If a and b are positive, is (a^-1 + b^-1)^-1 less than (a^-1

Question

If a and b are positive, is (a^-1 + b^-1)^-1 less than (a^-1 * b^-1)^-1 ?

1) a = 2b

2) a + b > 1

A
B
C
D
E

OA will follow, please discuss

FN · Answer

so this simplifies to ab/(b+a) < ab?

since b and a are positive we can say

ab<ab(b+a)? which basically means its asking if a and b are fraction...and less than 1

1)

a=2b lets just pick number suppose b=3/7 then a=6/7

so 18/49 < (18/49)(9/7)?

yes..

suppose b=1 a=2 2<2(3) Yes

but suppose b=1/4 then a=1/2

1/8<1/8(3/4) NO...insuff

2)
a+b >1

Sufficient

scthakur · Answer

Expression in the main question can be simplified to

is ab/(a+b) < ab......and since both a and b are positive, this further simplifies to 
is (a+b) > 1........statement 2 clearly answers that.

Hence, B.

spriya · Answer

question is : ab/(a+b) < ab or ab(1/(a+b) -1 )<0 ???? (1) says a=2b , a=2b does not guarantee a+b>1 hence above expr can be +vbe or -ve INSUFFI (2)a+b>1 does not say a and b have same signs or opposite ,in both cases different values for the expr. (1) and (2) => SUFFI both are of same signs and again a+b>1 proves the relation given above IMO C

amitdgr · Answer

The best way to solve would be, simplify the question as much as possible

from the question we get to know that a and b are positive

so ab/(a+b) < ab can be written as ab(a+b) > ab and since ab is positive, we can divide both sides by ab ...

the simplified question is (a+b) > 1 ?

statement 1 says a = 2b ... this does not help me in telling whether a+b>1

incidentally statement 2 gives us the info directly that (a+b) > 1

so 2 is sufficient

Answer is B

stallone · Answer

i think its B !

because we need either ab<0 (impossible as a N b both are +ve) OR a+b>1

first stamnt doesnt help 2b+b may or may not be >1

2 stmnt proves a+b>1

hence B

x2suresh · Answer

ab/(a+b) < ab Question is ab(a+b)>ab? 1) a=2b.. a+b can be <1 or a+b>1 not sufficient 2) a+b>1 also ab is positive. ab(a+b)>ab is always true. sufficient. B

ssandeepan · Answer

(a^-1 + b^-1)^-1 less than (a^-1 * b^-1)^-1 ?

simplifyling the expression ab/(a+b) < ab ? or is 1 < ( a+ b) , which is stated in option 2 directly

so IMO B

spriya · Answer

oops i didnt read the questio properly again!!!

If a and b are positive, is (a^-1 + b^-1)^-1 less than (a^-1

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