Author 
Message 
Intern
Joined: 12 Oct 2008
Posts: 13

1
This post was BOOKMARKED
If a, b, c and are positive and a^2+c^2 =202, what is the value of bac?
(1) b^2+c^2=225 (2) a^2+b^2=265
from 1 we get b^2a^2=23.
(b+a)(ba) =23, as 23 a prime number, b+a =23 and ba = 1, => b=12 and a =11. so c=9
Hence statement 1 is sufficient to answer the question.
Is the solution incorrect? if yes why? Help Please.



Math Expert
Joined: 02 Sep 2009
Posts: 39760

Re: M06 Q34 [#permalink]
Show Tags
01 Apr 2012, 13:04
AmarSharma wrote: If a, b, c and are positive and a^2+c^2 =202, what is the value of bac?
(1) b^2+c^2=225 (2) a^2+b^2=265
from 1 we get b^2a^2=23.
(b+a)(ba) =23, as 23 a prime number, b+a =23 and ba = 1, => b=12 and a =11. so c=9
Hence statement 1 is sufficient to answer the question.
Is the solution incorrect? if yes why? Help Please. The problem with your solution is that you assume, with no ground for it, that variables represent integers only. From (b+a)(ba)=23 you cannot say that b+a=23 and ba=1, because for example b+a can be 46 and ba can be 1/2. If a, b, c and are positive and a^2+c^2=202, what is the value of bac?(1) b^2+c^2=225. Not sufficient on its own. (2) a^2+b^2=265. Not sufficient on its own. (1)+(2) Subtract a^2+c^2=202 from b^2+c^2=225: b^2a^2=23. Now, sum this with a^2+b^2=265: 2b^2=288 > b^2=144 > b=12 (since given that b is a positive number). Since b=12 then from b^2a^2=23 we get that a=11 and from a^2+c^2=202 we get that c=9. Sufficient. Answer: C. Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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. ,11 Mixed Questions, 12 Fresh Meat 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., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 12 Oct 2008
Posts: 13

Re: M06 Q34 [#permalink]
Show Tags
01 Apr 2012, 21:43
Bunuel wrote: AmarSharma wrote: If a, b, c and are positive and a^2+c^2 =202, what is the value of bac?
(1) b^2+c^2=225 (2) a^2+b^2=265
from 1 we get b^2a^2=23.
(b+a)(ba) =23, as 23 a prime number, b+a =23 and ba = 1, => b=12 and a =11. so c=9
Hence statement 1 is sufficient to answer the question.
Is the solution incorrect? if yes why? Help Please. The problem with your solution is that you assume, with no ground for it, that variables represent integers only. From (b+a)(ba)=23 you cannot say that b+a=23 and ba=1, because for example b+a can be 46 and ba can be 1/2. If a, b, c and are positive and a^2+c^2=202, what is the value of bac?(1) b^2+c^2=225. Not sufficient on its own. (2) a^2+b^2=265. Not sufficient on its own. (1)+(2) Subtract a^2+c^2=202 from b^2+c^2=225: b^2a^2=23. Now, sum this with a^2+b^2=265: 2b^2=288 > b^2=144 > b=12 (since given that b is a positive number). Since b=12 then from b^2a^2=23 we get that a=11 and from a^2+c^2=202 we get that c=9. Sufficient. Answer: C. Hope it's clear. Thanks. I have to be more careful with my assumptions.



Manager
Joined: 16 Feb 2011
Posts: 195
Schools: ABCD

Re: M06 Q34 [#permalink]
Show Tags
13 Apr 2012, 06:19
Bunuel wrote: AmarSharma wrote: If a, b, c and are positive and a^2+c^2 =202, what is the value of bac?
(1) b^2+c^2=225 (2) a^2+b^2=265
from 1 we get b^2a^2=23.
(b+a)(ba) =23, as 23 a prime number, b+a =23 and ba = 1, => b=12 and a =11. so c=9
Hence statement 1 is sufficient to answer the question.
Is the solution incorrect? if yes why? Help Please. The problem with your solution is that you assume, with no ground for it, that variables represent integers only. From (b+a)(ba)=23 you cannot say that b+a=23 and ba=1, because for example b+a can be 46 and ba can be 1/2. If a, b, c and are positive and a^2+c^2=202, what is the value of bac?(1) b^2+c^2=225. Not sufficient on its own. (2) a^2+b^2=265. Not sufficient on its own. (1)+(2) Subtract a^2+c^2=202 from b^2+c^2=225: b^2a^2=23. Now, sum this with a^2+b^2=265: 2b^2=288 > b^2=144 > b=12 (since given that b is a positive number). Since b=12 then from b^2a^2=23 we get that a=11 and from a^2+c^2=202 we get that c=9. Sufficient. Answer: C. Hope it's clear. Bunuel  I have a question  The question states that a,b,c are positive. It doesn't state that they are positive integers. Essentially, I could have a=10.99 etc... Do you think that the answer would be E) then? Please help me Thanks Voodoo



Math Expert
Joined: 02 Sep 2009
Posts: 39760

Re: M06 Q34 [#permalink]
Show Tags
13 Apr 2012, 06:29
voodoochild wrote: Bunuel wrote: AmarSharma wrote: If a, b, c and are positive and a^2+c^2 =202, what is the value of bac?
(1) b^2+c^2=225 (2) a^2+b^2=265
from 1 we get b^2a^2=23.
(b+a)(ba) =23, as 23 a prime number, b+a =23 and ba = 1, => b=12 and a =11. so c=9
Hence statement 1 is sufficient to answer the question.
Is the solution incorrect? if yes why? Help Please. The problem with your solution is that you assume, with no ground for it, that variables represent integers only. From (b+a)(ba)=23 you cannot say that b+a=23 and ba=1, because for example b+a can be 46 and ba can be 1/2. If a, b, c and are positive and a^2+c^2=202, what is the value of bac?(1) b^2+c^2=225. Not sufficient on its own. (2) a^2+b^2=265. Not sufficient on its own. (1)+(2) Subtract a^2+c^2=202 from b^2+c^2=225: b^2a^2=23. Now, sum this with a^2+b^2=265: 2b^2=288 > b^2=144 > b=12 (since given that b is a positive number). Since b=12 then from b^2a^2=23 we get that a=11 and from a^2+c^2=202 we get that c=9. Sufficient. Answer: C. Hope it's clear. Bunuel  I have a question  The question states that a,b,c are positive. It doesn't state that they are positive integers. Essentially, I could have a=10.99 etc... Do you think that the answer would be E) then? Please help me Thanks Voodoo We have a system of equations, which gives us fixed values of a, b and c: From b^2=144 > b=12 (since b>0 then b=12 is not a valid solution); From b^2a^2=23 > 144a^2=23 > a^2=121 > a=11 (since a>0 then a=11 is not a valid solution); From a^2+c^2=202 > 121+c^2=202 > c^2=81 > c=9 (since c>0 then c=9 is not a valid solution). Now, we are not told that a, b, and c are integers but how did this affect the solution? How can a solution of a^2=121 be a=10.99 or any other value but a=11 (or a=11 which we discarded because of a>0)?
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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. ,11 Mixed Questions, 12 Fresh Meat 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., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 16 Feb 2011
Posts: 195
Schools: ABCD

Re: M06 Q34 [#permalink]
Show Tags
13 Apr 2012, 08:15
Thanks Bunuel. You are correct. I didn't think about the system of equations.











