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Author:  Bunuel [ 28 Feb 2014, 03:09 ] 
Post subject:  Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
Author:  Bunuel [ 28 Feb 2014, 03:09 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
SOLUTION Is 1/(a  b) > b  a ? (1) a < b > we can rewrite this as: \(ab<0\) so LHS is negative, also we can rewrite it as: \(ba>0\) so RHS is positive > negative<positive. Sufficient. (2) 1 < a  b > if \(ab=2\) (or which is the same \(ba=2\)) then LHS>0 and RHS<0 and in this case the answer will be YES if \(ab=2\) (or which is the same \(ba=2\)) then LHS<0 and RHS>0 and in this case the answer will be NO. Not sufficient. Answer: A. 
Author:  anairamitch1804 [ 26 Jan 2017, 18:27 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
Statement 1: a < b Thus, ab<0, implying that ba>0. Is 1/(negative) < positive? YES. SUFFICIENT. Statement 2: 1 < a  b It's possible that ab = 2, implying that ba = 2. Plugging ab=2 and ba=2 into 1/(ab) < ba, we get: 1/2 < 2? NO. It's possible that ab = 2, implying that ba = 2. Plugging ab=2 and ba=2 into 1/(ab) < ba, we get: 1/2 < 2? YES. Since in the first case the answer is NO but in the second case the answer is YES, INSUFFICIENT. The correct answer is A. 
Author:  HKHR [ 01 Mar 2014, 02:21 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND Edition Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b Statement 1: a < b Thus, ab<0, implying that ba>0. Therefore, LHS is negative and RHS is positive. Which implies LHS<RHS. Therefore Sufficient. Statement 2: 1 < a  b This statement implies 1<(ab)<1 Substitute ab = 2 and ab= 2 we get different answers for both cases. INSUFFICIENT. Therefore answer is A. 
Author:  lool [ 09 Mar 2014, 13:49 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
Bunuel wrote: SOLUTION Is 1/(a  b) > b  a ? (1) a < b > we can rewrite this as: \(ab<0\) so LHS is negative, also we can rewrite it as: \(ba>0\) so RHS is positive > negative<positive. Sufficient. (2) 1 < a  b > if \(ab=2\) (or which is the same \(ba=2\)) then LHS>0 and RHS<0 and in this case the answer will be NO if \(ab=2\) (or which is the same \(ba=2\)) then LHS<0 and RHS>0 and in this case the answer will be YES. Not sufficient. Answer: A. for the second statement; 1 < a  b > 1< ab or ab < 1 AND ab < 1 > 1< ba therefore LHS will be negative and RHS will be positive >negative<positive. Sufficient. what is wrong with my approach ? 
Author:  Bunuel [ 09 Mar 2014, 14:02 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
lool wrote: Bunuel wrote: SOLUTION Is 1/(a  b) > b  a ? (1) a < b > we can rewrite this as: \(ab<0\) so LHS is negative, also we can rewrite it as: \(ba>0\) so RHS is positive > negative<positive. Sufficient. (2) 1 < a  b > if \(ab=2\) (or which is the same \(ba=2\)) then LHS>0 and RHS<0 and in this case the answer will be NO if \(ab=2\) (or which is the same \(ba=2\)) then LHS<0 and RHS>0 and in this case the answer will be YES. Not sufficient. Answer: A. for the second statement; 1 < a  b > 1< ab or ab < 1 AND ab < 1 > 1< ba therefore LHS will be negative and RHS will be positive >negative<positive. Sufficient. what is wrong with my approach ? From \(1 < a  b\) we can have two cases: A. \(1 < ab\) > \((\frac{1}{a  b}=positive) > (b  a=negative)\) > answer YES. B. \(ab<1\) > \((\frac{1}{a  b}=negative) < (b  a=positive)\) > answer NO. Two different answers, hence insufficient. Hope it's clear. 
Author:  coolredwine [ 11 Mar 2014, 01:24 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
I did it like this: We can reduce the given statement as: 1/(ab)>(ba) > Multiplying both sides by (ab), we get: 1>(ab)(ba) Taking negative out from RHS: 1<(ab)(ab), which is what we have to prove. Now, Statement 1: a<b > ab<0. Squaring both sides: (ab)(ab)<0. Hence, the answer would be No. Thus, sufficient. Statement 2: 1<ab > 1<(ab) or 1>(ab). Thus insufficient. Hence, answer is A. Please do let me know if this is a good way to proceed with such questions. Thanks. 
