Set 25 q 27 & q29

[ankit0uc]

Q27.
If M is a positive integer, then M^3 has how many digits?
(1) M has 3 digits.
(2) M^2 has 5 digits
__________________________________________________ _____________-

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient



Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient



BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE
is sufficient.



EACH statement ALONE is sufficient



Statements (1) and (2) TOGETHER are NOT sufficient

Q29.
if X>1 and Y>1, is X<Y?
(1) X^2/(XY+X)<1
(2) XY/Y^2-Y<1


IMO B

[genius_in_the_gene]

1)
Let m= 999= 1000-1

1000^3 has 9 digits, so 999 should have more than 8 digits

if m=100 then m^3 will have 6 digits

Not suff

2) M^2 has 5 digits
so M is roughly between 100 and 300.
For 100 M^3 will have 6 digits and for 300 7 digits
Not Suff

1 and 2 states the same thing that m has 5 digits.
ANS E

[genius_in_the_gene]

1)

X^2/(XY+X)<1
x/(y+1)<1
since x and y are >1
so x<y+1
Not suff

2)
XY/Y^2-Y<1
x/y-1 <1
x<y-1

or x<y
Suff
ANS B