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

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Senior Manager
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r, t, and s are all integers, is t/ (s^2) an integer? 1) [#permalink]

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10 Feb 2004, 16:24
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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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10 Feb 2004, 16:39
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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10 Feb 2004, 16:54
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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Best Regards,

Paul

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11 Feb 2004, 00:40
Senior Manager
Joined: 23 Aug 2003
Posts: 461
Location: In the middle of nowhere

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11 Feb 2004, 10:03
The answer is C...but I dont have the official explanation..

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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Joined: 03 Jul 2003
Posts: 652

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11 Feb 2004, 10:23
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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Joined: 23 Aug 2003
Posts: 461
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11 Feb 2004, 12:14

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"

11 Feb 2004, 12:14
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