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# r, t, and s are all integers, is t/ (s^2) an integer? 1)

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r, t, and s are all integers, is t/ (s^2) an integer? 1) [#permalink]  10 Feb 2004, 15:24
r, t, and s are all integers, is t/ (s^2) an integer?

1) t/rs is an integer

2) r/s is an integer

Vivek.
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"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

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1) and 2) by themselves are insufficient. From t/rs multiplied with r/s equals t/s^2 since both are integers the resulting should be an integer or C)
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C)

From 1:
Let T = 12
R = 1
S = 3
Then T/RS = 12 / 1*3 = 4 and T/S^2 = 12 / 3^2 = 12/9 = 4/3 which is not an integer
Let T = 12
R = 3
S = 1
Then T/RS = 12 / 3*1 = 4 and T/S^2 = 12 / 1^2 = 12 which IS an integer
Thus 1 is not sufficient

From 2:
Let T = 12
R = 3
S = 1
Then R/S = 3/1 = 3 and T/S^2 = 12 / 3^2 = 4/3 which is not an integer
Let T = 12
R = 2
S = 1
Then R/S = 2/1 = 2 and T/S^2 = 12 / 1^2 = 12 which IS an integer
Thus 2 is not sufficient

Combining both statements we we will always be able to get an integer by ensuring that S (R/S being an integer) is the least of the 2 divisors (T/RS being an integer). I'm not sure how to explain this but I tried a few numbers and always get T/S^2 being an integer
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The answer is C...but I dont have the official explanation..

Vivek.
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mdfrahim wrote:

r, t, and s are all integers, is t/ (s^2) an integer?

1) t/rs is an integer

2) r/s is an integer

From Qustion stem: asked Is t/(s^2) an INT ?
or t = a * s^2; is "a" an INT ? --- (0)

From 1:
t/rs = b ; b= INT
t = b * rs ---- (1)

Where "b" or "r" could be either multiple of "s" or not.
If "b" or "r" is multiple of "s" ,then "a" is an INT.
If not, "a" is not an INT

INSUFF

From 2:
r/s = c; c = INT
r = c * s ---(2)

The does not give any relation between t and r&s.
INSUFF

From (1)+(2)
t= b * rs ; b = INT
r = c * s ; b = INT
togather,
t = b * c * s * s = bc * s^2
If b & c are INT, then bc = a is also INT.

SUFF

INT: Integer

Good Luck!
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Vivek.
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"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

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