Author:  Bunuel [ 11 Mar 2014, 01:46 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
coolredwine wrote: I did it like this: We can reduce the given statement as: 1/(ab)>(ba) > Multiplying both sides by (ab), we get: 1>(ab)(ba) Taking negative out from RHS: 1<(ab)(ab), which is what we have to prove. Now, Statement 1: a<b > ab<0. Squaring both sides: (ab)(ab)<0. Hence, the answer would be No. Thus, sufficient. Statement 2: 1<ab > 1<(ab) or 1>(ab). Thus insufficient. Hence, answer is A. Please do let me know if this is a good way to proceed with such questions. Thanks. Unfortunately, most of it is wrong. We cannot multiply 1/(ab)>(ba) by ab, because we don't know its sign. If ab is positive, then we would have 1 > (ba)(ab); If ab is negative, then we would have 1 < (ba)(ab): flip the sign when multiplying by negative value. Never multiply (or reduce) an inequality by variable (or by an expression with variable) if you don't know its sign. Next, you cannot square ab<0 and write (ab)^2<0. This is obviously wrong: the square of a number cannot be less than zero. We can only raise both parts of an inequality to an even power if we know that both parts of the inequality are nonnegative (the same for taking an even root of both sides of an inequality). Adding/subtracting/multiplying/dividing inequalities: helpwithaddsubtractmultdividmultipleinequalities155290.html Hope this helps. 
Author:  Lucky2783 [ 10 Apr 2015, 03:30 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND Edition Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b Data Sufficiency Question: 120 Category: Arithmetic; Algebra Arithmetic operations; Inequalities Page: 161 Difficulty: 650 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions Project Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 1/(a  b) > b  a ? \(\frac{1+(ab)^2}{(ab)}\) > 0 ? we can see that numerator is always +ive . all we need to know is a>b? (1) a < b ; then \(\frac{1+(ab)^2}{(ab)}\) < 0 . Sufficient. (2) 1 < a  b case 1 : ab < 1 or a<b1 > a<b case 2: ab>1 or a> b+1> a>b not sufficient. Ans : A 
Author:  EgmatQuantExpert [ 08 May 2015, 00:40 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
Going through the solutions posted above, I realized that this question is a good illustration of the importance of first analyzing the question statement before moving to St. 1 and 2 in a DS question. Most students dived straight into Statement 1 and then tried to draw inferences from St. 1 to determine whether the inequality given in the question statement was true or not. Imagine if you had done this instead before going to St. 1: The question is asking if: \(\frac{1}{ab} < ba\) Case 1: a  b is positive (that is, a > b) Multiplying both sides of an inequality with with the positive number (ab) will not change the sign of inequality. So, the question simplifies to: Is 1 < (ba)(ab) Now, b  a will be negative. So, the question simplifies to: Is \(1 < (ab)^2\) . . . (1) \((ab)^2\), being a square term, will be >0 (Note: a  b cannot be equal to zero because then the fraction given in the question: 1/ab becomes undefined) So, \((ab)^2\) will be < 0 Therefore, the question simplifies to: Is 1 < (a negative number?) And the answer is NO. Case 2: a  b is negative (that is, a < b) Multiplying both sides of an inequality with the negative number (ab) will change the sign of inequality. So, the question simplifies to: Is 1 > (ba)(ab) Now, b  a will be positive. So, the question simplifies to: Is \(1 > (ab)^2\) . . . (2) Again, by the same logic as above, we see that the question simplifies to: Is 1 > (a negative number?) And the answer is YES Thus, from the question statement itself, we've inferred that: If a > b, the answer to the question asked is NO If a < b, the answer to the question asked is YES Thus, the only thing we need to find now is whether a > b or a < b. Please note how we are going to Statement 1 now with a much simpler 'To Find' task now. One look at St. 1 and we know that it will be sufficient. One look at St. 2 and we know that it doesn't give us a clear idea of which is greater between a and b, and so, is not sufficient. To sum up this discussion, spending time on analyzing the question statement before going to the two statements usually simplifies DS questions a good deal. Hope this helped! Japinder 
