If Jim earns x dollars per hour, it will take him

[nehag84]

If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

(1) Tom makes 20% less per hour than Jim does.

(2) x + y = $43.75

OA is B.

I applied the following concept. Pls let me know where I did I go wrong?

According to the Question stem, Jim earns x dollars per hour and if he works 4 hours he earns exactly enough to purchase the jacket. That means the jacket costs 4x dollars. Similarly Tom earns y dollars per hour and it will take him 5 hours to earn enough money for the jacket, which means the cost of jacket is 5y. As in both the cases it is the same jacket, hence 4x=5y.

And with this equation, I can get an answer with both 1 and 2. Hence according to me, the answer should have been D.

[mxs2009]

the questions asks: How much does the jacket cost? In other words, you need a dollar amount for Jim, Tom or both. Statement A only gives you a percentage.
Tom makes 20% less per hour than Jim does.

Try plugging in some numbers: if Jim makes $5/hr, then Tom makes $4/hr
using your equation 4x=5y, we see that $20=$20

But if Jim makes $10/hr and Tom makes $8/hr, $40=$40. we do not have enough data to answer how much the jacket costs.

hope that helps

[elaine1920]

Just add one thing:

By using the first condition, you can get X (1-20%)=Y, which we can reduce to 4x=5y. So it is the same equation in the question. Thus you can't use it to solve the question.

[enniguy]

Just add one thing:

By using the first condition, you can get X (1-20%)=Y, which we can reduce to 4x=5y. So it is the same equation in the question. Thus you can't use it to solve the question.

I ended up with the same answer as nehag84. But considering elaine1920's reply, it is clear that B is the answer. But isn't this method better than the one provided by Manhattan? It got very confusing to me to the extent that I dint understand it.

If we know, 4x = 5y and an equation 4x+5y = $43.75. Then, effectively we have just 1 equation with 1 variable since either x or y can be converted to the other. I just wanted to know if it was me or everyone found manhattan's solution difficult.

[Ben Ku]

Thanks all for contributing to the solution to this question. I think the approaches you guys brought up are clearer than the official solution on the MGMAT CAT Exam.

Often the explanations are written as a teaching tool to understand the concepts behind the problem. Here, the explanations emphasize that it's a rate-work problem. Also for statement (2), the explanations tried to help the test-taker understand what x+y means (it's the combined rates). However, I'm in agreement that the explanations are not the most straight forward approach to this question.

[bdinardo1]

Thanks all for contributing to the solution to this question. I think the approaches you guys brought up are clearer than the official solution on the MGMAT CAT Exam.

Often the explanations are written as a teaching tool to understand the concepts behind the problem. Here, the explanations emphasize that it's a rate-work problem. Also for statement (2), the explanations tried to help the test-taker understand what x+y means (it's the combined rates). However, I'm in agreement that the explanations are not the most straight forward approach to this question.

If when trying to solve this we realized it was a combined rates why can't the 2 rate problems be combined like so:
Rate * Time = $(price of jacket)
Jim/ x * 4 = Price of Jacket
Tom/ y * 5 = Price of Jacket
J+T/ x+y * 9 = 2P.

Although I got the right answer by quickly recognizing (X+Y) it did not yield the correct number.

[jnelson0612]

Thanks all for contributing to the solution to this question. I think the approaches you guys brought up are clearer than the official solution on the MGMAT CAT Exam.

Often the explanations are written as a teaching tool to understand the concepts behind the problem. Here, the explanations emphasize that it's a rate-work problem. Also for statement (2), the explanations tried to help the test-taker understand what x+y means (it's the combined rates). However, I'm in agreement that the explanations are not the most straight forward approach to this question.

If when trying to solve this we realized it was a combined rates why can't the 2 rate problems be combined like so:
Rate * Time = $(price of jacket)
Jim/ x * 4 = Price of Jacket
Tom/ y * 5 = Price of Jacket
J+T/ x+y * 9 = 2P.

Although I got the right answer by quickly recognizing (X+Y) it did not yield the correct number.

Let's walk through your math a little bit. I agree with your first two lines:
The jacket price can be expressed as x * 4 = 4x (Jim).
The jacket price can also be expressed as y * 5 = 5y (Tom).

So two jackets cost 4x + 5y.

Notice that you are saying that two jackets cost (x+y) * 9, or 9x + 9y. You can see that that is a lot larger than the actual cost of two jackets, 4x + 5y.

[dhlee922]

i understand that the 2 equations method is easier to solve and understand, but reading the explanation on the CAT, i am getting a different answer.

CAT explanation says:

Since Time = Work/Rate, Time = 1 jacket/(9/20 jackets per hour) = 20/9 hours.

Since the combined pay rate of the Jim and Tom is equal to the sum of the individual pay rates of the two; hence, the combined pay rate in dollars per hour is X + Y. When the two work together, AmountEarned = CombinedPayRate x Time = (X + Y) x 9/20. Since statement (2) states that X + Y = $43.75, this statement is sufficient to compute the cost of the jacket (it is not necessary to make the final calculation).

shouldnt it actually say, (X+Y) x 20/9?

or if 9/20 is correct, why is that the case?

I understand it as $X/hr and $Y/hr, so ($X/hr + $Y/hr) x (20hr/9) therefore "hr" cancel and you get($X + $Y) x 20/9

[jlucero]

i understand that the 2 equations method is easier to solve and understand, but reading the explanation on the CAT, i am getting a different answer.

CAT explanation says:

Since Time = Work/Rate, Time = 1 jacket/(9/20 jackets per hour) = 20/9 hours.

Since the combined pay rate of the Jim and Tom is equal to the sum of the individual pay rates of the two; hence, the combined pay rate in dollars per hour is X + Y. When the two work together, AmountEarned = CombinedPayRate x Time = (X + Y) x 9/20. Since statement (2) states that X + Y = $43.75, this statement is sufficient to compute the cost of the jacket (it is not necessary to make the final calculation).

shouldnt it actually say, (X+Y) x 20/9?

or if 9/20 is correct, why is that the case?

I understand it as $X/hr and $Y/hr, so ($X/hr + $Y/hr) x (20hr/9) therefore "hr" cancel and you get($X + $Y) x 20/9

I don't have the CAT explanation in front of me, but your logic looks correct to me. Let me forward this to our curriculum folks and someone will respond soon.

Update: It looks like this was indeed a mistake in the explanation. It's been updated and should now be correct. Thanks for the input everyone!