Is a b? (1) a

Question

Is  a > b ?

(1)  a < 2b

(2)  (a – b)^2 = 1

pushpitkc · Answer

(1) a < 2b Let's test some values in order to check if a > b Case 1: a = 3, b = 2 Here, the statement is TRUE Case 2: a = 0, b = 1 Here, the statement is FALSE (Insufficient) (2) (a – b)^2 = 1 Let's test some values in order to check if a > b Case 1: a = 3, b = 2 Here, the statement is TRUE Case 2: a = 0, b = 1 Here, the statement is FALSE (Insufficient) When we combine the information in both the statements, we can't clearly say if a > b or a < b (Insufficient - Option E)

sidsst · Answer

This is a great question for DS.

Lets go with option 2 first :

it says [m](a-b)^2 =1
-> a-b= 1 ...(i) or a-b = -1 ...(ii)

Now from (i) a = b+1 , also b+1 > b answer : YES
from (ii) a = b -1 , b-1 > b answer : NO

two different answers. Thus this is not sufficient.

Now option (1) :

Here it will be much easier to assume values and try to get two different answers.

a<2b so we can take a=4 and b=3 (4<6) and also 4>3 {a>b} answer : YES
we can also take a=-1 and b=1 (-1< 1) but is {a>b} in this case answer : NO
hence this is also not sufficient.

BOTH THE STATEMENTS ARE NOT SUFFICIENT TO ANSWER THE QUESTION.
ANSWER : E

jedit · Answer

It should be E

1- Let us create a table with all possible values of a and b.

i - a is +ive and b is +ive
ii - a is +ive and b is -ive
iii - a is -ive and b is +ive
iv - a is -ive and b is -ive

Statement 1 rules out (ii) while rest of them are all possible in which a can be larger or smaller than b.

2- If we simplify it, we get two scenarios

a = b + 1 or
a = b - 1

This again does not confirm the sign of a and b.

Combining, we still do not know the sign of a and b for sure. Hence  E  should be the answer.

bumpbot · Answer

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Is a > b? (1) a < 2b (2) (a – b)^2 = 1

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