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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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15 Jan 2017, 18:47
\(2^a2^b<4\)? 1) a+b<1. 2) a+b>0. ==> If you modify the original condition and the question, from \(2^a^+^b<4=2^2\), you get a+b<2? Then, for con 1), the range of the question includes the range of the condition, and therefore it is sufficient. For con 2), you get a+b=1 yes, but a+b=3 no, and therefore it is not sufficient. Answer A
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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15 Jan 2017, 21:14
MathRevolution wrote: The question below is also a 5051level question.
If x, y and z are different integers, what is the value of y?
1) The average (arithmetic mean) of x, y and z is 2 2) x<y<z
==> In the original condition, there are 3 variables (x, y, z), and in order to match the number of variables to the number of equations, there must be 3 equations, and therefore E is most likely to be the answer. By solving con 1) & con 2), you get (x+y+z)/3=2. Since it is x<y<z, you always get median=average=y=2. Hence it is unique and sufficient.
The answer is C. Answer: C Your solution is wrong. You can let x = 2, y = 0, z = 8 and still meet all of the conditions. You are confounding the mean with the median. E is the correct answer choice.
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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16 Jan 2017, 18:55
Is n an even? 1) 3n=even 2) 5n=even ==> In the original condition, there is 1 variable (n), and therefore D is most likely to be the answer. For con 1) n=2 yes and n=2/3 no, so it is not sufficient. For con 2), n=2 yes and n=2/5 no, so it is not sufficient. By solving con 1) and con 2), you always get n=even, and hence it is sufficient. Therefore, the answer is C. Answer: C
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18 Jan 2017, 18:12
In a certain factory, the production line which produces the bags has the probability that a bag selected at random is defective is 0.02. If 6 bags are selected at random, what is the probability that at least one bag is defective? \(A. 0.02^6\) \(B. (0.02)(0.98)^6\) \(C. 1(0.02)^6\) \(D. 0.98^6\) \(E. 1(0.98)^6\) ==> probability that at least one bag is defective=1probability that all bags are not defective=\(1(10.02)^6\). Hence, the answer is E. Answer: E
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19 Jan 2017, 18:52
The probability which event E occurs is 0.7 and the probability which event F occurs is 0.3. When event E and event F are independent, what is the range including the probability that neither E occurs nor F occurs? A. 0.01~0.1 B. 0.1~0.2 C. 0.2~0.4 D. 0.4~0.6 E. 0.6~0.8 ==> It is about the probability that event E and F don’t occur. Then, (10.7)(10.3)=(0.3)(0.7)=0.21 is derived, which includes C. Answer: C
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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22 Jan 2017, 22:38
Which of the following options is the smallest？ A. 33% B. 3/10 C. 1/3 D. 0.3333 E. 0.333 ==> A. 33%=0.33 B. 3/10=0.3 C. 1/3=0.3333… D. 0.3333 E. 0.333 Hence, amongst them, C is the smallest. Answer: C
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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24 Jan 2017, 02:57
\(4^^4/16^^3=?\) A. 4 B. 1/4 C. 8 D. 1/8 E. 16 ==> \(4^^4=(2^2)^^4=2^^8\) and \(16^^3=(2^4)^^3=2^^1^2\) is derived. Then, \(4^^4/16^^3=2^^8/2^^1^2=2^^8^^(^^1^2^)=2^4=16\). Hence, the answer is E. Answer: E
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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27 Jan 2017, 04:33
When a positive integer n has 4 different factors, n=? 1) n has only 1 prime factor 2) n<10 ==> In the original condition, there is 1 variable(n), which should match with the number of equations. Then, 1 euqation is needed as well. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. For 1), \(n=2^3, 3^3\),…, which is not sufficient. For 2), only n=\(2^3\) is possible, which is unique and sufficient. Hence, the answer is B. Answer: B
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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30 Jan 2017, 02:59
If rs>0, which of the following cannot be true? A. r>0 B. s>0 C. r+s>0 D. r+s<0 E. r<0<s ==> With 0 in the middle, r and s has to be at the same place, E. r<0<s is impossible. Therefore, the answer is E. Answer: E
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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31 Jan 2017, 00:16
