If s is a positive integer and s^4 = 120t, which of the following must

Question

If s is a positive integer and s^4 = 120t, which of the following must be integers ?

I. t/(2^2*3^3*5^2)

II. t/(2*3*5)

III. t/(2*3*5*15)

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

stne · Answer

When an integer is quadrupled we will have  4  of that integer.

2^4 = 2*2*2*2  
 3^4 = 3*3*3*3 
etc.

Now for  s^4  too we should have  4  of the same kind

but in  120 *t = 2*2*2*3*5 *t  we do not have 4 of each kind, which should be the case

Hence  t  should compensate for the missing quadruples ! mimimum value of  t = 2*3*3*3*5*5*5

Hence

I. t/(2^2*3^3*5^2) = Need not be an integer.

II. t/(2*3*5) = Must be an integer

III. t/(2*3*5*15) = Must be an integer.

Ans D

Hope it helps.

vasu1104 · Answer

s^4 = 120t
s^ = 2^3*3*5*t

here for s to be integer, we need each num's exponent on RHS in the multiple of 4.
since 3 and 5 only have 1 each and 2 has 3, t must be 3^3*5^3*2

now from the option only second and third can divide 3 and leave integer as ans.

choice D

vasu1104 · Answer

s^4 = 120t
s^ = 2^3*3*5*t

here for s to be integer, we need each num's exponent on RHS in the multiple of 4.
since 3 and 5 only have 1 each and 2 has 3, t must be 3^3*5^3*2

now from the option only second and third can divide 3 and leave integer as ans.

choice D

vasu1104 · Answer

s^4 = 120t
s^ = 2^3*3*5*t

here for s to be integer, we need each num's exponent on RHS in the multiple of 4.
since 3 and 5 only have 1 each and 2 has 3, t must be 3^3*5^3*2

now from the option only second and third can divide 3 and leave integer as ans.

choice D

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