CAT 1 - DS - Expensive Jacket

[mayank]

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

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Solution Provided:

This question can be restated in several ways. Let Work = amount earned (i.e., amount needed to purchase the jacket). Recall, Work = Rate x Time. Since the number of hours that either Jim or Tom need to work in order to purchase the jacket is given, we need only know either person's rate of pay to determine the cost of the jacket; hence, the question can be restated as either: "What is x?" or "What is y?".

Also, since the amount of time needed for either Jim or Tom to purchase the jacket is given, it can be shown that the amount of time needed for them working together to purchase the jacket can also be calculated. The formula Work = Rate x Time also applies when Jim and Tom work together; hence, only the combined rate of Jim and Tom working together is required. Since the combined rate of two people working together is equal to the sum of their individual rates, the question can also be restated as: "What is X + Y?"

(1) INSUFFICIENT: This statement gives only the relative earning power of Jim and Tom. Since the original question states the amount of time needed for either Jim or Tom to earn enough money to purchase the jacket, it also gives us the relative earning power of Jim and Tom. Hence, statement (1) does not add any information to the original question.

(2) SUFFICIENT: Let Z = 1 jacket. Since Tom and Jim must 4 and 5 hours, respectively, to earn enough to buy 1 jacket, in units of "jacket per hour," Jim works at the rate of 1/4 jackets per hour and Tom works at the rate of 1/5 jackets per hour. Their combined rate is 1/4 + 1/5 = 5/20 + 4/20 = 9/20 jackets per hour. 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).

The correct answer is B.

Note: It is also not necessary to explicitly compute the time needed for Jim and Tom working together to earn the jacket (20/9 hours). It is only necessary to recognize that this number can be calculated in order to determine that (2) is sufficient.

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Now, my concern is that do I need to do all that calculation for Statement 2? From the question I get, 4x=5y (4x - 5y = 0). And from statement 2, I get x + y = 43.75. I have two variables and two equations ... Do I need to do anything more, I should be able solve the variables.

Did I miss something?

Thanks for your help.

[tejkumar.m]

Nope.. You need not..Check this out.

Given : 4X=5Y
and Jacket Cost = 4X = 5Y
Therefore, if we get to know either of X OR Y.. we are done with the answer.

Statement -1 : Y=0.8X ==> Y=8/10*X ==> Y=4/5X ==> 4X=5Y
Therefore, it is simplified to the given thing and nothing new it says. So, not Sufficient.

Statement -2 :
x + y = $43.75
and given is 4X-5Y = 0

2 linear equations and 2 variables.. So, sufficient.

Hence, B is correct choice

[mschwrtz]

Yes, you are both correct.

I'm going to take this opportunity to point out an important difference between Word Translation DS questions and algebra DS questions:

If you correctly translate a WT question and arrive at n equations with the same n variables, they are very likely to be n distinct linear equations, though of course you should verify. So the rule which you both correctly cite here will very likely apply.

If you are given n equations with n variables in an algebra question, something is almost certainly up. They may not be distinct (unlikely issue), or they may not be linear (more likely issue), or you may not need the values of all the variables (most likely issue). In the first two cases information which appears sufficient may not be, and in the third case information which does not appear sufficient may well be.