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24 May 2017, 00:36
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When a positive integer x is divided by 12, what is the remainder?
1) x is divisible by 9
2) When x is divided by 4, the remainder is 1
==> In the original condition, there is 1 variable and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For remainder questions, you find the first overlapping number after direct substitution, then you add the least common multiple of the dividing numbers.
For con 1), from x=9=12(0)+9, the remainder is 9.
For con 2), from x=4p+1=1,5,9…., the remainder of x=1=12(0)+1 is 1, and from x=5=12(0)+5, the remainder is 5, hence it is not unique and not sufficient.
By solving con 1) and con 2), the first overlapping number is 9 and the least common multiple of the dividing numbers is LCM(From 4,9+36, you get x=9, 9+36=45, 45+36=81,.., and the remainder when divided by 12 always becomes 9, hence it is unique and sufficient. Therefore, the answer is C.
Answer: C
1) x is divisible by 9
2) When x is divided by 4, the remainder is 1
==> In the original condition, there is 1 variable and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For remainder questions, you find the first overlapping number after direct substitution, then you add the least common multiple of the dividing numbers.
For con 1), from x=9=12(0)+9, the remainder is 9.
For con 2), from x=4p+1=1,5,9…., the remainder of x=1=12(0)+1 is 1, and from x=5=12(0)+5, the remainder is 5, hence it is not unique and not sufficient.
By solving con 1) and con 2), the first overlapping number is 9 and the least common multiple of the dividing numbers is LCM(From 4,9+36, you get x=9, 9+36=45, 45+36=81,.., and the remainder when divided by 12 always becomes 9, hence it is unique and sufficient. Therefore, the answer is C.
Answer: C
25 May 2017, 01:28
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r=?
1) r^3-r^2=0
2) r=-r
==> In the original condition, there is 1 variable (r), and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer.
For con 1), from r^2(r-1)=0, you get r=0,1, hence it is not unique and not sufficient.
For con 2), from 2r=0, you get r=0, hence it is unique and sufficient. Therefore, the answer is B.
Answer: B
1) r^3-r^2=0
2) r=-r
==> In the original condition, there is 1 variable (r), and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer.
For con 1), from r^2(r-1)=0, you get r=0,1, hence it is not unique and not sufficient.
For con 2), from 2r=0, you get r=0, hence it is unique and sufficient. Therefore, the answer is B.
Answer: B
25 May 2017, 17:41
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Is 12 a factor of x(y^2)?
1) X is a multiple of 24
2) Y is a multiple of 6
==> In the original condition, there are 2 variables (x,y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. However, for con 1), x has 12 as a factor from 24=2(12), hence yes, it is sufficient. For con 2), y^2 also has 36 as a factor, and from 36=3(12), y^2 has 12 as a factor as well, hence yes. The answer is D.
Answer: D
1) X is a multiple of 24
2) Y is a multiple of 6
==> In the original condition, there are 2 variables (x,y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. However, for con 1), x has 12 as a factor from 24=2(12), hence yes, it is sufficient. For con 2), y^2 also has 36 as a factor, and from 36=3(12), y^2 has 12 as a factor as well, hence yes. The answer is D.
Answer: D