Author:  AbdurRakib [ 11 Apr 2016, 00:00 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
[quote="Bunuel"]SOLUTION Is 1/(a  b) > b  a ? (1) a < b > we can rewrite this as: \(ab<0\) so LHS is negative, also we can rewrite it as: \(ba>0\) so RHS is positive > negative<positive. Sufficient. (2) 1 < a  b > if \(ab=2\) (or which is the same \(ba=2\)) then LHS>0 and RHS<0 and in this case the answer will be YES if \(ab=2\) (or which is the same \(ba=2\)) then LHS<0 and RHS>0 and in this case the answer will be NO. Not sufficient. Dear, Please Clarify me Rewrite like this one.I thought rewite variable without considering its Sign is Wrong 
Author:  Bunuel [ 11 Apr 2016, 00:03 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
AbdurRakib wrote: Bunuel wrote: SOLUTION Is 1/(a  b) > b  a ? (1) a < b > we can rewrite this as: \(ab<0\) so LHS is negative, also we can rewrite it as: \(ba>0\) so RHS is positive > negative<positive. Sufficient. (2) 1 < a  b > if \(ab=2\) (or which is the same \(ba=2\)) then LHS>0 and RHS<0 and in this case the answer will be YES if \(ab=2\) (or which is the same \(ba=2\)) then LHS<0 and RHS>0 and in this case the answer will be NO. Not sufficient. Dear, Please Clarify me Rewrite like this one.I thought rewite variable without considering its Sign is Wrong We cannot multiply an inequality by a variable if don't know its sign but we can add/subtract a value to both sides. To get ab<0 from a < b we are subtracting b from both sides and to get b  a > 0 we are subtracting a from both sides. 
Author:  CrackverbalGMAT [ 03 Jun 2019, 10:25 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
Let us look at this question differently here: While solving DS inequality questions, the best approach is to always breakdown the question stem if possible. To breakdown the question stem, there are three hygiene factors, that if followed will simplify your analysis of the question. 1. Always keep the RHS of the inequality as 0 2. Simplify the LHS to a product or division of values (product and division of terms are easier to analyze) 3. Always try and maintain even powered terms (as the sign of them will always be 0 or positive) Let us breakdown the question stem here: 1/(a  b) > b  a (1/(a  b))  (b  a) > 0 Since we have an option to get a squared term, before we take the LCM let us change b  a to a  b. (1/(a  b)) + (a  b) > 0 > (1 + (a  b)^2)/(a  b) > 0 Now since we have deconstructed the question stem to a division we just need to worry about the signs of the numerator and denominator. The RHS here is > 0, so we the numerator and denominator have to have the same sign. The numerator however will always be positive, since 1 + (a  b)^2 will always be positive. So we just need need the denominator to also be positive. The entire question stem can now be rephrased as 'Is a  b > 0'? Statement 1 : a  b < 0 This gives us a definite NO. So sufficient. Statement 2 : 1 < a  b a  b > 1. This only tells us that a  b > 1 or a  b < 1. So a  b can be both positive or negative. Insufficient. Answer: A Hope this helps! Aditya CrackVerbal Academic Team 
Author:  Kinshook [ 31 Aug 2019, 09:13 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
Bunuel wrote: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b The Official Guide For GMAT® Quantitative Review, 2ND Edition Asked: Is 1/(a  b) > b  a ? 1/(ab) + (ab) >0 (ab)^2 + 1 / (ab) >0 Since numerator >0 Q. a b >0 (1) a < b ab<0 ab is NOT >0 SUFFICIENT (2) 1 < a  b ab > 1 or ab < 1 NOT SUFFICIENT IMO A 
Author:  siddharth287 [ 29 Jan 2022, 07:02 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
Bunuel wrote: SOLUTION Is 1/(a  b) > b  a ? (1) a < b > we can rewrite this as: \(ab<0\) so LHS is negative, also we can rewrite it as: \(ba>0\) so RHS is positive > negative<positive. Sufficient. (2) 1 < a  b > if \(ab=2\) (or which is the same \(ba=2\)) then LHS>0 and RHS<0 and in this case the answer will be YES if \(ab=2\) (or which is the same \(ba=2\)) then LHS<0 and RHS>0 and in this case the answer will be NO. Not sufficient. Answer: A. statement 1 says a<b so if we substitute values for a and b. example a = 2 and b = 3 then from original equation we get 1/(23) > 32 ie 1/1 > 1 ie 1>1 how is that possible? And why is statment 1 sufficient then 
