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Math Revolution Approach (PS)

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New post 23 Jul 2017, 18:29
When 240n is the square of an integer, what is the least possible value of n?

A. 10
B. 15
C. 20
D. 25
E. 30

==> From 240n=4^2(3)(5)n=integer^2, the least possible value of n becomes (3)(5)=15.

The answer is B.
Answer: B
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New post 23 Jul 2017, 18:30
When |x|>1 and |x-3|>1, which of the following is contained in the scope of x?

A. -0.5
B. 0
C. 0.5
D. 1.5
E. 2.5

==> |x|>1 becomes x<-1 or 1<x, and for |x-3|>1, you get x-3<-1 or 1<x-3 --> x<2 or 4<x. Then, what satisfies both becomes 1<x<2 or 4<x.

The answer is D.
Answer: D
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New post 26 Jul 2017, 01:12
The length of a rectangular photograph is 2 longer than the width of the photograph. If the area of the photograph is 35, what is the width?

A. 3
B. 4
C. 5
D. 6
E. 7

==>If width=w, you get length=w+2, and from w(w+2)=35, w^2+2x-35=0, (w+7)(w-5)=0, w=-7,5, you get w=5.

The answer is c.
Answer: C
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New post 28 Jul 2017, 01:27
There is a sequence An, such that A1=1,A2=2, and An+2=An+1+An+An-1+….+A2+A1. What is the ratio of A14 to A11?

A. 32
B. 16
C. 8
D. 4
E. 2

==> If A11=A10+A9+A8+….+A2+A1=p, you get A12 =A11+A10+A11+….+A2+A1=2p, and from A13=4p, A14=8p, you get A14:A11=8p:p=8:1=8.

The answer is C.
Answer: C
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New post 30 Jul 2017, 18:59
There is a total of 1,800 pages that needs to be typed. If it takes 90 minutes when a types alone, 45 minutes when b types alone, and 30 minutes when c types alone. How many minutes does it take if 3 of them work together?

A. 10min
B. 12min
C. 15min
D. 18min
E. 20min

==> For work rate questions, if there is a “together and alone”, you need to solve the question reciprocally. In other words, A: 1,800pg/90mins, B:1,800pg/45mins, C: 1,800pg/30mins, and if you assume A&B&C:1,800pg/t mins, you get (1/90)+(1/45)+(1/30)=(1/t), and from (1+2+3)/90=1/t, you get t=15.

The answer is C.
Answer: C
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New post 30 Jul 2017, 19:00
When x is divided by 7, the remainder is 3. When x3 is divided by 7, what is the remainder?

A. 2
B. 3
C. 4
D. 5
E. 6

==> For remainder questions, it is important to use direct substitutions. From X=7p+3=3,10,17,…., if you substitute x=3, from x^3=3^3=27=7(3)+6, you get a remainder of 6.

Therefore, the answer is E.
Answer: E
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New post 02 Aug 2017, 00:59
If n is the product of 3 same prime numbers and 1 different prime number, then how many different factors of n are there?

A. 6
B. 8
C. 9
D. 12
E. 18

==> You get n=(3)(3)(3)(5), which becomes n=3^3*5^1. Thus, the number of factors of n becomes (3+1)(1+1)=8.

The answer is B.
Answer: B
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New post 03 Aug 2017, 01:29
When n is divided by 4, the remainder is 3. If 3^n+2 is divided by 5, what is the remainder?

A. 1
B. 2
C. 3
D. 4
E. 0

==> You get n=4p+3, which becomes 3^n+2=3^{4p+3}+2=(3^4)^p(3^3)+2=(~1)^p(27)+2=(~1)(27)+2=(~7)+2=~9. Thus, the remainder when it is divided by 5 becomes 4.

The answer is D.
Answer: D
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New post 04 Aug 2017, 02:25
Attachment:
8.2.png
8.2.png [ 14.1 KiB | Viewed 172 times ]


There are 2 circles, 1 big circle and 1 small circle, and they meet at one point. The diameter of the small circle is equal to the radius of the big circle, and the area of the big circle is 14π. What is the area of the small circle?

A. 3π
B. 3.5π
C. 4π
D. 4.5π
E. 7π

==> Ratio of length^2=Ratio of area, and since the ratio of the length is 2, the ratio of the area becomes 4, so you get 14π/4=3.5π.

The answer is B.
Answer: B
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New post 06 Aug 2017, 18:17
What is the sum of all digits of 2^{13}5^7?

A. 3
B. 4
C. 6
D. 8
E. 10

==> You get 2^{13}5^7=2^6(2^75^7)=64(10^7)=640,000,000. The sum of the 0's at the back always becomes 0, so you get 6+4=10.

