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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 Mar 2017, 01:13
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If \(x^2=2x+1, x^3\)=？

A. 4x
B. 5x+2
C. 5x-1
D. 3x+2
E. 3x-2

==> \(x^3=x(x^2)=x(2x+1)=2x^2+x=2(2x+1)+x=5x+2\)

Answer: B
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Math Revolution Approach (PS) [#permalink] New post   03 Mar 2017, 04:19
MathRevolution wrote:
If \(x^2=2x+1, x^3\)=？

A. 4x
B. 5x+2
C. 5x-1
D. 3x+2
E. 3x-2

==> \(x^3=x(x^2)=x(2x+1)=2x^2+x=2(2x+1)+x=5x+2\)

Answer: B


How did you get this part?
2x2+x=2(2x+1)+x
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Re: Math Revolution Approach (PS) [#permalink] New post   07 Mar 2017, 04:39
chandanindira wrote:
MathRevolution wrote:
If \(x^2=2x+1, x^3\)=？

A. 4x
B. 5x+2
C. 5x-1
D. 3x+2
E. 3x-2

==> \(x^3=x(x^2)=x(2x+1)=2x^2+x=2(2x+1)+x=5x+2\)

Answer: B


How did you get this part?
2x2+x=2(2x+1)+x



Since x^2 = 2x+1 (given)

So, 2 . x^2 = 2 . (2x+1)
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Re: Math Revolution Approach (PS) [#permalink] New post   08 Mar 2017, 01:16
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\(Let A=6^2^0, B=2^6^0, and C=4^5^0.\)

Which of the following is true?

A. A<B<C
B. A<C<B
C. B<A<C
D. B<C<A
E. C<B<A

==> You can compare the big and small numbers by making the base or the exponent the same. From\(A=6^2^0, B=2^6^0=(2^3)^2^0=8^2^0\),
you get 6<8, which becomes A<B, and from \(B=2^6^0=(2^2)^3^0=4^3^0, C=4^5^0,\)
you get 30<50, which becomes B<C.

Thus, you get A<B<C. The answer is A.
Answer: A
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Re: Math Revolution Approach (PS) [#permalink] New post   09 Mar 2017, 02:41
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Which of the following is equal to
\(3^m7^{m-1}\)?


\(A. 3(21^m)\)
\(B. 7(21^m)\)
\(C. 3(21^{m-1})\)
\(D. 7(21^{m-1})\)
\(E. 21^{m-1}\)

==> From \(3^m7^m^-^1=3(3^m^-^1)(7^m^-^1)=3(3*7)^m^-^1=3(21^m^-^1)\), the answer is C.

Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   10 Mar 2017, 03:13
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\(\frac{5.09}{0.149}\) is closest to which of the following?

A. 0.34
B. 3.4
C. 34
D. 340
E. 3,400

From \(\frac{5.09}{0.149} = \frac{5.10}{0.15} = \frac{510}{15} =34\), the answer is C.

Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   12 Mar 2017, 18:47
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In the x-y plane, what is the slope between y-intercept and a negative x-intercept of \(y=x^2+x-6\)?

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

==> From y=x2+x-6=(x+3)(x-2)=0, the x-intercept becomes (-3,0) or (2,0), and (0,-6). From these, the negative x-intercept is (-3,0) and the negative y-intercept is (0,-6). The slope of the straight line that passes through the two points becomes \(\frac{0-(-6)}{-3-0=-2}\)

The answer is A.
Answer: A
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Math Revolution Approach (PS) [#permalink] New post   Updated on: 16 Mar 2017, 18:21
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If m and n are positive integers, what is the number of factors of \(3^m7^n\)?

A. mn+m+n
B. m-n+1
C. (m-1)(n-1)
D. (m+1)(n+1)
E. mn

==> The number of factors of \(3^m7^n\) becomes (m+1)(n+1).

The answer is D.
Answer:D

Originally posted by MathRevolution on 12 Mar 2017, 18:49.
Last edited by MathRevolution on 16 Mar 2017, 18:21, edited 1 time in total.
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Re: Math Revolution Approach (PS) [#permalink] New post   15 Mar 2017, 02:13
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Of the people who purchase a house, 60% considers the landscape and 80% considers the color of the house. If 10% of the people who purchase a house considers neither the landscape nor the color of the house, what percent is the people who consider both the landscape and the color of the house?

A. 40%
B. 45%
C. 50%
D. 55%
E. 60%

Attachment:
question.png
question.png [ 4.97 KiB | Viewed 2420 times ]


If you set the intersection as a%, you get the figure above. Then, from (60-a)+a+(80-a)=90, you get 140-a=90 and a=50.

Therefore, the answer is C.
Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   16 Mar 2017, 01:27
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If \(3^x=\frac{1}{27}\), then x=?

A. -3
B. -2
C. -1
D. 2
E. 3

==>From \(3^x=\frac{1}{27}=3^-^3\)

you get x=-3.

