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(x + 3) (y  4) = 12. How many pairs of integers (x,y) satisfy
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03 Aug 2019, 22:56
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(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
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(x + 3) (y  4) = 12. How many pairs of integers (x,y) satisfy
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Updated on: 05 Aug 2019, 11:52
Hi Dillesh4096, (x+3) ≥3 and thus (y4) has to be positive in any combination in order to satisfy (x+3)(y4)= 12, (x+3) can take four values: 3, 4, 6 and 12. Correspondingly, (y4) must pair with following values: 4, 3, 2, 1. (x+3)(y4) =3*4... x=0,y=+/8, number of solution=1*2=2 =4*3...x=+/1,y=+/7, number of solution=2*2=4 =6*2...x=+/3,y=+/6, number of solution=2*2=4 =12*1...x=+/9,y=+/5, number of solution=2*2=4 Thus, total number of pairs of integers (x,y) that satisfy the equation = 2+4+4+4=14 Answer is (D) Hit that +1 kudo if you like my solutionPosted from my mobile device
Originally posted by chondro48 on 05 Aug 2019, 10:43.
Last edited by chondro48 on 05 Aug 2019, 11:52, edited 2 times in total.



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Re: (x + 3) (y  4) = 12. How many pairs of integers (x,y) satisfy
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04 Aug 2019, 10:19
x+3 ≥3....Hence x+3 can take 4 values 3, 4, 6 and 12 (x+3)(y4)=3*4....number of solutions=1*2=2 (x+3)(y4)=4*3....number of solutions=2*2=4 (x+3)(y4)=6*2....number of solutions=2*2=4 (x+3)(y4)=12*1....number of solutions=2*2=4 total number of pairs of integers (x,y)= 2+4+4+4=14 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



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Re: (x + 3) (y  4) = 12. How many pairs of integers (x,y) satisfy
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05 Aug 2019, 10:20
nick1816 wrote: x+3 ≥3....Hence x+3 can take 4 values 3, 4, 6 and 12 (x+3)(y4)=3*4....number of solutions=1*2=2 (x+3)(y4)=4*3....number of solutions=2*2=4 (x+3)(y4)=6*2....number of solutions=2*2=4 (x+3)(y4)=12*1....number of solutions=2*2=4 total number of pairs of integers (x,y)= 2+4+4+4=14 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 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



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Re: (x + 3) (y  4) = 12. How many pairs of integers (x,y) satisfy
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05 Aug 2019, 11:15
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!



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Re: (x + 3) (y  4) = 12. How many pairs of integers (x,y) satisfy
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05 Aug 2019, 10:36
@Dilesh4096... Same question from me Posted from my mobile device
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Re: (x + 3) (y  4) = 12. How many pairs of integers (x,y) satisfy
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05 Aug 2019, 10:55
I used the following concepts to solve this problem 1. If x=0, then there is only 1 value possible for x, that is x=0. If x=k, where k is nonzero positive real number, then there are 2 values of x are possible, that are +k and k. 2. If x=m, and y=n. Hence both x and y can have 2 values. total number of combinations possible for (x, y)=2*2=4 (x, y)= (m, n), (m,n), (m, n) and (m, n) You don't have to to find the solutions in all cases, as x and y are taking distinct values in all 4 cases. So, there can't be any overlapping possible. Just use the combinatorics, helping you to save some time. Mayank1996 wrote: nick1816 wrote: x+3 ≥3....Hence x+3 can take 4 values 3, 4, 6 and 12 (x+3)(y4)=3*4....number of solutions=1*2=2 (x+3)(y4)=4*3....number of solutions=2*2=4 (x+3)(y4)=6*2....number of solutions=2*2=4 (x+3)(y4)=12*1....number of solutions=2*2=4 total number of pairs of integers (x,y)= 2+4+4+4=14 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 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




Re: (x + 3) (y  4) = 12. How many pairs of integers (x,y) satisfy
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05 Aug 2019, 10:55






