If s=t^2, where t is a positive integer, what is the value of s?

Question

(1) s=r^3, where r is an integer.
(2) 10 < s < 100

chetan2u · Answer

Hi..
the Q stem tells us that s is a perfect square

lets see the statements-

(1) s=r^3, where r is an integer. 
It tells us that s is a cube of an integer..
so s is both cube and square..
so s can be 2^6 = (2^3)^2 = (2^2)^3
also 3^6 = (3^3)^2 = (3^2)^3
many answers possible 
Insuff

(2) 10 < s < 100 
s can be anything - 4, 9 ,16 and so on
Insuff

combined 
the lowest is 2^6 = 64 
and no other number <100 is possible .
1 which is <10 cannot be the value
C

y4nkee · Answer

(1)
For t from 1 to 10:
S=t^2 = {1, 2, 9, 16, 25, 36, 49, 64, 81, 100}
Not sufficient > Possible Answer: BCE

(2)
For r from 4 to 5:
S=r^3={16, 64, 125}
Not sufficient > Possible Answer CE

(1)+(2)
Common term is 64. Hence S=64. Answer is C

for

If s=t^2, where t is a positive integer, what is the value of s?

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