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03 Jul 2016, 17:31
If (1+x)y=y, which of the following must be true?

A. x=-1 or y=0

B. x=0 or y=0

C. x=1 or y=1

D. x=-1 or y=-1

E. x=0 or y=1

From y+xy=y, we get xy=0. Hence, the correct answer is B.

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04 Jul 2016, 23:40
A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(5)?

A. 2

B. 3/2

C. 5/3

D. 8/5

E. 13/8

Ans: If we substitute directly, the answer comes out to be D.

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05 Jul 2016, 21:12
What is the units digit of 3^66?

A. 1

B. 3

C. 5

D. 7

E. 9

ANS: From 3^1=3, 3^2=9, 3^3=27, 3^4=81, the unit digit repeats in 3-->9-->7-->1-->3. Then, from 3^66=3^(4(16)+2), the unit digt is same as that of ^2. Hence, the answer is 9 and the correct answer choice is E.

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06 Jul 2016, 16:52
Which of the following is closest to (10^19-10^3)/(10^17+1)?

A. 0.01

B. 0.1

C. 0.2

D. 1

E. 10

ANS: We get (10^17-10^3)/(10^17+1)≒(10^19)/(10^17)=1/100=0.01. Hence, the correct answer is A.

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08 Jul 2016, 21:41
Which of the following is closest to (10!-9!)/(10!+9!)?

A. 0.01

B. 0.1

C. 0.2

D. 1

E. 10

ANS: (10!-9!)/(10!+9!)=(10-1)9!/(10+1)9!≒9/11=1. Hence, the correct answer is D

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11 Jul 2016, 18:27
What is the scope including 1/21+1/12+1/13+......+1/30?

A 1/6~1/5

B. 1/5~1/4

C. 1/4~1/3

D. 1/3~1/2

E. 1/2~1

ANS: The sum of sequence is determined by the first and the last number. So, 1/3=10/30<1/21+1/12+1/13+......+1/30<10/21<10/20=1/2. The correct answer is D

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12 Jul 2016, 18:58
8√4n=(4√2)^8, n=?

A. 4^8

B. 4^10

C. 4^12

D. 4^16

E. 4^32

ANS: D

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14 Jul 2016, 01:08
What is the prime factors’ number of 24?

A. 2

B. 3

C. 4

D. 5

E. 6

ANS: From 24=3(2^3), we get 2,2,2 and 3. Hence, the number of prime factors is 4.

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14 Jul 2016, 21:25
a is an integer greater than 19 but less than 31, b is an integer greater than 29 but less than 41, what is the range of a/b?

A. 1/4

B. 1/2

C. 3/4

D. 1

E. 5/4

ANS: From 20≤a≤30 and 30≤b≤40, we get 1/2=20/40≤a/b≤30/30=1. Hence, range=Max-min=1-1/2=1/2 and the correct answer is B.

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18 Jul 2016, 04:15
What number is 72 more than three-fourth of itself?

A. 138

B. 225

C. 288

D. 324

E. 336

ANS: From n=72+(3n/4), n/4=72, n=72(4)=288

Hence, the correct answer is C

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18 Jul 2016, 09:24
If a, b are integers and |a-b|=8, which of the following is the smallest possible value of ab?

A. -16

B. 0

C. 16

D. 7

E. 40

ANS: a=4, b=-4. Hence, the answer is A.

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24 Jul 2016, 02:43
What is the units digit of 17^381?

A. 1

B. 3

C. 5

D. 7

E. 9

ANS: From ~7^1=~7, ~7^2=9, ~7^3=~3, ~7^4=~1, the units digit is 7-->9-->3-->1-->7, and it repeats like this. Then from 17^381=17^(4(95)+1), we can see that the units digit is same as 17^1, which is 7.

The answer is, then, D.

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25 Jul 2016, 19:37
What is the scope including 1/11+1/12+1/13+......+1/20?

A 1/6~1/5

B. 1/5~1/4

C. 1/4~1/3

D. 1/3~1/2

E. 1/2~1

ANS: The sum of a sequence of reciprocals is determined by the first and the end term. So, since 1/2=10/20<1/11+1/12+1/13+......+1/20<10/11<10/10=1, the correct answer is E.

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26 Jul 2016, 18:27
If two integers x,y (x>y) are selected from -5 to 4(inclusive), how many cases are there?

A. 15

B. 18

C. 36

D. 45

E. 90

ANS: 10C2=45. Hence, the correct answer is D.

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31 Jul 2016, 09:02
Which of the following is equal to 1(1/5)%?

A. 0.012/100

B. 0.12/100

C. 1.2/100

D. 12/100

E. 12/10

ANS: If we substitute %=1/100, we get 1(1/5)%=(1+1/5)%=(6/5)%=( 6/5)( 1/100)= (1.2)/100

So, the answer is C.

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04 Aug 2016, 04:45
1+2+2^2+2^3+2^4+2^5=？

A. (2^3-1)(2^3+1)

B. 2^6+1

C. 2^5-1

D. 2^5+1

E. 2^5-2

ANS: From 1+2+2^2+2^3+2^4+2^5=1(2^6-1)/(2-1)=2^6-1=(2^3-1)(2^3+1), the correct answer is A.

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04 Aug 2016, 19:20
If (x^3-2x^2+x-1)^2-1=(x-a)(x-b)(x-c)(x-d)(x-e)(x-f), then abcdef=?

A. 0

B. 25

C. -25

D. 24

E. -24

ANS: If we substitute x=0, from (-1)^2-1=(-a)(-b)(-c)(-d)(-e)(-f)=abcdef, we get abcdef=0.

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07 Aug 2016, 17:53
Which of the following lines has x-intercept and y-intercept that are integers?

A. y=3x+1

B. y=√x+1

C. y=-2/x

D. y=x^2-1

E. xy=1

ANS: Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers and the correct answer is D.

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08 Aug 2016, 18:24
What is the tens digit of 7^381?

A. 0

B. 3

C. 5

D. 7

E. 9

ANS: From ~7^1=~07, ~7^2=~49, ~7^3=~43, ~7^4=~01, the tens digit repeats 0-->4-->4-->0-->0. Then, from 7^381=7^(4(95)+1), the tens digit is same as ~7^1. Hence, it is 0.

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22 Aug 2016, 19:52
If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?

A. √2

B. ±√2

C. 1

D. 2

E. √5

*Answer: If we solve the question, we get x=±√2.

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