Peterson comparison problem

[elenavn]

Hey guys,
I was wondering what you thought about this problem. You need to compare

6x+7y=45 and xy

I thought the answer was a, since no matter what combination you select, the product of x and y is always smaller than 45. Also, they can never be equal.

Thanks so much!!!!

[pankajagg]

is this question complete ??

BTW maximum value of the product of x and y is 45*45/12*14

this is attained at y = 45/14 and x= 45/12

[elenavn]

Yes, the question is complete. It appeared in a practise test in Peterson's. But they gave D as the right answer (not enough info given). I thought the answer was A.

I got approximately the same thing for the maximum by guessing. How did you get your number?

[vertical_horizon]

Hey, be careful, x & y are not supposed to be interger, or posititve or something like that. Don't be cheated .

phuong

[pankajagg]

6x + 7y = 45

=> x = (45 - 7y)/6

Let z = x*y
=> z = y*(45 - 7y)/6

Diffrenciate with respect to y and equate it to 0 (for maximum)

solve for y to get y = 45/14

=> x = 45/12 (from 6x + 7y = 45)

therefor x*y = 45*45/12*14

there are some answers wrong in GRE prep CD's

More over 6x + 7y = 45 and xy can be equal but for that x, y has to be complex numbers (if GRE has complex numbers in course then probably D is the answer)

[Sri]

I guess u dont have to actually solve such problems at all...Just plug-in some numbers and cross check....

Case 1 : if x = 0; 6x+7y = 45 (x = 45/6) and xy = 0 ; So, A is greater
Case 2 : if x = -1; 6x+7y = 45 (y = 51/7) and xy = -51/7 ; So, A is greater
Case3 : if x = 1/6; 6x+7y = 45 (y = 44/6) and xy = 44/36 ; So again A is greater
Case 4 : if x = -1/6 again xy is negative and 6x+7y is positive, therefore A is greater...

Since it satisfies all the conditions I would go with A as well...Yah, there are some mistakes in the Peterson's guide!!.

HTH
-Sri.

[pankajagg]

but sri ...does it take care of complex numbers (but first tell me do we have complex numbers in GRE? )

becoz if there are no complex numbers then i'll choose A , otherwise D

actually i didnt prepared for maths ..so i dont have idea abt the course