Data Sufficiency

Question 1
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If M is a positive integer, then M^3 has how many digits?
(1) M has 3 digits.
(2) M^2 has 5 digits

Correct Ans E - Why B is incorrect

Question 2
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if X>1 and Y>1, is X<Y?
(1) X^2/(XY+X)<1
(2) XY/Y^2-Y<1

Qusetion 1:

In such kinda sum you should just observe the figure and conclude, Calculating values take loads of time.

I & II both fails for the following values.

M = 100
M^2 = 10000 ( 5 digits )
M^3 = 1000000 ( 7 digits )

M = 315
M^2 = 99225 ( 5 digits )
M^3 = 31255875 ( 8 digits )

Ans E.

Question 2:

if X>1 and Y>1, is X<Y?

I. X^2/(XY+X)<1
i.e. X^2< XY+Y
i.e. X < Y + 1

Since X & Y both are positive , this does not mean that X < Y, INSUFF

II. XY/Y^2-Y<1
i.e. XY<Y^2-Y
i.e. X < Y - 1
Since X & Y both are positive X < Y, SUFF

Ans B.