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by neoreaves » Wed Apr 28, 2010 9:08 am
Jane can paint the wall in J hours, and Bill can paint the same wall in B hours. They begin at noon together. If J and B are both even numbers is J=B?

(1) Jane and Bill finish at 4:48 p.m.
(2) (J+B)^2=400
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by gmatmachoman » Wed Apr 28, 2010 9:20 am
neoreaves wrote:Jane can paint the wall in J hours, and Bill can paint the same wall in B hours. They begin at noon together. If J and B are both even numbers is J=B?

(1) Jane and Bill finish at 4:48 p.m.
(2) (J+B)^2=400
good question man!!
IMO C

st 1 gives :

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

st 2 gives :
J+B = 20 (assuming hours cant be negative)


Combining both st1 & st2 : we have

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

20/JB =5/24

(20 *24)/5 =JB

JB = 96

Now J & B can take any values like (12, 8 ), (48,2) or (16, 6)...so on where their product should equal 96.

But J +B =20, so we are left with (12,8) only.

But 96 is NOT a perfect square. SO J is not qual to B

Pick C

Am i correct?? While solving I am very hasty..correct me plz!
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by liferocks » Wed Apr 28, 2010 5:11 pm
I think ans should be B

from 1 ,clearly we cannot say anything.
from 2, if J=B we will get
2J^2=400 or J^2=200

now J^2 is not a perfect square...I am assuming J ans B are rational numbers

hence J cannot be equal to B

Ans B
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by gmatmachoman » Wed Apr 28, 2010 9:33 pm
liferocks wrote:I think ans should be B

from 1 ,clearly we cannot say anything.
from 2, if J=B we will get
2J^2=400 or J^2=200

now J^2 is not a perfect square...I am assuming J ans B are rational numbers

hence J cannot be equal to B

Ans B
@LR

U r supposed to prove whether J =B or not!

But u took as that as the necessary condition & started to derive! Plz chk that
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by liferocks » Wed Apr 28, 2010 9:38 pm
gmatmachoman wrote:
liferocks wrote:I think ans should be B

from 1 ,clearly we cannot say anything.
from 2, if J=B we will get
2J^2=400 or J^2=200

now J^2 is not a perfect square...I am assuming J ans B are rational numbers

hence J cannot be equal to B

Ans B
@LR

U r supposed to prove whether J =B or not!

But u took as that as the necessary condition & started to derive! Plz chk that
Its correct that I am supposed to prove whether J =B or not!
if I take J=B and reach a impossible scenario doesn't it mean that the assumption is in correct i.e J<>B ?
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by rockeyb » Wed Apr 28, 2010 11:31 pm
@liferocks ,

I think you have missed an important point in the discussion .

In assuming J = B you are not assuming both J and B to be even . If J and B both are even numbers we can say both J and B will have at least one 2 in its factors .

If that is the case then J becomes 2J and since we are considering J = B we can say that B= 2J .

Now putting these values in statement (2) .

(J+B)^2 = 400 .

(2J+2J)^2 = 400

4J = 20

J = 5.

So going by your method of analogy we can say we have arrived at a possible situation by considering J= B .

Now similarly we can arrive at an impossible situation by considering either J and B have more than one 2 as their factor such as J= 2J and B= 6B or B= 4B . The out come will depend on how many 2 are there in each B and J .

And since we can not definitely say this assuming J= B would be incorrect in this case.
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by liferocks » Wed Apr 28, 2010 11:48 pm
rockeyb wrote:@liferocks ,

I think you have missed an important point in the discussion .

In assuming J = B you are not assuming both J and B to be even . If J and B both are even numbers we can say both J and B will have at least one 2 in its factors .

If that is the case then J becomes 2J and since we are considering J = B we can say that B= 2J .

Now putting these values in statement (2) .

(J+B)^2 = 400 .

(2J+2J)^2 = 400

4J = 20

J = 5.

So going by your method of analogy we can say we have arrived at a possible situation by considering J= B .

Now similarly we can arrive at an impossible situation by considering either J and B have more than one 2 as their factor such as J= 2J and B= 6B or B= 4B . The out come will depend on how many 2 are there in each B and J .

And since we can not definitely say this assuming J= B would be incorrect in this case.
Got your point but we do not have to go till J/B as even or odd.
I made a mistake in the calculation ,when I assumed J=B from the second scenario I got
2J^2=400
this is actually 4J^2=400 and j^2=100
so we cannot conclude.
..Method is correct but I applied it incorrectly.
Agree with C.
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by harshavardhanc » Thu Apr 29, 2010 12:04 am
IMO A.

Statement 1 :

They together took 24/5 hrs to complete the work.

We know that if J & B work together, they will take (J*B)/(J+B) hrs to complete the work.

Equating these two :

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

Now, assume that J=B , we will get J^2/ (2J) = 24/5 OR J=48/5 which goes against the given info that both are even.

Hence, our assumption, J=B, is wrong.

In other words, we can definitely say that two equal even numbers cannot satisfy this condition.


So, this statement is sufficient. We get a definite NO.


Statement 2:

this gives us that J+B =20, J & B can be (10,10)(18,2) etc.

