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Math Revolution Approach (PS)

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Re: Math Revolution Approach (PS) [#permalink] New post   30 Apr 2017, 18:13
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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 only
E. II and III only

==> From n=m(m+1)(m+2) , where m=integer, the product of 3 consecutive integers is always a multiple of 6. Thus, I and II is always true. For III, if m=1, from n=(1)(2)(3)=6, it is not a multiple of 4, hence it is false.

Therefore, the answer is D.
Answer: D
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Re: Math Revolution Approach (PS) [#permalink] New post   04 May 2017, 01:23
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Attachment:
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5.1.png [ 3.5 KiB | Viewed 1437 times ]


The table shown above represents the relationship of the working hours and the number of 20 employees who participate in the project. What is the median working hour of the 20 employees?

A. 9.5
B. 10.0
C. 10.5
D. 11.0
E. 11.5

==> The median working hour of 20 employees is the average of 10th and 11th working hours. In other words, median working hour=(10+11)/2=10.5.

The answer is C.
Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   04 May 2017, 01:24
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If two circles have the same center and the larger circle’s area is \(16π\), what is the smaller circle’s area?

A. \(π\)
B. \(4π\)
C. \(9π\)
D. \(12π\)
E. \(16π\)


==> The area of the larger circle=\(16π=πr^2\), so r=4. Since width=1, you get 4-1=3, and the area of the smaller circle=\(3^{2π}=9π\).

The answer is C.
Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   05 May 2017, 01:51
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If x+y=3 and \(x^2+y^2=7\), then xy=?

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

==> You get \((x+y)^2=x^2+y^2+2xy\), and if you substitute this, from \(3^2=7+2xy\), you get 2xy=2, and xy=1.

Therefore, the answer is D.
Answer: D
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Re: Math Revolution Approach (PS) [#permalink] New post   07 May 2017, 18:02
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\((\frac{1}{7})+(\frac{1}{8})+(\frac{1}{9})\) is in between?

A. \((\frac{1}{6}) and (\frac{1}{5})\)
B. \((\frac{1}{5}) and (\frac{1}{4})\)
C. \((\frac{1}{4}) and (\frac{1}{3})\)
D. \((\frac{1}{3}) and (\frac{1}{2})\)
E. \((\frac{1}{2}) and 1\)

==>The sum of consecutive reciprocal numbers is decided by the first and the last number. In other words, you get
(1/9)+(1/9)+(1/9)< (1/7)+(1/8)+(1/9)< (1/7)+(1/7)+(1/7), and if you reorganize this, from
=1/3=3/9=(1/9)+(1/9)+(1/9)<(1/7)+(1/8)+(1/9)<(1/7)+(1/7)+(1/7)=3/7<3/6=1/2, you get between (1/3) and (1/2).

The answer is D.
Answer: D
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Re: Math Revolution Approach (PS) [#permalink] New post   07 May 2017, 18:03
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In the xy-plane, a triangle T is formed by x-axis, y-axis, and the line with equation y=4x+k. If the area of the triangle T is smaller than 2, what is the range of k?

A. k<-4, 4<k
B. -4<k<4
C. k<-3, 5<k
D. -3<k<5
E. k<-2, 8<k

==>Since y=4x+k passes through (0,k) and (-k/4,0), from the area of the triangle=(1/2)k(k/4)<2, you get k2<16, k2-16<0, (k-4)(k+4)<0, -4<k<4.

The answer is B.
Answer: B
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Re: Math Revolution Approach (PS) [#permalink] New post   10 May 2017, 01:31
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If a prime number m can be expressed as \(2^n-1\), where n is a positive integer, which of the following can be the value of m?

A. 11
B. 15
C. 31
D. 63
E. 97

==> If n=5, you get \(2^5-1=31\). The answer is C.

Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   11 May 2017, 01:25
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A store currently charges the same price per pound of salad. If the current price per pound were to be increased by $0.2, 0.5 pound smaller salad could be bought for $9. What is the current price of salad per pound?

A. $1.6
B. $1.7
C. $1.72
D. $1.8
E. $1.84

==> If you set the price of the salad per pound as $p, for n pounds, you get np=(n-0.5)(p+0.2)=9. From np=np+0.2n-0.5p-0.1, if you substitute 0.2n=0.5p+0.1, and n=2.5p+0.5, you get p=1.8.

The answer is D.
Answer: D
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Re: Math Revolution Approach (PS) [#permalink] New post   12 May 2017, 01:43
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If \(x^2=√3\), then \(x^8\)=?

A. 2
B. \(2√3\)
C. 4
D. \(3√3\)
E. 9

==> From \(x^8=(x^2)^4=(√3)^4=9\), the answer is E.

Answer: E
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Re: Math Revolution Approach (PS) [#permalink] New post   14 May 2017, 18:33
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For a positive integer n, when 12n is divided by 15, which of the following cannot be the remainder?