Is \(x^y>1\)? 1) x>1 2) y<1 ==> 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. By solving con 1) and con 2), you get (x,y)=(2,1/2) yes, but (x,y)=(2,2) no, NOT sufficient. Therefore, the answer is E. Answer: E
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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01 Feb 2017, 18:10
Is x2y2<15? 1) xy<3 2) x+y<5 ==> If you modify the original condition and the question, you get \(15<x^2y^2<15?\), 15<(xy)(x+y)<15? 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. By solving con 1) and con 2), from 3<xy<3 and 5<x+y<5 to 15<(xy)(x+y)<15, it is always yes, hence it is sufficient. Therefore, the answer is C. Answer: C
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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02 Feb 2017, 18:41
What number is 23 more than threefourth of itself? A. 82 B. 92 C. 108 D. 116 E. 124 ==> From n=(3/4)n+23, you get 4n=3n+92, hence n=92. Therefore, the answer is B. Answer: B
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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06 Feb 2017, 18:22
If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30, what is the smallest number? A. 5 B. 10 C. 15 D. 20 E. 25 ==> From 5n,5n+5, 5n+10, 5n+15, 5n+20, the average is 5n+10, and from 5n+10=30, you get 5n=20, n=4. The smallest number=5n=5(4)=20, hence the answer is D. Answer: D
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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09 Feb 2017, 19:29
If \(n=2^23^35^37\), how many factors of n are there? A. 18 B. 36 C. 54 D. 96 E. 108 ==> The number of factors becomes (2+1)(3+1)(3+1)(1+1)=96, hence the answer is D. Answer: D
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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12 Feb 2017, 18:28
In the xy plane, If line k does not pass through the origin, is the slope of the line K negative? 1) The yintercept of the line K is 4 times the xintercept of the line K 2) The product of the yintercept and the xintercept of the line K is positive ==> In the original condition, there are 2 variables(there are 2 variables for a line > slope and yintercept). In order to match with the number of equations, you need 2 equations. For 1) 1 equation and for 2) 1 equation, which is likely to make C the answer. Through 1) & 2), 1)=2) is derived and it is yes for each condition. Hence, it is sufficient and the answer is D. Answer: D
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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13 Feb 2017, 19:12
Is x>y? 1) x+a>xa 2) ax>ay ==> 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. By solving con 1) and con 2), from con 1), you get a>a, 2a>0, or a>0, and from con 2), you get ax>ay, and the inequality sign doesn’t change even if you divide both sides by a because since a>9, you get x>y, hence yes, it is always sufficient. Therefore, the answer is C. Answer: C
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13 Feb 2017, 22:15
Why not B? Sent from my SMN910C using GMAT Club Forum mobile app

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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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14 Feb 2017, 19:43
If m and n are integers greater than 1, mn=? 1) \(m^n=16\) 2) \(m=2\) ==>In the original condition, there are 2 variables (m, n), 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), you get m=2 and n=4, hence it is sufficient, and the answer is C. However, this is an integer question, one of the key questions, so you apply CMT 4 (A: if you get C too easily, consider A or B). For con 1), from mn=16=24=42, you get (m,n)=(2,4),(4,2), which always becomes mn=8, hence it is sufficient. Therefore, the answer is A, not C. Answer: A
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18 Feb 2017, 08:15
If 1 male, 2 females, and 1 child are to be randomly selected from 8 males, 10 females, and 8 children, how many such cases are possible? A. 980 B. 1,440 C. 1,880 D. 2,480 E. 2,880 ==> You get 8C1*10C2*8C1=(8)(45)(8)=2,880. The answer is E. Answer: E
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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19 Feb 2017, 18:49
If x and y are positive integers, is xm+y a multiple of 9? 1) m is a multiple of 3 2) x+y is a multiple of 9 ==> In the original condition, there are 3 variables (x, y, m) and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), (x,y,m)=(1,8,3) yes, but (x,y,m)=(2,7,3) no, hence it is not sufficient. Therefore, the answer is E. Answer: E
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