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10 Jan 2017, 19:39
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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12 Jan 2017, 18:15
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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13 Jan 2017, 01:48
There are a bunch of buildings and their building numbers are all even numbers. If the numbers are 312 between 590 inclusive, what is the number of buildings?

A. 139 B. 140 C. 141 D. 142 E. 143

==> The number of consecutive even numbers of odd numbers=(the last term+the first term) )/2 +1.

That is, (590-312)/2 +1=139+1=140. That is, (590-312)/2 +1=139+1=140 and the answer is B.

Answer: B

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15 Jan 2017, 18:40
\(4^-^4/16^-^3=?\)

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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15 Jan 2017, 18:46
There is a sequence an for a positive integer such that a

3 =a

1 +a

2 , a

4 =a

3 +a

2 +a

1 , a

n =a

n-1 +a

n-2 +a

n-3 +….+a

2 +a1. If a

n =p, a

n+2 =?

A. 2p B. 4p C. 8p D. 16p E. 24p

==> Since a

n =a

n-1 +a

n-2 +a

n-3 +….+a

2 +a

1 =p,

a

n+1 =a

n + a

n-1 +a

n-2 +a

n-3 +….+a

2 +a

1 =p+p=2p

a

n+2 =a

n+1 +a

n +a

n-1 +a

n-2 +a

n-3 +….+a

2 +a

1 =2p+p+p=4p.

Hence, the answer is B.

Answer: B

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17 Jan 2017, 01:16
(1/7!)-(1/8!)=?

A. 1/6! B. 1/7! C. 7/8! D. 8/7! E. 7/6!

==> As 8!=8(7!), (1/7!)-(1/8!)=(1/7!)-(1/8!)=8/8(7!)-1/7!=(8/8!)-(1/8!)=(8-1)/8!=7/8! is derived.

Hence, the answer is C.

Answer: C

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19 Jan 2017, 01:30
If x=-1 and n is the sum of the first 100 prime numbers, what is the value of \(x^n+x^n^+^1+x^n^+^2\)?

A. -2 B. -1 C. 0 D. 1 E. 2

==> From n=2+3+5+…….+p, prime is all odd numbers apart from 2.

Then, n=2+99 odd numbers=2+odd=odd is derived.

And \(x^n+x^n^+^1+x^n^+^2=(-1)^o^d^d+(-1)^e^v^e^n+(-1)^o^d^d=-1+1-1=-1\) .

Hence, the answer is B.

Answer: B

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20 Jan 2017, 06:24
(√3+√2)/(√3-√2) is approximately between which two numbers?

A. 3 and 4 B. 4 and 5 C. 5 and 8 D. 9 and 11 E. 11 and 13

==>From \(√3+√2/√3-√2=(√3+√2)^2/(√3-√2)( √3+√2)=3+2+2√6/3-2=5+2√6=5+2(2.xxx)=9.xxx\),

the answer is D.

Answer: D

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22 Jan 2017, 22:32
If sphere A’s volume is 64 times of sphere B’s volume, sphere A’s surface area is how many times of sphere B’s surface area?

A. 4 B. 8 C. 12 D. 16 E. 32

==> Since sphere A’s volume is 64 times of sphere B’s volume, sphere A’s length is Sphere A’s \(3√64\)times of sphere B’s length, in other words,\(3√4^3=4\). However, since the ratio of the surface area is equal to the square of ratio of the length, you get 4^2=16, hence 16 times.

Therefore, the answer is D.

Answer: D

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22 Jan 2017, 22:37
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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25 Jan 2017, 05:11
If f(n)=n(n+1), which of following is equal to f(8)/f(2)?

A. f(3)

B. f(4)

C. f(5)

D. f(6)

E. f(7)

==>You get f(8)/f(2)=8*9/2*3=4*3=f(3), so the answer is A.

Answer: A

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26 Jan 2017, 00:58
Which of the following is closest to \(√0.08\)?

A. 0.03

B. 0.04

C. 0.3

D. 0.8

E. 0.9

You get \(√0.08=about √0.09=√0.3^2=0.3\), so the answer is C.

Answer: C

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27 Jan 2017, 04:22
If \(2^x+2^x+2^x+2^x=2^a\), x=?

A. a-2

B. a+2

C. 2-a

D. 2a

E. a-4

==> From \(2^x+2^x+2^x+2^x=(1+1+1+1)2^x=4(2^x)=2^22^x=2^2^+^x=2^a\), you get \(2+x=a, x=a-2\).

Therefore, the answer is A.

Answer: A

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30 Jan 2017, 02:52
Attachment:

a.png [ 3.42 KiB | Viewed 257 times ]
Which absolute value of the following is the greatest?

A. a+b

B. b+d

C. c+e

D. c+d

E. b+e

==> On the straight line, the greatest absolute value is |a+b|=|-1.8+(-1.3)|=3.1.

Therefore, the answer is A.

Answer: A

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01 Feb 2017, 02:30
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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02 Feb 2017, 02:53
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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03 Feb 2017, 02:06
What is the number of the shortest routes from X to Y through Z?

A. 8 B. 12 C. 16 D. 18 E. 20

Attachment:

1.png [ 10.49 KiB | Viewed 239 times ]
==> The number of cases of x heading to z is 4!/2!2!=6. The number of cases of Z heading to y is 2, which makes 6*2=12.

Hence, the answer is B.

Answer: B

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05 Feb 2017, 18:54
What is the units digit of \(7^2^0\)?

A. 1

B. 3

C. 5

D. 7

E. 9

==> Since \(~7^1=~7, ~7^2=~9, ~7^3=~3, ~7^4=~1\), the exponent has a cycle of four, which makes 20=4*5. Then, \(7^2^0=(7^4)^5=~1\) is derived and the answer is A.

Answer: A

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08 Feb 2017, 01:09
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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09 Feb 2017, 05:12
When \(8^x=16\), x=?

A. \(\frac{2}{3}\)

B. \(\frac{3}{2}\)

C. \(\frac{3}{4}\)

D.\(\frac{4}{3}\)

E. \(\frac{4}{5}\)

==>From \(8^x=16 to 2^3^x=2^4, you get 3x=4, x=\frac{4}{3}\). Therefore, the answer is D.

Answer: D

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