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Math Revolution Approach (PS)

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MathRevolution
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Re: Math Revolution Approach (PS) [#permalink] New post   03 Jul 2016, 17:31
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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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Re: Math Revolution Approach (PS) [#permalink] New post   04 Jul 2016, 23:40
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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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Re: Math Revolution Approach (PS) [#permalink] New post   05 Jul 2016, 21:12
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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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Re: Math Revolution Approach (PS) [#permalink] New post   06 Jul 2016, 16:52
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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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Re: Math Revolution Approach (PS) [#permalink] New post   08 Jul 2016, 21:41
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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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Re: Math Revolution Approach (PS) [#permalink] New post   11 Jul 2016, 18:27
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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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Re: Math Revolution Approach (PS) [#permalink] New post   12 Jul 2016, 18:58
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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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Re: Math Revolution Approach (PS) [#permalink] New post   14 Jul 2016, 01:08
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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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Re: Math Revolution Approach (PS) [#permalink] New post   14 Jul 2016, 21:25
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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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Re: Math Revolution Approach (PS) [#permalink] New post   18 Jul 2016, 04:15
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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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Re: Math Revolution Approach (PS) [#permalink] New post   18 Jul 2016, 09:24
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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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Re: Math Revolution Approach (PS) [#permalink] New post   24 Jul 2016, 02:43
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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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Re: Math Revolution Approach (PS) [#permalink] New post   25 Jul 2016, 19:37
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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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Re: Math Revolution Approach (PS) [#permalink] New post   26 Jul 2016, 18:27
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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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Math Revolution Approach (PS) [#permalink] New post   31 Jul 2016, 09:02
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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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Re: Math Revolution Approach (PS) [#permalink] New post   04 Aug 2016, 04:45
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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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Re: Math Revolution Approach (PS) [#permalink] New post   04 Aug 2016, 19:20
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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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Re: Math Revolution Approach (PS) [#permalink] New post   07 Aug 2016, 17:53
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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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Re: Math Revolution Approach (PS) [#permalink] New post   08 Aug 2016, 18:24
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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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Re: Math Revolution Approach (PS) [#permalink] New post   22 Aug 2016, 19:52
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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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Re: Math Revolution Approach (PS) [#permalink]
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