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The Ultimate Q51 Guide [Expert Level]

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New post 18 Jan 2017, 18:12
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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
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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 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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New post 21 Feb 2017, 18:50
What is the difference between the circumferences of 2 circles such that the diameters of the circles are 10 and 11?

A. \(\frac{π}{2}\)
B. \(π\)
C. \(\frac{3π}{2}\)
D. \(2π\)
E. \(\frac{5π}{2}\)

==> The circumference of a circle is πd, thus \(π(11-10)= π\). Therefore, the answer is B.
Answer: B
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New post 23 Feb 2017, 20:30
John traveled 150 miles. What is the average speed of John on the trip?

1) John traveled the first 100 miles at the rate of 50 miles per hour
2) John traveled the last 100 miles at the rate of 50 miles per hour

==> In the original condition, he travels the total 150 miles by dividing it to two trips of 50 miles each. Hence, since there are 6 variables, E is most likely to be the answer. In order for C to be the answer, there must be a word “constant rate” mentioned.

Therefore, E is the answer.
Answer: E
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New post 26 Feb 2017, 21:36
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.
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New post 01 Mar 2017, 18:56
What is the difference between the hypotenuse’s length of the right triangle with 2 shorter sides of 10 and 24 and the hypotenuse’s length of the right triangle with 2 shorter sides of 7 and 24?

A. 1
B. 2
C. 3
D. 4
E. 5

==>For Pythagorean Theorem, 5:12:13=10:24:26 and 7:24:25 appear most frequently. Thus, the length of hypotenuse each becomes 26 and 25, and the difference becomes 26-25=1.

The answer is A.
Answer: A
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Re: The Ultimate Q51 Guide [Expert Level]   [#permalink] 01 Mar 2017, 18:56

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