Is 1/(a - b)

Question

Is 1/(a - b) < b + a?
 
(1) (a + b)(a – b) < 1
(2) ab > a – b

rohit8865 · Answer

combined also not suff

if a=0.5 , b=0.6 then YES
but if a=-0.5 ,b = -0.6 then NO

Ans E

HKD1710 · Answer

1/(a-b) < (b+a)

stmt-1: (a + b)(a – b) < 1 -- to use this statement

multiply numerator and denominator by the same value i.e. (a + b) of left side of 1/(a-b) < (b+a) and that becomes

(a + b)/(a + b)*(a-b) < (b+a)

(a + b)/ (less than 1) < (b+a)

now if (a + b)*(a-b) is 1/2 then 2(a + b) > (b+a) shows that 1/(a-b) < (b+a) is not true.

but if (a + b)*(a-b) is negative say -1 then -(a + b) < (b+a) i.e 1/(a-b) < (b+a) is true.

stmt-2: ab > a – b
see we do not get to know sign of a and b here. insufficient.

combining stmt-1 and stmt-2 would also not be hepful because we cannnot deduce anything helpful from ab > a-b that could be substitued in stmt-1. Because ab > a-b does not tell anything about signs.

Bunuel: Due you think that this reasoning is sufficient. because putting values will take more time.

insufficient.

Answer should be E.

Trap: we tend to multiply and divide by variables in inequality.
Learning: we should only do so if we know a variable is +ve or in absolute mod form or have even exponent.

laddaboy · Answer

Question : 1/(a-b) < b+a i.e is 1 < a^2-b^2 or is a^2-b^2 > 1

1 ) a^2-b^2 < 1 Suff

2) ab > a-b
say a =2 and b = 3 then 6(ab) > -1(a-b) True and a^2-b^2 = 4-9 = -5 < 1
a=-3 and b = -2 then 6(ab) > -1(a-b) True and a^2-b^2 = 5 > 1
InSuff

Hence answer is A.

AbhishekGopal · Answer

Is 1/(a-b) < b+a ?

1) (a+b) (a-b) < 1

2) ab> a-b

Statement 1 - SUFFICIENT:

First we simplify the question stem...

= 1/(a-b) < b+a
= 1 < (a+b) (a-b)
= 1 < a^2 - b^2

Is 1 < a^2 - b^2?

Statement 1 says that (a+b) (a-b) < 1 and hence this is sufficient  .

Statement 2 - INSUFFICIENT:

We do not know the sign of a and b, hence it is insufficient.

Hence the OA is A.

Hi  Bunuel , please do let me know if my answer is correct and my approach for the same.

Bunuel · Answer

The OA will be automatically revealed on Tuesday 28th of March 2017 05:41:55 AM Pacific Time Zone

rohit8865 · Answer

AbhishekGopal

as far as reasoning is concerned , highlighted part is not correct ,to my understanding..

ScottTargetTestPrep · Answer

We need to determine whether 1/(a - b) < b + a, or equivalently, whether a + b > 1/(a - b). Statement One Alone: (a + b)(a – b) < 1 If we divide both sides by a - b, we would have: a + b < 1/(a - b) if a - b is positive, OR a + b > 1/(a - b) if a - b is negative. Since we don’t know whether a - b is positive or negative, we can’t determine whether a + b > 1/(a - b) or a + b < 1/(a - b). Statement one alone is not sufficient to answer the question. Statement Two Alone: ab > a – b If a = 1 and b = 2, then 1/(a - b) < b + a since 1/-1 = -1 < 2 + 1 = 3. However, if a = 3/4 and b = 2/3, then 1/(a - b) > b + a since 1/(1/12) = 12 > 2/3 + 3/4. Statement two alone is not sufficient to answer the question. Statements One and Two Together: We can use the same examples as in statement two because both examples also satisfy statement one. If a = 1 and b = 2, (a + b)(a - b) = (3)(-1) = -3 < 1, and if a = 3/4 and b = 2/3, (a + b)(a - b) = (17/12)(1/12) = 17/144 < 1. However, in the former example, 1/(a - b) < b + a, and in the latter, 1/(a - b) > b + a. The two statements together are still not sufficient to answer the question. Answer: E

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Is 1/(a - b) < b + a?

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