Is a/b

Question

Is a/b<1/2?

1). a/(b-1)<1/2
2). (a-1)/b<1/2

ywilfred · Answer

a/b < 1/2 -> 2a 2a < b-1 -> 2a-1 < b. Sufficient. 1 less than 2a will be even smaller than 2a. 2) 2a-2 < b. Sufficient. 2 less than 2a wil be even smaller than 2a. Ans D

TeHCM · Answer

ywilfred, how do you know if a or b is not negative?

giddi77 · Answer

This one seems to be more difficult.

1. (a,b) = (1,4)
a/(b-1) = 1/3 (< 1/2) & a/b = 1/4 < 1/2 ==> true

(a,b) = (2,0.5)
a/(b-1) = 2/(0.5-1) = -4 (< 1/2) & a/b = 2/(0.5) = 4 > 1/2 ==> False

INSUFF.

2. (a,b) = (1,4)
(a-1)/b = 0 < 1/2 & a/b = 1/4 < 1/2 ==> true

(a,b) = (2,4)
(a-1)/b = 1/4 < 1/2 & a/b = 1/2 ==> false.

INSUFF.

Combining (1) & (2),....

I am stuck! :stupid

(1,4) and (-1,-5) work for both equations and also a/b < 1/2

I am not able to come up with numbers to prove the eqn false. On my exam I would choose C!

(1,4) and (-1,-5) work for both equations and also a/b < 1/2 I am not able to come up with numbers to prove the eqn false. On my exam I would choose C!

razrulz · Answer

u say (1 < 2a) << 2a ? how? i dont get it , how do u correlate this to the given equation

ywilfred · Answer

2a 2a Not possible as it violates 2a-2 2a 2a

duttsit · Answer

Is it E?

Is a/b<1/2?

S1:
a/(b-1)<1/2

it means
=> b <> 1
case1: a = 0 => ans = yes.
case 2: a > 0, b = 0 => ans = undefined
case 3: a = -2, b = -4 => ans = no
INSUFFICIENT

S2: (a-1)/b<1/2
it means:
=> b <> 0
case 1: a = 1, = 3 => ans = yes
case 2: a = 1, b = 1 => ans = no
INSUFFICIENT

Together:
we know:
b <> 0, b <> 1

case 1: a = 0, b > 1 => ans = yes
case 2: a = 1, b = 1/2 => ans = no
(only case where ans = no is when 0 : not equal to

business · Answer

I think its A 2a b-1 we can say b>(b-1)>2a sufficient - So A case 2 : 2(a-1) b, we can say (b+2)>2a>b or (b+2)>b>2a so not sufficient!

duttsit · Answer

How did you get bold part? As we do not know sign of a,b (+ve, -ve or 0) we can not possibly simplify this way. For example: a/b < 1/2 multiple both side by 2 gives 2a/b < 1 now, we cannot simplify this to: 2a 0 and b < 0 we will have 2a > b if a > 0 and b > 0 we will have 2a < b

TeHCM · Answer

OA is E, thanks Duttsit!! I really was trying to avoid picking numbers (takes too long) and use some kind of logic....but my mind is too muddled :crying

duttsit · Answer

Hey TeCHM, I still think analytical way of solving problems is always good. This way you can almost be sure about your answer. It also gives you hint about numbers to pick. However, for this problem, the analytical method I tried ran too lengthy to explain here. I would certainly think this is hard bin question. Cheer up!! :beer

giddi77 · Answer

Thanks for the solution and nice advice duttsit!

Is a/b<1/2? 1). a/(b-1)<1/2 2). (a-1)/b<1/2

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