liferocks , Harsha ,

I am not trying to prove that your method is wrong , in fact I agree that your method is perfectly fine .

Just a bit confused as to what is the correct method to solve this problem . I think this much discussion is enough to get the OA and OE .

@Fiver as Hrasha said we can not apply odd or even concept to rational numbers so 1/5 is out of the window .

waiting for OA and some explanation also.

Fiver wrote:

rockeyb wrote: Can we assume that J and B are integers ?
Lets say J = B = 12 mins = 1/5 hrs (I am still considering J and B = even )

so lets put this in to your calculation :

Good point. Did not think about this possibility;
however on second thoughts, the question says that 'Jane can paint the wall in J hours, and Bill can paint the same wall in B hours'.
This means that both 'J & B' are expressed in hours as rightly pointed out by you.
But this part 'If J and B are both even numbers' means that the same 'J & B', expressed in hours, are also even and hence they have to be integers expressed in hours and not fractions expressed in hours.

Let me know what your thoughts are.

Hi,

only integers have the qualities "odd" and "even"... so if we're told that a number is even, it's automatically an integer.

rockeyb wrote: @Fiver as Hrasha said we can not apply odd or even concept to rational numbers so 1/5 is out of the window .

Stuart Kovinsky wrote:
Hi,

only integers have the qualities "odd" and "even"... so if we're told that a number is even, it's automatically an integer.

Hi Rockeyb & Stuart, thanks for your responses, but that's exactly what i am trying to point out.
My point is the same as yours- both J & B are integers.

Hereunder, I have highlighted the main point of my earlier explanation.

Fiver wrote:Good point. Did not think about this possibility;
however on second thoughts, the question says that 'Jane can paint the wall in J hours, and Bill can paint the same wall in B hours'.
This means that both 'J & B' are expressed in hours as rightly pointed out by you.
But this part 'If J and B are both even numbers' means that the same 'J & B', expressed in hours, are also even and hence they have to be integers expressed in hours and not fractions expressed in hours.

Let me know what your thoughts are.

"Jane can paint the wall in J hours, and Bill can paint the same wall in B hours." Can be rewritten:

(1/J) = Jane can paint 1 wall in J hours or Jane paints 1/J wall per hour.

(1/B) = Bill can paint 1 wall in B hours or Bill paints 1/B wall per hour.

They work together so you they will finish the job in:

(1/J) + (1/B)

Does J=B;

(1/J) + (1/B) = 2/x, when x = J or B. ??????

This questions is asking do they finish the job in half the time it would take them to individually do it? If they both work at the same rate individually, then combined they will finish it in half the time. For exambple, if they both work at (1/3) of the job per hour then combined they work at

(1/3) + (1/3) = 2/3

2/3 is twice the rate per hour, thus it would take them half the time to complete they are combined working twice as fast.

(1) Jane and Bill finish at 4:48 p.m.

(1) Tells us that they finised the job in 288/60 hours (288 minutes from noon to 4:48 pm, assuming its the same day, devided by 60 to give us hours). This fraction simplifies to 24/5. Thus,

(1/J) + (1/B) = 1/(24/5)

Logical stated combined Jane can finish 1 wall in J hours. Bill can finish one wall in B hours. Combined they can finish one wall in 24/5 hours (every 4.8 hours).

1/(24/5) simplifies because

(1/1) / (24/5) = (1/1) x (5/24) = 5/24, thus;

(1/J) + (1/B) = (5/24)

Thus, Bill and Jane combined can finish 5 jobs in 24 hours. This does not tell us that J=B it only tells us how fast Jane and Bill work together not how fastly either of them work by themselves.

(1) is insufficient.

(2) (J+B)^2=400

Simplified:

J+B = Sqrt(400)
J+B = 20

This tells us that combined the hours to take to do the job are 20. This is not sufficient to prove that J = B because;

1+19 = 20
2+18 = 20
3+17 = 20 and so on...

(2) is insufficient.

Together we can combine the statements in the following way:

Further work on our equation from 1 shows us:

(1/J) + (1/B) = (5/24) Multiply all term by (J)(B)(24) to get rid of the fractions and get:

24B + 24J = 5JB

24(J+B) = 5JB (2) tells us J+B = 20, thus

24(20) = 5JB

480 = 5JB

480/5=JB

96=JB

or, if J=B, then,

J^2=96 or B^2=96.

The question says J and B are"even numbers". According to Stuart above, only integers can have even or odd qualities. Thus, J=/=B, because 96 is not a perfect square. C is the answer.

@pranab & @harsha bhai,

Now that u guys have to decide whether u r going for C/ A??

Plz see my last post or sks8 post. he has given some detailed post...

Plz do reach to some conclusion..

gmatmachoman wrote:@pranab & @harsha bhai,

Now that u guys have to decide whether u r going for C/ A??

Plz see my last post or sks8 post. he has given some detailed post...

Plz do reach to some conclusion..

macho dost,

I've already said in one of my previous post that statement 1 alone is sufficient to tell us that J and B cannot be equal even numbers.

in the sks8's "detailed" post, he missed one important information while solving for st1. he did not take into account that both J and B are even. That makes a BIG difference.

an equation was derived : 1/J + 1/B = 5/24

now, try to figure out two even numbers for J and B, which give you the figure on the right hand side of the equation. You'll find that they won't be equal.

That's it ! there you are ! you've got your answer.

let me know if you still need further explanation.

Yeah, harsha's definitely got this one.

We know that J and B are even (integers), and that they both began working at noon.

Is J = B?

(2) (J + B)^2 = 400

So, J + B = 20. Not enough to determine whether J = B. (Could be 10 + 10 but also 8 + 12). Insufficient. Eliminate B and D.

(1): So, they worked for 4.8 hours to finish the job together.
Now, if J = B, then that would mean that each of J and B finish the job in 9.6 hours (twice as long) working by themselves. But 9.6 is not an integer, and so this would breach information in the question stem. Thus, J cannot equal B. Sufficent....choose A.