Math Is Fun Forum

simone

Member

Registered: 2007-10-05

Posts: 19

problems - logic

could you please help me work this problems out?

FIRST PROBLEM
The equation:

|x/2| + |y/2| = 5

encloses a certain region on a coordinate plane. What is the area of this region?

SECOND PROBLEM
How many different numbers are there such that   ax + b = c  (a,b,and c are constants)  ?
1.   c>b
2.   a>1

A. Statement 1. is sufficient
B. Statement 2. is sufficient
C. Statements 1. and 2. together are sufficient
D. Each statement alone is sufficient
E. Both statements together are not sufficient

thank you
   

thank you.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: problems - logic

In the first problem, the required region is the square formed by joining the points (10,0), (0,10), (−10,0), (0,−10). I’ll let you find the area of the region yourself.

I’m not entirely sure what the second problem wants (though as it stands I’d go for E).

simone

Member

Registered: 2007-10-05

Posts: 19

Re: problems - logic

thank you!

HallsofIvy

Guest

Re: problems - logic

could you please help me work this problems out?

FIRST PROBLEM
The equation:

|x/2| + |y/2| = 5

encloses a certain region on a coordinate plane. What is the area of this region?

If x and y are both positive, that is x/2+ y/2= 5 or x+ y= 10, the straight line through (0,10) and (10, 0).  If x and y are both negative, that is -x/2- y/2= 5 or x+ y= -10, the straight line through (0,-10) and (-10,0).  If x is positive and y negative, that is x/2- y/2= 5 or x- y= 10, the straight line through (0, -10) and (10,0).  Finally, if x is negative and y positive, that is -x/2+ y/2= 10 or y- x= 10, the straight line through (0, 10) and (-10, 0).  It is easy to show that the length of each of those line segments is sqrt{100+ 100}= 10sqrt(2) and so the figure is a square.  It's area is the square of that.

SECOND PROBLEM
How many different numbers are there such that   ax + b = c  (a,b,and c are constants)  ?
1.   c>b
2.   a>1

A. Statement 1. is sufficient
B. Statement 2. is sufficient
C. Statements 1. and 2. together are sufficient
D. Each statement alone is sufficient
E. Both statements together are not sufficient

?Do you mean how many different values for x?  If a is not 0, then 1: x= (c-b)/a! If a is 0, there are none.  If that is a correct understanding of the problem, then statement 2, that a> 1 (and so not 0) is sufficient to distinguish between the two possibilities.