Below is one of the Quant question that i encountered in MGMAT CAT

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

Can someone please explain why Stmt 1 is insufficient?

Thanks.

let's turn statement one into an equation: y = 0.8x. (note that 0.8x is twenty percent less than x.)

note that, from the problem statement, the amount of money that jim makes in 4 hours must equal the amount of money that tom makes in 5 hours.
therefore,
(4 hrs) (x $/hr) = (5 hrs)(0.8x $/hr)
this reduces to 4x = 4x. that's not a helpful equation -- it's actually true for absolutely any value of x at all. therefore, it turns out that this statement actually provides no new information at all.

(if you have intuition about these sorts of things, think about it for a sec -- "i make 20% less than you do" is exactly the same as saying "i need 5 hours to earn the same amount of money that you make in 4 hours.")

Dears.

What is the ANS?

Let us try...

From the question...
Jim has to work 4 hours to earn exactly enough money to buy the jacket. Therefore, cost of the Jacket = 4x

The question also states that Tom has to work exactly 5 hours to earn exactly enough money to buy the jacket. Therefore, cost of the Jacket = 5y

Therefore, 4x = 5y ---> Equation 1

Statement 1
Tom makes 20% less per our than Jim does. (y is 20% < x. In other words, y is only 80% of x)
That means, .8x = y ---> Equation 2
Usually, two equations are sufficient to solve for x & y. However, in this particular case, we will not be able to find the values of x and y. This is because, both Equations 1 & 2 are same!

Multiply Equation 2 with 5 => 4x = 5y => Equation 1. This is because, both question and statement 1 gave us the same information in two different sentences.

Therefore, statement 1 is insufficient.

Statement 2
x+y = 43.75 ---> Equation 3.
Combining Equations 1 & 3, we can find the cost of jacket. Statement 2 is sufficient.

Answer should be B.

The answer is indeed B.

_________________
Jamie Nelson
ManhattanGMAT Instructor