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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   08 Feb 2017, 01:09
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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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Re: Math Revolution Approach (PS) [#permalink] New post   09 Feb 2017, 05:12
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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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Re: Math Revolution Approach (PS) [#permalink] New post   09 Feb 2017, 05:41
MathRevolution wrote:
If (n+2)!/n!=156, n=?
A. 2/131 B. 9 C. 10 D. 11 E. 12

==> From (n+2)!/n!=156 and (n+2)(n+1)n!/n!=(n+2)(n+1)=156=13*12, you get n+2=13, n=11.

Therefore, the answer is D

Adding to this since it's a quadratic we will get 2 solutions 11,-14 but since -14 is not an option so n=11 is correct.


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Re: Math Revolution Approach (PS) [#permalink] New post   12 Feb 2017, 18:25
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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. \(3\frac{π}{2}\)
D. \(2π\)
E. \(5\frac{π}{2}\)

==> The circumference of a circle is \(π\)d, thus \(π(11-10)= π\).

Therefore, the answer is B.
Answer: B
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Re: Math Revolution Approach (PS) [#permalink] New post   12 Feb 2017, 18:27
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What is the number of multiples of 25 between \(5^4\) and\(5^5\), inclusive?

A. 75
B. 96
C. 101
D. 121
E. 125

==> The number of multiples become (last-first/n)+1, then you get \(\frac{5^5-5^4}{25}+1=\frac{(5-1)5^4}{25}+1=4(5^2)+1=101\).

Therefore, the answer is C.
Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   15 Feb 2017, 01:08
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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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Re: Math Revolution Approach (PS) [#permalink] New post   18 Feb 2017, 08:04
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What is the range of 30 consecutive even numbers?

A. 54
B. 56
C. 58
D. 60
E. 62

==> The number of consecutive numbers become (last-first/2)+1=(range/2)+1. In other words, from (range/2)+1=30, you get range/2=29, range=2(29)=58.

The answer is C.
Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   18 Feb 2017, 08:08
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\(8^1^0-8^2\) is the approximation of which of the following?

A. \(8^7\)
B. \(8^8\)
C. \(8^9\)
D. \(8^1^0\)
E. \(8^1^1\)

==> You get \(8^1^0-8^2=(8^8-1)8^2≒(8^8)(8^2)=8^1^0\).

The answer is D.
Answer: D
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Re: Math Revolution Approach (PS) [#permalink] New post   19 Feb 2017, 18:45
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When \(f(x)=x^2(1-x)^2\), which of the following is equal to f(1-x)?

A. f(x)
B. f(x)/x
C. f(-x2)
D. f(x2)
E. f(1)

==> You get \(f(1-x)=(1-x)^2(1-(1-x))^2=(1-x)^2x^2=f(x)\).

Therefore, the answer is A.
Answer: A
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Re: Math Revolution Approach (PS) [#permalink] New post   19 Feb 2017, 18:47
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Which of the following equivalent to \((1/8)^4\)?

A. \((0.5)^5\)
B. \((0.25)^3\)
C. \((0.25)^6\)
D. \((0.4)^3\)
E. \((0.8)^2\)

==> You get \((1/8)^4=((1/2)^3)^4=(1/2)^1^2=((1/2)^2)^6=(1/4)^6=(0.25)^6\).

Therefore, the answer is C.
Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   23 Feb 2017, 01:10
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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: Math Revolution Approach (PS) [#permalink] New post   24 Feb 2017, 02:14
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10+8÷3×6-2=?

A. 24
B. 34
C. 22
D. 12
E. 11

==> When calculating the numbers, even if there are no brackets, multiplication and division come first.
You get 10+8÷3×6-2=10+(8/3)6-2=10+16-2=24.

The answer is A.
Answer: A
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Re: Math Revolution Approach (PS) [#permalink] New post   25 Feb 2017, 23:20
MathRevolution wrote:
In the x- y plane, there are 4 points (0,0), (0,4), (6,4), and (6,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 2/5

ANS: As you can see from the diagram below, the correct answer is 1/3. Hence, B is our answer choice.

Please describe how 1/3 is correct?
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Re: Math Revolution Approach (PS) [#permalink] New post   26 Feb 2017, 21:30
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Attachment:
1.png
1.png [ 2.59 KiB | Viewed 1451 times ]

There is a circle inscribed in a square, shown on the above figure. If the length of the square is 2, what is the area of one of the 4 regions shaded?

A. \(1-π\)
B. \(2-π\)
C. \(4-π\)
D. \(1-(\frac{π}{2})\)
E. \(1-(\frac{π}{4})\)

==> The area of the square-area of the \(circle=2^2- π=4- π\), and since it asks for one of the 4 regions shaded, you get \(\frac{4- π}{4}=1-(\frac{π}{4})\).

The answer is E.
Answer: E
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Re: Math Revolution Approach (PS) [#permalink] New post   26 Feb 2017, 21:34
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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

==>The sum of consecutive reciprocal number sequence is decided by the first number and the last number. Thus, from
10/20=1/11+1/12+.....+1/20<1/11+1/12+.....+1/20<1/11+1/12+.....+1/20=10/11, you get 1/2=10/20<1/11+1/12+.....+1/20<10/11<1, which becomes 1/2~1.

Therefore, the answer is E.
Answer: E
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Math Revolution Approach (PS) [#permalink] New post   Updated on: 26 Feb 2017, 22:23
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MathRevolution wrote:
In the x- y plane, there are 4 points (0,0), (0,4), (6,4), and (6,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 2/5

ANS: As you can see from the diagram below, the correct answer is 1/3. Hence, B is our answer choice.

Attachments

1.png
1.png [ 10.85 KiB | Viewed 1447 times ]


Originally posted by MathRevolution on 26 Feb 2017, 21:50.
Last edited by MathRevolution on 26 Feb 2017, 22:23, edited 2 times in total.
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Math Revolution Approach (PS) [#permalink] New post   26 Feb 2017, 21:55
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As you can see from the diagram above, the area of the red rectangle is 24 and the area of the triangle below green line is 8.
The ratio of the area of the triangle to that of the red rectangle is 1/3.
Hence, B is our answer choice.
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Math Revolution Approach (PS) [#permalink] New post   26 Feb 2017, 22:14
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awdxzs wrote:
MathRevolution wrote:
If (n+2)!/n!=156, n=?
A. 2/131 B. 9 C. 10 D. 11 E. 12

==> From (n+2)!/n!=156 and (n+2)(n+1)n!/n!=(n+2)(n+1)=156=13*12, you get n+2=13, n=11.

Therefore, the answer is D

Adding to this since it's a quadratic we will get 2 solutions 11,-14 but since -14 is not an option so n=11 is correct.


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Hello, goalMBA1990

The area of the red rectangle is 24 and the area of the triangle below green line is 8. The ratio of the area of the triangle to that of the red rectangle is 1/3.
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Re: Math Revolution Approach (PS) [#permalink] New post   26 Feb 2017, 22:22
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As you can see from the diagram above, the area of the red rectangle is 24 and the area of the triangle below the green line is 8.
The ratio of the triangle area to the red rectangle area is 8/24 or 1/3.
Hence, B is our answer choice.
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Re: Math Revolution Approach (PS) [#permalink] New post   26 Feb 2017, 22:25
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As you can see from the diagram below, the area of the red rectangle is 24 and the area of the triangle below green line is 8.
The ratio of the area of the triangle to that of the red rectangle is 1/3.
Hence, B is our answer choice.
Attachments

1.png
1.png [ 10.85 KiB | Viewed 1449 times ]

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Re: Math Revolution Approach (PS) [#permalink]
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