right simplification for statement 1:- I got only 1 value for a i.e. a=2 a square = 2a a * a = 2a a = 2 if its not correct simplification please explain, why? Yes, that's not correct. Never reduce an equation by a variable (or expression with a variable), if you are not certain that the variable (or the expression with a variable) doesn't equal to zero. We can not divide by zero.So, if you divide (reduce) a^2=a by a you assume, with no ground for it, that a does not equal to zero thus exclude a possible solution (notice that both a=2 AND a=0 satisfy the equation). Hope it's clear.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!, 11 New DS set. NEW!!!
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Thank you Bunuel for clarifying d doubt Bunuel wrote: crackgmat2013 wrote: guptasulabh7 wrote: (A)a(a-2) = 0
a = 0 or a =2
In sufficient
b/c = ((a+b)^2 - (a+b)^2)/(a+b)^2
b/c=0
b=0
Sufficient
Ans:B Is this the right simplification for statement 1:- I got only 1 value for a i.e. a=2 a square = 2a a * a = 2a a = 2 if its not correct simplification please explain, why? Yes, that's not correct. Never reduce an equation by a variable (or expression with a variable), if you are not certain that the variable (or the expression with a variable) doesn't equal to zero. We can not divide by zero.So, if you divide (reduce) a^2=a by a you assume, with no ground for it, that a does not equal to zero thus exclude a possible solution (notice that both a=2 AND a=0 satisfy the equation). Hope it's clear. |
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