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Re: [#20] 2 Min. Challenge : X-Y [#permalink]
12 Mar 2004, 19:22

praetorian123 wrote:

Rules

1. Time Yourself 2. Solve on a seperate sheet of paper 3. Write your solution here, and your time, please.

1/X+1/Y=36/323. Find X-Y.

(1) X and Y are primes (2) X>Y>1

Ans should be "B" - Option 2 is sufficient but option 1 is not.

Let me greet you first Praetorian, good question !
Here the equation (X+Y)/(XY) gives you two choices, 17 or 19. Now to determine the exact value of X and Y, we need to check the options individually.
Option - 1 Said, X and Y are primes - Now if you take X=17 Y is 19 and otherway around if X=19 Y becomes 17.
So option - 1 do not help to find X-Y.

what if X and Y are not integers. Although I cannot prove it there may be some real number pair which addsup to 36 and product is 323.

Anand.

I believe B also. X and Y have to be either 17 or 19. When it comes to finding numbers other than 17 or 19 which add up to 36 and product is 323, you'll have to use calculator and get into nasty calculations. Question could have specified that X and Y were integers though...

Took me about 2 min to find the pair... First stem kind of gave me the hint that X and Y were prime so it hastened the process. After finding X and Y, it was obvious that answers could not be anything other than prime numbers

Re: [#20] 2 Min. Challenge : X-Y [#permalink]
13 Mar 2004, 17:38

praetorian123 wrote:

Rules

1. Time Yourself 2. Solve on a seperate sheet of paper 3. Write your solution here, and your time, please.

1/X+1/Y=36/323. Find X-Y.

(1) X and Y are primes (2) X>Y>1

C is the correct answer.

Quoting Akamai here:

Restating the question stem, we get:

(X + Y)/(XY) = 36/323

(1) restricts X and Y to prime integers. With little experimentation, we can discover that 323 = 19 * 17, two prime numbers. Just by inspection, we can see that X and Y can be 19 and 17 or 17 and 19 respectively and satisfy the equation. Moreover, since X and Y are primes, they are the ONLY solutions to the equation. However, we don't know which one is which so we cannot ascertain what X-Y is. Hence (1) is NOT sufficient and we must eliminate A and D.

(2) tells us that X > Y and both are positive. However, it does not restrict the solution to prime number, or even integers. Hence, there are probably an infinite number of solutions to the equation and (2) is also not sufficient and we must eliminate B.

Using both, (1) tells us that X and Y must be 17 & 19 or 19 and 17, and (2) tells us that X is larger, so we now know which solution is the correct one and we can answer the question. Hence, the correct answer is C.