The answer is A.
Answer: A
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Re: Math Revolution Approach (PS) [#permalink] New post   19 Mar 2017, 18:02
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Which of the following is equal to (x+2)!/(x+1)!?

A. x-1
B. 1+(1/x)
C. 1
D. x+1
E. x+2

==> According to n!=n(n-1)!, you get (x+2)!/(x+1)!=(x+2)(x+1)!/(x+1)!=x+2.

Therefore, the answer is E.
Answer: E
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Re: Math Revolution Approach (PS) [#permalink] New post   19 Mar 2017, 18:07
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Attachment:
1.png
1.png [ 6.76 KiB | Viewed 2417 times ]

If DB=2, AC=12, and X is the center of the circle shown as the above figure, what is the area of the circle?

A. \(20π\)
B. \(80π\)
C. \(100π\)
D. \(120π\)
E. \(160π\)

Attachment:
23.png
23.png [ 5.03 KiB | Viewed 2408 times ]

You get the figure shown above, and according to the Pythagorean Theorem, you get \(r^2=(r-2)^2+6^2=r^2-4r+4+36\), and if you get rid of \(r^2\) on both sides and simplify the equation, from 4r=40, you get r=10. Thus, it becomes the area of the circle, which is \(π10^2=100π\).

The answer is C.
Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   20 Mar 2017, 03:42
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How many possible 6-digit code numbers can be formed from three a, two b, and one c?

A. 40
B. 50
C. 60
D. 70
E. 80

==> You get a,b,b, c,c,c, which is 6!/(2!)(3!)=60.

Therefore, the answer is C.
Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   22 Mar 2017, 02:49
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If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30, what is the smallest number of them?

A. 5
B. 10
C. 15
D. 20
E. 25

==> If the average of 5 consecutive multiples of 5 is 30, from 20,25,30,35,40, the smallest multiple of 5 becomes 20.

Therefore, the answer is D.
Answer: D
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Re: Math Revolution Approach (PS) [#permalink] New post   23 Mar 2017, 01:22
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What is the number of integers x such that \(4<x^2-4x+4<16\)?

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

==> Since \(x^2-4x+4=(x-2)^2\), from \(4<(x-2)^2<16\), you get -4<x-2<-2 or 2<x-2<4, and if you simplify it, from -2<x<0 or 4<x<6, you get x=integer=-1,5, and thus 2.

Therefore, the answer is B.
Answer: B
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Re: Math Revolution Approach (PS) [#permalink] New post   24 Mar 2017, 03:56
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If n is the product of 3 consecutive integers, which of the following must be true?

I. a multiple of 2 II. a multiple of 3 III. a multiple of 4

A. I only
B. II only
C. III only
D. I and II
E. II and III

==> If n is the product of 3 consecutive integers, it is always even and has 3, so it is always a multiple of 6. Thus, I and II is correct and for III, since n=1*2*3=6 is not a multiple of 4, hence it is incorrect.

The answer is D.
Answer: D
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Re: Math Revolution Approach (PS) [#permalink] New post   26 Mar 2017, 18:32
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If Tom goes y miles in x hours, how many miles does he go per minute, in terms of x and y?

A. 60x/y
B. y/60x
C. 60y/x
D. x/60y
E. 60xy

==>You get miles:hours=y(miles):x(hours)=y(miles):60x(minutes), and from y:60x=some:1, you get some=y/60x.

The answer is B.
Answer: B
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Re: Math Revolution Approach (PS) [#permalink] New post   29 Mar 2017, 02:01
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If two times x is 5 greater than three times y, what is the value of y, in terms of x?

A. y=2x-5
B. y=6x-5
C. y=(x/2)-5
D. y=(x/3)-5
E. y=(2x-5)/3

==> According to the Ivy Approach, you get is:”=” and greater than:”+”, so you get 2x=5+3y. From 3y=2x-5, y=(2x-5)/3, the answer is E.

Answer: E
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Re: Math Revolution Approach (PS) [#permalink] New post   30 Mar 2017, 02:19
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If the sum of the annual salaries of n persons is $x and the monthly salary per person is $y, what is the value of n in terms of x and y?

A. $x/12y
B. $12x/y
C. $12xy
D. $12y/x
E. $xy/12

==> Since the monthly salary per person is $y, the annual salary per person becomes $12y and the total sum of the annual salaries of n number of people becomes $12ny. Since it is $x, from $12ny=$x, you get n=x/12y.

The answer is A.
Answer: B
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Re: Math Revolution Approach (PS) [#permalink] New post   31 Mar 2017, 01:35
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√3 is what percent of √12?

A. 20%
B. 25%
C. 30%
D. 46%
E. 50%

==> According to the ivy approach, you get is:”=”, what: “some”, and percent:”1/100”. Also, you substitute √12=2√3, and from √3=some(1/100)2√3, if you get rid of √3 on both sides, you get 1=(some)2/100, some=50.

The answer is E.
Answer: E
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