Is k greater than t? (1) kt = 24 (2) k^2 t^2

Question

Is k greater than t?

(1) kt = 24

(2) k^2 > t^2

BrentGMATPrepNow · Accepted Answer

Target question :    Is k greater than t?

When I SCAN the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the  target question . So, I’m going to head straight to……

Statements 1 and 2 combined    
There are several values of k and t that satisfy BOTH statements. Here are two: 
 Case a : k = 24 and t = 1. In this case, the answer to the target question is  YES, k is greater than t 
 Case b : k = -24 and t = -1. In this case, the answer to the target question is  NO, k is not greater than t 
Since we can't answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

ramkaswan · Answer

(1) many possibilities,obviously not sufficient. (2)k^2>t^2--->k>t if k,t>0 or k

saswat1987 · Answer

This is a  YES or NO type DS questions  and we need to find out   if k>t or not   ?

1. kt =24.. k & t could be +ve or -ve and the value will change accordingly.  E.g. --> k = 6 / -6 and t = 4 / -4, in both cases the kt=24 but the main question will change depending on the +ve and -ve values of k and t.   Insufficient.

2. k^2 > t^2, same problem as above but here  both k = 6 / -6 and t = 4 / -4 will hold the statement but the main question will change depending on the +ve and -ve values of k and t.   Insufficient.

1. & 2. combined still confusion remains,  hence E.

PriyamRathor · Answer

Bunuel ,

Can you please explain.

I am not able to understand how the answer is E.

S1. kt = 24

Here, it is understood that K can be  1, 24  and t can be  24, 1 .
Hence not sure whether K > t.

S2. k ^2 > t^2

Hence K^2 - t^2 >0

Hence (k-t) (k+t)>0

Hence k >t or K > -t

Now I am not able to understand how on combining S1 and S2 confusion still remains?

Thanks.

Bunuel · Answer

Aren't you making two unsupported assumptions ? One that n and k are necessarily integers, and two that they are necessarily positive ?

Sababa1561 · Answer

The statement asks if,

k > t or k-t>0 (Tips: always keep your RHS 0)

Now, Statement 1 says, kt=24. There can be many values for kt. For e.g. k=6 & t=4 or k=-6; t=-4 etc.

So, statement 1 is insufficient

Statement 2 says, k^2-t^2>0
or, (k+t) (k-t) >0 for it to be true either both (k+t) & (k-t) are positive or both are negative.

So, statement 2 is insufficient

Even if we try to plug in values from statement 1 in statement 2 we cannot conclude on the signs for these.

So, C is also not an option.

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Is k greater than t? (1) kt = 24 (2) k^2 > t^2

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