Source:- Manhattan Lab # 2 - Data sufficency - Yes / No testing LAB

Question Number 206. I belive this is an OG number.

Question:-

[question deleted because it is an OG question]

Statement 1 is in Insufficient because we don’t know if x is a positive or negative. If x is positive fraction ½ than statement one is sufficient but if x is negative – ½ than it will not work because when squared it will return a positive answer. Statement Insufficient

Statement two is insufficient because we don’t know what is the value of x it can be a fraction or not a fraction.

When we combine both statements we know from statement two that x is positive and statement one tells us it is a fraction. Sufficient. I think “C” is the correct answer.

On the LAB correct answer was marked as “A”. Can someone explain.

Using 1:
x^2 is less than x

try using different values and find which value of x does satisfy the above given condition
-> if x is negative for example -1 , X^2 = 1 which is greater than X, so it does not satisfy
-> if x is positive greater than 1, let x =2 , X^2 =4 , still greater
-> if x = 0 , X^2 = 0, still not less than X.
-> if x is between 0 and 1, if x = 1/2 , x^2 = 1/4, which is less

the conclusion is is x is between 0 and 1, SUFFICIENT
Note: properties like this has to be remembered to save time in actual GMAT.

Using 2: X^3 is positive,
this only means X is +ve and does not give any range


ANS therefore is A

thank you blue_lotus for your reply

But if x is -1/2 it will still yeild positive 1/4.

than x can be positive 1/2 or negative -1/2 and in both than for statement one answer is may be.

What am i missing here?

thanks in advance

If x is -1/2, then x^2 is 1/4.

1/4 > -1/2 so
x^2 > x

However, Statement 1 states x^2 < x
Therefore -1/2 is not a valid value for x in this case.

As blue_lotus showed, only positive fractions meet the criteria for Statement 1 and therefore can sufficiently answer the question if x is between 0 and 1.

tmmyc is right, -1/2 does not meet the mentioned criterial .
Any negative number will not meet the criteria as
square of any negative number whether it is an integer or fraction,it will be positive, and postive number is always greater than negative number.

so we can conclude that the number range we are looking for is not less than 0. i.e x > 0

Ah Haa

Thanks allot guys.

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