Consider two positive even integers less than 15 (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?
+532 so it is looking for ab+a+b, if you add one to that, they will still be the same, distinct or not distinct, so it wont change it so you can just make it ab+a+b+1, which factors as (a+1)(b+1). now you are just trying to find those values.
a,b=2,4,6,8,10,12,14
i found no way to do this other than casework..
if a = 2 then it equals 9,15,21,27,33,39, and 45
if a = 4 then it equals 15,25,35,45,55,65, and 75
if a = 6 then it equals 21,35,49,63,77,91, and 105
if a = 8 then it equals 27,45,63,81,99,117, and 135
if a = 10 then it equals 33,55,77,99,121,143, and 165
if a = 12 then it equals 39,65,91,117,143,169, and 195
if a = 14 then it equals 45,75,105,135,165,195, and 225
counting them, and listing, you get the numbers 9, 15, 21, 27, 33, 39, 45, 25, 35, 55, 65, 75, 49, 63, 77, 91, 105, 81, 99, 117, 135, 121, 143, 165, 169, 195, and 225, for a total of 27 numbers.
HOPE THIS HELPED!!
(may be 28, im not sure)
+130071 asdf is correct....
Since the integers do not have to be distinct (different).....we have....
2*2 + 2 + 2 = 8 4*4 + 4 + 4 = 24 6*6 + 6 + 6 = 48 8*8 + 8 + 8 = 80
2*4 + 2 + 4 = 14 4*6 + 4 + 6 = 34 6*8 +6 + 8 = 62 8*10 + 8 + 10 = 98
........20 ........ 44 ......76 ......116
........26 .........54 ......90 ......134
........32 .........64 ......104
........38 .........74
........44
10*10 + 10 + 10 = 120 12 * 12 + 12 + 12 = 168 14 * 14 + 14 + 14 = 224
10*12 + 10 + 12 = 142 12*14 + 12 + 14 = 194
..... 164
We have (7)*(8) / 2 - 1 = 27 different values.....
