Is rst > rs/t? (1) rst > 2 (2) t > 2

Is rst > rs/t?

rs(t-1/t)>0 ....(1)

(1) rst > 2 >0
either two are negative or all are positive. Which two are negative decides the answer of eq(1). Insufficient.

(2) t > 2
no inf about rs.Insufficient.

combining 1 and 2
rst>2 and t>2
rs>2/t>0
Eq 1 becomes rs(t-1/t) some positive value i.e. >0. Sufficient.

Am i allowed to do the following with the given information

Is rst > rs/t?

---- Can i cancel r and s on both sides to give me --- t >(1/t) ?

Am i not allowed to do that because i dont know the individual signs on R and S ?

We cannot divide \(rst > \frac{rs}{t}\) by rs because we don't know the sign of rs (or individual sign of r and s, to get the sign of rs). If rs > 0, then when dividing we get \(t > \frac{1}{t}\) BUT if rs < 0, then when dividing we get \(t < \frac{1}{t}\) (recall that we should flip the sign of an inequality if we multiply/divide it by negative value).

Never multiply (or reduce) an inequality by a variable (or the expression with a variable) if you don't know its sign.

Hope it helps.

Hi - why is the following not a factor in the analysis in order to get to the solution ...

--- determining if RS is an integer value or a fraction vs T is an integer value or a fraction ...

the information given in statement 1 and statement 2 combined seems to suggest RS + and T + but how do we know if RS or T are integers or fractions ?

Wouldnt that alter the equation we have to test

--- if RS is an positive integer but T is fraction
OR

--- if RS is a fraction and T is fraction

OR

--- if RS is fraction and T is a positive integer

Given the right hand side of the equation to test is RS/T ....my concern is knowing if RS and T are fractions or integers as well....

Please let me know if my concern is valid ?

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There are 3 variables and 0 equation. Thus the answer E is most likely.

Condition 1)
There are counterexamples as follows.

\(rst = 4\) and \(t = 2\)
\(\frac{rs}{t} = \frac{rst}{t^2} = \frac{4}{4} = 1\)
Then \(rst > rs/t\)

\(rst = 4\) and \(t = \frac{1}{2}\)
\(\frac{rs}{t} = \frac{rst}{{t^2}} = {4}/{(\frac{1}{2})^2} = 16\)
Then \(rst < \frac{rs}{t}\).

Thus this condition is not sufficient.

Condition 2)
There are counterexamples as follows.

\(rs = 4\) and \(t = 2\)
\(rst = 8\) and \(\frac{rs}{t} = 2\)
Then \(rst > \frac{rs}{t}\)

\(rs = 4\) and \(t = -2\)
\(rst = -8\) and \(\frac{rs}{t} = -2\)
Then \(rst < \frac{rs}{t}\)

Thus this condition is not sufficient.

Condition 1) and 2)
Since \(t > 2\), \(\frac{1}{2} > \frac{1}{t} > 0\) and so \(t > \frac{1}{t}\).
Since \(t > 2\) and \(rst > 2\), \(rs > 0\).
When we multiply rs to the both sides of \(t > \frac{1}{t}\), \(rst > \frac{rs}{t}\).

Thus both conditions together are sufficient.

Therefore the answer is C.


For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.

Hi,

I think you can follow simple steps to solve any GMAT quant question:

a. Simplify question first: Is rst > rs/t?
It means whether rs( t-1/t)>0?

b. Lets look at options- start with option 2 as its simple to verify.

Statement (2): t > 2 ( here we dont know anything about rs)- so NS.
Statement: rst>2, here you can see multiple cases:
1. rs<0 and t<0, and rst>2 ( you can have multiple cases)
2. rs>0 and t>0, once again you can have multiple scenarios.

On combining, since t>2, you know t is not a fraction therefore t-1/t would always be positive. Also if t >0 and rst>2, means rs>0 and therefore rs(t-1/t) has to be >0.

So correct answer C. hope it makes sense?

imo C
from 2 we do not know about rs hence insufficient .
from 1 rst>2 we can have many cases for example rst=4
so we can rs=4 and t=1
then rs/t=4
hence not greater but if we take rs=2 and t=2
rst=4 but rs=2 ant t=2 so rs/t=1 hence rst >rs/t
hence insufficient
but taken together we can not have t=1 and rst >2 so it will always hold true .

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