Lindsay paints

[rdwngs22]

Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

A. 1/3x
B. x/x-3
C. x-1/3x
D. x/x-1
E. x-1/x

OA:C

I'm having trouble solving this question with the VIC method. I choose 1/2 for lindsay and 1/2 for joseph. With x = 2 I solve that Joseph can paint 1/6 of the room in 20 minutes and when I plug x = 2 into the answer choices both A and C are correct. Where am I going wrong?

[sharath.nair]

This is how I approached the problem.

Both Lindsay and Joseph can complete painting in the room in one hour. Lindsay can complete 1/x of the room in one hour. Therefore, Joseph can complete 1-(1/x) or (x-1)/x of a room in one hour.

As 20 minutes is one third of an hour (60 min). Therefore Joseph would complete one third of the work he would complete in one hour which is (x-1)/3x.

I think you should go this way rather than substitute 2. By Substituting 2, you are assuming that both work equally fast which may or may not be wrong.

Hope you have got the point.

[rdwngs22]

I guess I'm still confused as to why you cannot assume that they both work at the same rate. There is nothing in the problem that says they must work at different rates.

[Ben Ku]

You're not doing anything wrong in terms of the math. If you let x = 2, then Joseph's rate is 1 room/2 hours, so Joseph can paint 1/6 of a room in 20 minutes. If you plug in x = 2 in the answer choices, indeed A and C both give you consistent answers. In this case, you need to plug in a different value for x and try again.

The key is using the "Picking Numbers" approach to VICs is to select the RIGHT numbers. When you let Lindsay's rate be 1/2, then Joseph's rate is also 1/2. Because of this, there is a possibility of several answer choices that work.

Let's instead say x = 3. In this case, Lindsay's rate is 1/3, and Joseph's rate is 2/3. This means Joseph can paint 2 rooms in 3 hours. So Joseph can paint 2/9 of a room in 20 minutes. Plugging in x = 3, the only one that works is C.

I hope that helps.

[pradebbana]

Is it a legitimate question then, do we get such questions in the actual exam.

I selected A, assuming target to be 1/6 and moved on!

I think its just an ambiguous question.

[jnelson0612]

Is it a legitimate question then, do we get such questions in the actual exam.

I selected A, assuming target to be 1/6 and moved on!

I think its just an ambiguous question.

Yes, you absolutely will see similar questions. What about the question makes you think that it might not be a legitimate question?