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In Episode 3 of our GMAT Ninja Critical Reasoning series, we tackle Discrepancy, Paradox, and Explain an Oddity questions. You know the feeling: the passage gives you two facts that seem completely contradictory....- May 05
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30 Jan 2017, 02:42
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Is a=b?
1) |a|=|b|
2) a=1
==> In the original condition, there are 2 variables (a,b) 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. By solving con 1) and con 2), from a=±b, (a,b)=(1,1) yes, but (a,b)=(1,-1) no, hence it is not sufficient.
Therefore, the answer is E.
Answer: E
1) |a|=|b|
2) a=1
==> In the original condition, there are 2 variables (a,b) 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. By solving con 1) and con 2), from a=±b, (a,b)=(1,1) yes, but (a,b)=(1,-1) no, hence it is not sufficient.
Therefore, the answer is E.
Answer: E
30 Jan 2017, 02:45
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What is the perimeter of a certain right triangle?
1) The length of hypotenuse is 4
2) The area of triangle is 4.5
==> In the original condition, for the right triangle, there are 2 variables 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. By solving con 1) and con 2) and assume the two hypotenuses of the triangle as a and b, you get \(a^2+b^2=4^2=16\), and from ab/2=4.5, you get ab=9. Then, from \((a+b)^2=a^2+b^2+2ab=16+2(9)=16+18=34\), you get a+b=√34, so the perimeter of the right triangle=a+b+4=√34+4, hence it is unique and sufficient.
Therefore, the answer is C.
Answer: C
1) The length of hypotenuse is 4
2) The area of triangle is 4.5
==> In the original condition, for the right triangle, there are 2 variables 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. By solving con 1) and con 2) and assume the two hypotenuses of the triangle as a and b, you get \(a^2+b^2=4^2=16\), and from ab/2=4.5, you get ab=9. Then, from \((a+b)^2=a^2+b^2+2ab=16+2(9)=16+18=34\), you get a+b=√34, so the perimeter of the right triangle=a+b+4=√34+4, hence it is unique and sufficient.
Therefore, the answer is C.
Answer: C
01 Feb 2017, 02:29
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When a positive integer n is divided by 2, what is the remainder?
1) The remainder is 1 when n is divided by 5
2) The remainder is 1 when n is divided by 10
==> In the original condition, there is 1 variable (n) 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 can solve it by using direct substitution.
For con 1), from n=5p+1(p=any positive integer), you get n=1,6,… However, from n=1=2(0)+1, you get r=1, but n=6=2(3)+0, you get r=0, hence it is not unique and not sufficient.
For con 2), from n=10q+1(q=any positive integer), you get n=1,11,21,… However, for all cases, the remainder=1, hence it is unique and sufficient.
Therefore, the answer is B
1) The remainder is 1 when n is divided by 5
2) The remainder is 1 when n is divided by 10
==> In the original condition, there is 1 variable (n) 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 can solve it by using direct substitution.
For con 1), from n=5p+1(p=any positive integer), you get n=1,6,… However, from n=1=2(0)+1, you get r=1, but n=6=2(3)+0, you get r=0, hence it is not unique and not sufficient.
For con 2), from n=10q+1(q=any positive integer), you get n=1,11,21,… However, for all cases, the remainder=1, hence it is unique and sufficient.
Therefore, the answer is B
