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The Ultimate Q51 Guide [Expert Level]

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New post 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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New post 15 Jan 2017, 21:14
MathRevolution wrote:
The question below is also a 5051-level 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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New post 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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New post 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=1-probability that all bags are not defective=\(1-(1-0.02)^6\).

Hence, the answer is E.
Answer: E
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New post 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, (1-0.7)(1-0.3)=(0.3)(0.7)=0.21 is derived, which includes C.

Answer: C
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New post 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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New post 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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New post 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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New post 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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New post 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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New post 01 Feb 2017, 18:10
Is |x2-y2|<15?
1) |x-y|<3
2) |x+y|<5

==> If you modify the original condition and the question, you get \(-15<x^2-y^2<15?\), -15<(x-y)(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<x-y<3 and -5<x+y<5 to -15<(x-y)(x+y)<15, it is always yes, hence it is sufficient. Therefore, the answer is C.
Answer: C
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New post 02 Feb 2017, 18:41
What number is 23 more than three-fourth 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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New post 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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New post 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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New post 12 Feb 2017, 18:28
In the x-y plane, If line k does not pass through the origin, is the slope of the line K negative?
1) The y-intercept of the line K is 4 times the x-intercept of the line K
2) The product of the y-intercept and the x-intercept of the line K is positive

==> In the original condition, there are 2 variables(there are 2 variables for a line -> slope and y-intercept). 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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New post 13 Feb 2017, 19:12
Is x>y?

1) x+a>x-a
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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New post 13 Feb 2017, 22:15
Why not B?

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New post 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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New post 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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New post 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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Re: The Ultimate Q51 Guide [Expert Level]   [#permalink] 19 Feb 2017, 18:49

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