Dillesh4096 wrote:
(|x| + 3) (|y| - 4) = 12. How many pairs of integers (x,y) satisfy this equation ?
A. 8
B. 12
C. 10
D. 14
E. 16
[/quote]
Can you Please explain this bit :
number of solutions=1*2=2
number of solutions=2*2=4
number of solutions=2*2=4
number of solutions=2*2=4[/quote]
Detailed Solution:(|x| + 3) (|y| - 4) = 12
Possible values of 12 can be 12*1, 6*2, 4*3
Note that, minimum value of (|x| + 3) is 3 as
lxl CANNOT be less than 0--> Possible values of (|x| + 3) are 3, 4, 6, 12
Case 1: When lxl + 3 = 3 ; (|y| - 4) = 4
--> lxl = 0
--> (lyl - 4) = 4
--> lyl = 8
--> y = ±8
Possible values of (x, y) = (0,8) & (0, -8) --
2 solutionsCase 2: When lxl + 3 = 4 ; (|y| - 4) = 3
--> lxl = 1
--> x = ±1
--> (lyl - 4) = 3
--> lyl = 7
--> y = ±7
Possible values of (x, y) = (1,7), (1, -7), (-1, 7) & (-1, -7) --
4 solutionsCase 3: When lxl + 3 = 6 ; (|y| - 4) = 2
--> lxl = 3
--> x = ±3
--> (lyl - 4) = 2
--> lyl = 6
--> y = ±6
Possible values of (x, y) = (3,6), (3, -6), (-3, 6) & (-3, -6) --
4 solutionsCase 4: When lxl + 3 = 12 ; (|y| - 4) = 1
--> lxl = 9
--> x = ±9
--> (lyl - 4) = 1
--> lyl = 5
--> y = ±5
Possible values of (x, y) = (9,5), (9, -5), (-9, 5) & (-9, -5) --
4 solutionsTotal number of solutions = 2 + 4 + 4 + 4 = 14
Hope it's clear!