ADDING, SUBTRACTING AND FINDING THE LEAST COMMON MULTIPLE

     
Difficulty: 700-Level Absolute Values/Modulus Inequalities Source: OG 10 Source: Official Guide Source: Quant reviews 1st Source: Quant reviews 2nd
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Is 1/(a - b) > b - a ? (1) a #permalink>
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28 Feb 2014, 03:09
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SOLUTIONIs 1/(a - b) > b - a ?(1) a we can rewrite this as: (a-b0) so RHS is positive --> negative

(2) 1 if (a-b=2) (or which is the same (b-a=-2)) then LHS>0 and RHS0 and in this case the answer will be NO. Not sufficient.Answer: A._________________
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Statement 1: a 0. Is 1/(negative) YES. SUFFICIENT. Statement 2: 1 It"s possible that a-b = 2, implying that b-a = -2. Plugging a-b=2 và b-a=-2 into 1/(a-b) 50% NO. It"s possible that a-b = -2, implying that b-a = 2. Plugging a-b=-2 và b-a=2 into 1/(a-b) 1/-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._________________
Statement 1: a Thus, a-b0. Therefore, LHS is negative & RHS is positive. Which implies LHSStatement 2: 1 This statement implies 1Substitute a-b = 2 và a-b= -2 we get different answers for both cases. INSUFFICIENT.Therefore answer is A.

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SOLUTIONIs 1/(a - b) > b - a ?(1) a we can rewrite this as: (a-b0) so RHS is positive --> negative(2) 1 if (a-b=2) (or which is the same (b-a=-2)) then LHS>0 và RHS0 and in this case the answer will be YES. Not sufficient.Answer: A.
SOLUTIONIs 1/(a - b) > b - a ?(1) a we can rewrite this as: (a-b0) so RHS is positive --> negative(2) 1 if (a-b=2) (or which is the same (b-a=-2)) then LHS>0 và RHS0 & in this case the answer will be YES. Not sufficient.Answer: A.

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From (1 A. (1 ((frac1a - b=positive) > (b - a=negative)) --> answer YES.B. (a-b ((frac1a - b=negative) answer NO.Two different answers, hence insufficient.Hope it"s clear._________________
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I did it lượt thích this:We can reduce the given statement as:1/(a-b)>(b-a) -> Multiplying both sides by (a-b), we get: 1>(a-b)(b-a)Taking negative out from RHS: 1Now, Statement 1: a a-bStatement 2: 1 1(a-b). Thus insufficient.Hence, answer is A.Please bởi vì let me know if this is a good way khổng lồ proceed with such questions.Thanks.
I did it like this:We can reduce the given statement as:1/(a-b)>(b-a) -> Multiplying both sides by (a-b), we get: 1>(a-b)(b-a)Taking negative out from RHS: 1Now, Statement 1: a a-bSquaring both sides: (a-b)(a-b) Hence, the answer would be No. Thus, sufficient.Statement 2: 1 1(a-b). Thus insufficient.Hence, answer is A.Please bởi let me know if this is a good way khổng lồ proceed with such questions.Thanks.

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Unfortunately, most of it is wrong.We cannot multiply 1/(a-b)>(b-a) by a-b, because we don"t know its sign.If a-b is positive, then we would have 1 > (b-a)(a-b);If a-b is negative, then we would have 1 (b-a)(a-b): 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 a-bWe can only raise both parts of an inequality khổng lồ an even nguồn if we know that both parts of the inequality are non-negative (the same for taking an even root of both sides of an inequality).Adding/subtracting/multiplying/dividing inequalities: help-with-add-subtract-mult-divid-multiple-inequalities-155290.htmlHope this helps._________________
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Data SufficiencyQuestion: 120Category: Arithmetic; Algebra Arithmetic operations; InequalitiesPage: 161Difficulty: 650
1/(a - b) > b - a ?(1) a (2) 1 1/(a - b) > b - a ?(frac1+(a-b)^2(a-b)) > 0 ? we can see that numerator is always +ive . All we need khổng lồ know is a>b? (1) a (2) 1 case 1 : a-b a case 2: a-b>1 or a> b+1------> a>b not sufficient. Ans : A
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 lớn St. 1 và 2 in a DS question.Most students dived straight into Statement 1 & then tried to draw inferences from St. 1 lớn 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:(frac1a-b Case 1: a - b is positive (that is, a > b)Multiplying both sides of an inequality with with the positive number (a-b) will not change the sign of inequality.So, the question simplifies to: Is 1 Now, b - a will be negative.So, the question simplifies to: Is (1 ((a-b)^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/a-b becomes undefined)So, (-(a-b)^2) will be Therefore, the question simplifies to: Is 1 and the answer is NO.Case 2: a - b is negative (that is, a Multiplying both sides of an inequality with the negative number (a-b) will change the sign of inequality.So, the question simplifies to: Is 1 > (b-a)(a-b)Now, b - a will be positive.So, the question simplifies to: Is (1 > -(a-b)^2) . . . (2)Again, by the same lô ghích as above, we see that the question simplifies to: Is 1 > (a negative number?) và the answer is YESThus, from the question statement itself, we"ve inferred that:If a > b, the answer khổng lồ the question asked is NOIf a , the answer to the question asked is YESThus, the only thing we need to find now is whether a > b or a Please cảnh báo how we are going to lớn Statement 1 now with a much simpler "To Find" task now.

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One look at St. 1 & we know that it will be sufficient.One look at St. 2 & we know that it doesn"t give us a clear idea of which is greater between a và b, & so, is not sufficient.To sum up this discussion, spending time on analyzing the question statement before going to lớn the two statements usually simplifies DS questions a good deal.Hope this helped!Japinder_________________
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