The answer is E.
Answer: E
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New post 06 Aug 2017, 18:19
If you are flipping the coin 4 times, what is the probability of landing on head two times?

A. 3/5
B. 4/5
C. 3/7
D. 4/7
E. 3/8

==> Probability=Want/Total. Total=since the number of ways when throwing the coins each becomes head or tail 2 times, you get 2*2*2*2=16. Want=if it lands on head 2 times, it lands on tail 2 times, so you get 4!/2!2!=6. Thus, the probability=6/16=3/8.

The answer is E.
Answer: E
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New post 09 Aug 2017, 18:09
There are 5 apples in a bag. 4 apples are good but 1 apple is rotten. If you take out 2 apples from the bag, what is the probability that 1 apple selected is rotten?

A. 1/3
B. 1/4
C.2/5
D. 3/5
E.1/7

==> From probability=want/total, want=selecting one rotten apple and one good apple, and total=selecting 2 of 4 apples, so you get
probability=4C1*1C1/5C2=(4)(1)/(5*4/2!)=4/10=2/5.

The answer is C.
Answer: C
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New post 10 Aug 2017, 01:14
There is a sequence of r, t, s, 1, 4, 3, 8, 15, 26. Each number of the sequence is the sum of the 3 previous numbers. r=?

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

==> You get r+t+s=1, from t+s+1=4, you get t+s=3, and from r+t+s=r+3=1, you get r=1-3=-2.

The answer is A.
Answer: A
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New post 11 Aug 2017, 01:04
When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone?

A. 30hrs
B. 33hrs
C. 35hrs
D. 37hrs
E. 40hrs

==> For work rate questions, you solve “together and alone” reciprocally. It takes A 14hrs alone, and if you set the hours it took B to work alone as B hrs, from (1/14)+(1/B)=1/10 and 1/B=(1/10)-(1/14)=1/35, you get B=35.

The answer is C.
Answer: C
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New post 11 Aug 2017, 17:34
MathRevolution wrote:
If x and y are integers, what is the least positive number of 24x+15y?
A. 1
B. 3
C. 6
D. 9
E. 12

Since 24(2)-15(3)=3, B is the correct answer.
Simplify to 3(8x-5y)
Since gcd(5,8)=1 there are 2 integers a,b such that 5a+8b=1
Hence the smallest positive number is 3.



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New post 13 Aug 2017, 18:21
Attachment:
8.10.png
8.10.png [ 4.39 KiB | Viewed 95 times ]


What is the area of a trapezoid ABCD as above figure?

A. 84 B. 96 C. 104 D. 120 E. 150

==> The area of a trapezoid is (base1+base2)height/2.

Attachment:
AA.png
AA.png [ 4.11 KiB | Viewed 94 times ]


As shown above, the height becomes 8. Then, the area becomes (16+10)8/2=26*4=104.

The answer is C.
Answer: C
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New post 13 Aug 2017, 18:24
What is the value of (-2)^2+(1/3)^{-3}+(-4)^3?

A. -27
B. -29
C. -33
D. 33
E. 29

==> From (-2)^2+(1/3)^{-3}+(-4)^3=4+(3^{-1}){-3}+(-4)^3=4+33-64=4+27-64=-33, the answer is C.

Answer: C
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New post 16 Aug 2017, 02:42
In the xy-coordinate plane there are 4 points A(2,0), B(4,0), C(4,2), and D(2,2). If the line which passes through an origin bisects the area of the rectangle ABCD, what is the slope of the line?

A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 1/6

Attachment:
8.16.png
8.16.png [ 9.06 KiB | Viewed 77 times ]

The line should pass through the center (3,1) of the square ABCE. Thus its slope is 1/3.

Ans: B
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New post 17 Aug 2017, 00:54
If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n?

A. -5 B. -4 C. -3 D. 4 E. 5


=>0.00001 < 0.000025 < 0.0001
10^{-5} < 0.000025 < 10^{-4}

Ans: A
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New post 20 Aug 2017, 18:26
An alarm of a certain clock rings every 20 minutes. If the clock's alarm first rings at 15:20, when will the 12th alarm of the clock ring?
A. 17:30 B. 18:00 C. 18:30 D. 19:00 E. 19:30


=>The third alarm rings at 16:00, the sixth alarm rings at 17:00. Thus every third alarm rings every hour on the hour. The 12th alarm rings at 19:00.

Ans: D
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Re: Math Revolution Approach (PS)   [#permalink] 20 Aug 2017, 18:26

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