Simple DS problem gone bad

[nk_81]

John is 'j' years old and Keith is 'k' years old.... and both are atleast 1 year old. is j > k?

1) jk = 2j

2) j + k = 2j

Now KAPLAN says on B is sufficient. Their reasoning is , if we consider equation 1 jk=2j, canceling out j would give us k=2, and thus there is only the value of 'k' and no value of 'j'. Hence INSUFFICIENT.

HOW?

My logic tells me... correct me if I am wrong. since k=2, the only way jk=2j with k=2 is when j=1. Hence the answer to " j>k " is NO

Am I right or am i losing it???? it seems a pretty straight forward answer that I got wrong.

[anshumishra]

John is 'j' years old and Keith is 'k' years old.... and both are atleast 1 year old. is j > k?

1) jk = 2j

2) j + k = 2j

Now KAPLAN says on B is sufficient. Their reasoning is , if we consider equation 1 jk=2j, canceling out j would give us k=2, and thus there is only the value of 'k' and no value of 'j'. Hence INSUFFICIENT.

HOW?

My logic tells me... correct me if I am wrong. since k=2, the only way jk=2j with k=2 is when j=1. Hence the answer to " j>k " is NO

Am I right or am i losing it???? it seems a pretty straight forward answer that I got wrong.

Question : j>k ?

Statement 1:
jk = 2j => k=2 (j,k!=0)
Insufficient, as no info about j

Statement 2:
j+k = 2j
=> k = j => sufficient (As we can conclusively say that j is not greater than k)

Hence B.

[nk_81]

Hi Anshu,

Can you elaborate on that please. In words if possible.

Dint get this......j,k!=0 ???

Thanks
Naveen

[anshumishra]

Hi Anshu,

Can you elaborate on that please. In words if possible.

Dint get this......j,k!=0 ???

Thanks
Naveen

Naveen, can you quote what you didn't get exactly, I'll try to explain that part.

Dint get this......j,k!=0 ???

The equation : jk = 2j
=> j*(k-2) = 0,
Now either J = 0 or k-2
But the question has mentioned both are atleast 1 year old. So that means j != 0
Hence k= 2.

[nk_81]

Anshu,

How much ever I try to wrap my head around it... for some reason I am unable to comprehend why this can't be the case.

I am putting the value back in the equation it was derived from, that seems strange to me as well and in the process ...

j*k=2*j ; k=2; for k to be equal to 2 since the equation jk=2j is true, j has to be 1...since 2 times j = 2j....does that make sense?

[anshumishra]

Anshu,

How much ever I try to wrap my head around it... for some reason I am unable to comprehend why this can't be the case.

I am putting the value back in the equation it was derived from, that seems strange to me as well and in the process ...

j*k=2*j ; k=2; for k to be equal to 2 since the equation jk=2j is true, j has to be 1...since 2 times j = 2j....does that make sense?

j*k=2*j ; k=2; for k to be equal to 2 since the equation jk=2j is true, j has to be 1

Lets check with few values.
j=1,k=2
j*k = 1*2 = 2 and 2*j = 2*1 = 2
j=2,k=2
j*k = 2*2 = 4 and 2*j = 2*2 = 4
j=3, k=2
j*k = 3*2 = 6 and 2*j = 2*3 = 6

So, you can see for any value of j the equation holds.

[lunarpower]

you can divide both sides of any equation by any quantity that is known to be nonzero. (with inequalities, you have to be more careful -- you can't divide both sides by a quantity unless it is known to be nonzero and its sign is known, unless you split the result into cases according to the unknown sign.)

so, since j is not 0:
jk = 2j
divide by j
--> k = 2.
no information about j.

--

re: your confusion about the other post, that poster was using the symbol "!=" as a substitute for "≠".
this is accepted notation in formal logic classes, but it's still sort of weird on a forum (especially because, in certain contexts, it can be misinterpreted as a factorial).

TO EVERYONE
if you don't know how to type "≠", just open up a search engine, type in "not equal sign", and then copy and paste from one of the zillions of results that show up.
the same goes for ">" and "<" -- either google/copy/paste or just use normal "<" and ">" with the underline enabled. that makes first a lot more readable than they are if you use ">=" or "<=", the latter of which looks like an arrow.

[anshumishra]

re: your confusion about the other post, that poster was using the symbol "!=" as a substitute for "≠".
this is accepted notation in formal logic classes, but it's still sort of weird on a forum (especially because, in certain contexts, it can be misinterpreted as a factorial).

TO EVERYONE
if you don't know how to type "≠", just open up a search engine, type in "not equal sign", and then copy and paste from one of the zillions of results that show up.
the same goes for ">" and "<" -- either google/copy/paste or just use normal "<" and ">" with the underline enabled. that makes first a lot more readable than they are if you use ">=" or "<=", the latter of which looks like an arrow.

lunarpower,

You are right. I used "!=" as a substitute for "≠". In my future posts I'll use the other notation. Thanks for pointing that out, as I myself in many cases have used "!" as factorial notation.