Is 0

Question

Is 0 < a/b < 1 ?

(1) ab > 1 
(2) a − b < 1

Staphyk · Answer

Is 0 < a/b < 1 ?
Basically saying is a/b a positive proper fraction? Yes/No

(1) ab > 1
(1•2)>1 so a/b =1/2 yes
(2•1)>1 so a/b = 2 No (Not sufficient)

(2) a − b < 1
1/4 - 1/2 < 1 so a/b= (1/4)/(1/2)=1/2 yes
1/2 -1/4 <1 so a/b= (1/2)/(1/4)= 2
No
Not sufficient
(1+2) still can’t solve this corona virus
so E like Epidemic

Posted from my mobile device

Staphyk · Answer

Hmm wondering why not many replies here? What’s going on mathematicians ?

Posted from my mobile device

MARVEL13 · Answer

Hit and Trial..

A alone insufficient

B Alone insufficient

Already spent more than 2mins and still not sure of C? ---->Hit E

Posted from my mobile device

DinoPen · Answer

Took me 2:32...

1) I tested numbers:
(a,b) = (2,1) -> No
(a,b) = (1,2) -> Yes
Not Sufficient

2) I also tested numbers:
(a,b) = (2,3) -> No
(a,b) = (1/2, 1) Yes
Not Sufficient

1-2) From statement 1 + 2: I obtained

a - b + 1 < ab + 1
a < ab + b

You could start inserting numbers but the logic will flip when having negatives vs positive numbers (a,b) Hence, you can't come up with a reliable solution. So I just tapped E.

E

asadL · Answer

Help me with this step, how did you got this, particularly, when did you flip the inequalities?

Posted from my mobile device

DinoPen · Answer

asadL

(1) ab > 1
(2) a − b < 1

From 1 and 2
1 < ab
a - b < 1

Equality signs are in the same direction. Hence, you can add them together.

a - b + 1 < ab + 1

Basshead · Answer

Is 0 < a/b < 1 ?

(1) ab > 1

ab > 0
This statement tells us that a and b are both positive or both negative. However, we can't conclude 0 < a/b < 1. INSUFFICIENT.

(2) a − b < 1

a < b + 1
This statement tells us that b +1 is greater than a. However, we can't conclude 0 < a/b < 1. INSUFFICIENT.

(1&2)

We know a and b must have the same signs AND a < b + 1

if a = -3 b = -3

0 < -3/-3 < 1; false

if a = 2 b = 3
0 < 2/3 < 1; true

INSUFFICIENT.

Answer is E.

bumpbot · Answer

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Is 0 < a/b < 1 ? (1) ab > 1 (2) a − b < 1

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