Author:  Bunuel [ 29 Jan 2022, 08:06 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
siddharth287 wrote: Bunuel wrote: SOLUTION Is 1/(a  b) > b  a ? (1) a < b > we can rewrite this as: \(ab<0\) so LHS is negative, also we can rewrite it as: \(ba>0\) so RHS is positive > negative<positive. Sufficient. (2) 1 < a  b > if \(ab=2\) (or which is the same \(ba=2\)) then LHS>0 and RHS<0 and in this case the answer will be YES if \(ab=2\) (or which is the same \(ba=2\)) then LHS<0 and RHS>0 and in this case the answer will be NO. Not sufficient. Answer: A. statement 1 says a<b so if we substitute values for a and b. example a = 2 and b = 3 then from original equation we get 1/(23) > 32 ie 1/1 > 1 ie 1>1 how is that possible? And why is statment 1 sufficient then The question asks whether 1/(a  b) > b  a. If we can give a definite YES answer to the question (YES, 1/(a  b) IS greater than b  a) OR a definite NO answer to the question (No, 1/(a  b) is NOT greater than b  a), then the statement is sufficient (recall that a definite NO answer to a DS question is also sufficient). Now, since a < b, then a  b < 0 and b  a > 0, thus 1/(a  b) = 1/negative = negative, while b  a = positive, so 1/(a  b) < b  a, which means that the answer to the question is NO, 1/(a  b) is NOT greater than b  a. That's why the first statement is sufficient. Check the links below for DS Strategies and Tactics
GMAT Tip of the Week: The Heart of Data Sufficiency GMAT Tip of The Week: Tonya Harding Teaches Data Sufficiency CTrap Questions Veritas Prep blog on CTrap. Manhattan GMAT blog on CTrap. Another Manhattan GMAT blog on CTrap. Warning: Don't Fall Into the C Trap on Data Sufficiency Questions Easy (A)/(B) Trap in Data Sufficiency Questions on the GMAT How to Breakdown Data Sufficiency Sequence Questions on the GMAT How to Make Abstract Data Sufficiency Questions More Concrete Math Knowledge is Often Insufficient on Data Sufficiency Why You Should Do the Math on Data Sufficiency GMAT Questions GMAT Tip of the Week: No Resolution! GMAT Tip of the Week: LeBron James Says Don't Be Cavalier About Your Initial Data Sufficiency Decision Data Sufficiency: Why Are you Here? GMAT Tip of the Week: Kanye West Teaches You How To Live The Data Sufficiency Good Life When Do You Have Enough Information on Data Sufficiency GMAT Questions? Must Know Data Sufficiency Strategies For other subject check Ultimate GMAT Quantitative Megathread. Hope it helps. 
Author:  DHRJ0032 [ 29 Jan 2022, 10:16 ]  
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b  
Well this question can be solved very easily with the graphical approach. Let, ab=x Now, rephrase the question: Is 1/x>x? Clearly from graph , for x>0, 1/x>x. 1)x<0 No, for x<0 , 1/x<x SUFFICIENT. 2)x>1 For x>1 , YES for x<1, NO INSUFFICIENT. A it is. Posted from my mobile device

Author:  sacharya [ 31 Mar 2022, 21:42 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
\(1/(a  b) > b  a ?\) Simplifying this further \(1/(a  b)  (ba) >0 ?\) \(1+(ab)^{2}/(ab) > 0 ?\) \(1+(ab)^{2}\) is always positive; we need to find if (ab) is positive or neg Stmt 1: a<b ab<0 (ab) negative Sufficient Stmt 2: 1 < a  b i.e. a  b > 1 (ab) > 1 OR (ab) > 1 case 1. (ab) > 1, (ab) will be positive case 2. (ab) > 1 (ab) < 1 , (ab) will be negative Not Sufficient Ans A 
Author:  gmatprepguy2049 [ 11 Apr 2022, 05:34 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
Where are the options for the question? I'm not able to see them 
Author:  Bunuel [ 11 Apr 2022, 07:50 ] 
Post subject:  Re: Is 1/(a  b) > b  a ? (1) a < b (2) 1 < a  b 
gmatprepguy2049 wrote: Where are the options for the question? I'm not able to see them Hi, This is a data sufficiency question. Options for DS questions are always the same. The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether— A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked. D. EACH statement ALONE is sufficient to answer the question asked. E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed. I suggest you to go through the following post ALL YOU NEED FOR QUANT. Hope this helps. 
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