Not sufficient.

Let's see the OA.
Last edited by harshavardhanc on Thu Apr 29, 2010 12:31 am, edited 2 times in total.
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by liferocks » Thu Apr 29, 2010 12:22 am
@harshavardhanc

from the second if we take J=B we get J=B=10 but it does not rule out the option for J<>B ie J=12 and B=8
so we cannot say anything about J and B
statement 2 is not sufficient.

The method of negative approach is we will assume that the ans is true and try to reach an impossible scenario.but if we get valid result we have to consider the other scenario.
Please check.

for the first statement..I completely missed that both J and B are even.Thanks for reminding :)
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by harshavardhanc » Thu Apr 29, 2010 12:29 am
liferocks wrote:@harshavardhanc

from the second if we take J=B we get J=B=10 but it does not rule out the option for J<>B ie J=12 and B=8
so we cannot say anything about J and B
statement 2 is not sufficient.

The method of negative approach is we will assume that the ans is true and try to reach an impossible scenario.but if we get valid result we have to consider the other scenario.
Please check.

for the first statement..I completely missed that both J and B are even.Thanks for reminding :)
agreed! post edited! :) ;)
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by Fiver » Thu Apr 29, 2010 12:33 am
neoreaves wrote:Jane can paint the wall in J hours, and Bill can paint the same wall in B hours. They begin at noon together. If J and B are both even numbers is J=B?

(1) Jane and Bill finish at 4:48 p.m.
(2) (J+B)^2=400
When J & B are both even and begin work at noon.
Is J = B ?

St1] Jane and Bill finish at 4:48 p.m.

I am assuming that:
1] Noon means 12 in the afternoon.
2] Both finish the work the same day.

Coming back to st1] the total hrs of combined work is 4.75 hrs.
We need to know whether 1/J + 1/B = 1/4.75
Now if J=B when both are even we get the following format:
1/J + 1/J = 2/J when J is even. This means the combined total hours must always be an integer, while 4.75 is not.
Hence we know that J is not equal to B, when both are even.

I choose A.
What's the OA?
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by rockeyb » Thu Apr 29, 2010 12:34 am
Harsha ,

I think you too did a minor mistake in your calculation .

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 :
We know that if J & B work together, they will take (J*B)/(J+B) hrs to complete the work.

Equating these two :

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

Now, assume that J=B , we will get J^2/ (2J) = 24/5 OR J=48/5 which goes against the given info that both are even.

Hence, our assumption, J=B, is wrong.

So, this statement is sufficient. We get a definite NO.
Now 1/J + 1/B = 24/5

JB /(J+B)= 24/5

put in J= B = 1/5 .

(J^2/25 ) / (2J/5) = 24/5

J / 10 = 24/ 5

J = 24 x 2 . ====> even satisfies .

So in fact we can still get J= B by considering that J is not an integer .
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by gmatmachoman » Thu Apr 29, 2010 12:41 am
harshavardhanc wrote:
liferocks wrote:@harshavardhanc

from the second if we take J=B we get J=B=10 but it does not rule out the option for J<>B ie J=12 and B=8
so we cannot say anything about J and B
statement 2 is not sufficient.

The method of negative approach is we will assume that the ans is true and try to reach an impossible scenario.but if we get valid result we have to consider the other scenario.
Please check.

for the first statement..I completely missed that both J and B are even.Thanks for reminding :)
agreed! post edited! :) ;)
@Harsha Bhai,

We need to be careful man.. I was going thru some of previous GMAT prep questions..They are not at all rocket science..but they are damn tricky!!

SO u r picking C for this??
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by harshavardhanc » Thu Apr 29, 2010 1:01 am
rockeyb wrote:Harsha ,

I think you too did a minor mistake in your calculation .

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 :


Now 1/J + 1/B = 24/5

JB /(J+B)= 24/5

put in J= B = 1/5 .

(J^2/25 ) / (2J/5) = 24/5

J / 10 = 24/ 5

J = 24 x 2 . ====> even satisfies .

So in fact we can still get J= B by considering that J is not an integer .
rocky,

thanks for trying to find a flaw! good job!

Definitely, we don't know if J and B are integers. But, if we assume them to be and in the end we get an answer which goes against the fact, it proves that assumption is incorrect and they are not equal integers. That's what liferocks and me are trying to use.

Anyway, if we read the question carefully, J and B are number of hours and the question is asking "if the number of hours is equal for both". You cannot make the conversion hours->minutes. Take the units as they are. You cannot convert a fraction and make it even as you have done while converting number of hours into minutes, showing that 12 is even. Nope, we can't do that.

Moreover, 1/5 is a rational number. Even and Odd concept doesn't apply to fractions.

So,

reasoning and calculations remaining the same, let me rephrase what I wanted to convey for st1.

you can definitely say that No two equal even numbers can satisfy the condition given in the statement. Hence, it is sufficient to answer the question.

Think about it! Let me know if you still find something hazy.

@Govi cheta

inna vishesham? ;)

nope, I pick A for this question.
Regards,
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by Fiver » Thu Apr 29, 2010 1:29 am
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.
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