A. 0
B. 3
C. 5
D. 6
E. 9

==>From 12n=15Q+r, 12 and 15 are the multiples of 3, so remainder=r must also be the multiple of 3. Therefore, 5 cannot be the remainder.

The answer is C.
Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   14 May 2017, 18:34
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G(x) is the greatest integer less than or equal to x and L(x) is the least integer greater than or equal to x. When x is not an integer, which of the following is the value of L(x)-G(x)?

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

==> You get G(x)=round down and L(X)=round up. Then, x≠integer, so if you substitute x=1.2, you get L(1.2)-G(1.2)=2-1=1.

The answer is D.
Answer: D
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Re: Math Revolution Approach (PS) [#permalink] New post   17 May 2017, 01:33
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If \(y≠0\) and \(\frac{x}{y}=3\), then \(\frac{(x-y)}{x}\)=?

A. \(-2\)
B. \(-1\)
C. \(\frac{-2}{3}\)
D. \(\frac{2}{3}\)
E. \(1\)

==> You get \(\frac{x}{y}=3\), \(x=3y\), then \(\frac{(x-y)}{x}=\frac{(3y-y)}{3y}=\frac{2y}{3y}=\frac{2}{3}\).

The answer is D.
Answer: D
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Re: Math Revolution Approach (PS) [#permalink] New post   18 May 2017, 01:08
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If two integers x and y such x>y are selected at random between -8 and 11, inclusive, how many cases are possible?

A. 150
B. 180
C. 190
D. 210
E. 240

==> Since two integers from -8 to 11 are being randomly selected and x>y, you use combination. Thus, the number of integers from -8 to 11 becomes 11-(-8)+1=20, so 20, then 20C2=(20)(19)/2!=190.

The answer is C.
Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   19 May 2017, 01:53
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What is the difference between the average (arithmetic mean) and the median of 40, 41, 42, 43, 44, 45, and 46?

A. 0
B. 1
C. 1.5
D. 2
E. 2.5

==> For consecutive integers, the median and the average is equal. Thus, the difference is always 0.

The answer is A.
Answer: A
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Re: Math Revolution Approach (PS) [#permalink] New post   21 May 2017, 18:00
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Which of the following points reflect to y=-x at (-3,2)?

A. (-2, 3)
B. (2,-3)
C. (3,2)
D. (3,-2)
E. (2,3)

==> In order to become symmetrical to y=-x, you need to substitute –y value on x coordinate, and –x value on y coordinate. Thus, you get (-3,2)-->(-2,3).

The answer is A.
Answer: A
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Re: Math Revolution Approach (PS) [#permalink] New post   21 May 2017, 18:01
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5 people including A and B line up in a row. How many possible cases are there such that at least one person stands between A and B?

A. 24
B. 36
C. 48
D. 60
E. 72

==> Since it is the number of cases such that at least one person stands between A and B when 5 people are lined up in a row, you need to subtract the number of cases where A and B stands next to each other from the total number of cases. Then, you get ABCDE-(AB)CDE, which becomes 5!-4!(2)=72. You get 4!(2) because there are cases where A and B switch the order in the line.

Therefore, the answer is E.
Answer: E
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Re: Math Revolution Approach (PS) [#permalink] New post   24 May 2017, 00:35
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[p] is the greatest integer less than or equal p. What is the value of [π-1]?

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

==>You get π-1=3.14-1=2.14, and thus [π-1]=[2.14]=2. The answer is A.
Answer: A
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Re: Math Revolution Approach (PS) [#permalink] New post   25 May 2017, 01:30
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Which of the following is equal to n!*(n+1)!?

A. (n!)^2
B. (n+1)!^2
C. n!^3(n+1)!^2
D. n!^3(n+1)
E. n!^2(n+1)

==> You get n!*(n+1)!=n!*(n+1)n!=(n!)^2(n+1). The answer is E.

Answer: E
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Re: Math Revolution Approach (PS) [#permalink] New post   25 May 2017, 17:41
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There are 6 red balls and 4 blue balls in a jar. If 2 balls are selected from the jar, what is the probability that 2 balls selected are red balls?

A. 1/10
B. 1/9
C. 3/10
D. 3/15
E. 2/15

==> You get 4C2/10C2==2/15. The answer is E.

Answer: E
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Re: Math Revolution Approach (PS) [#permalink] New post   29 May 2017, 00:02
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If a and b are different integers, which of the following cannot be the value of a^2+b^2?

A. 17
B. 25
C. 58
D. 77
E. 85

==> A. 17=4^2+1^2 (o)
B. 25=3^3+4^2 (o)
C. 58=7^2+3^2 (o)
D. 77=8^2+13 (x)
E. 85=9^2+2^2 (o)

As shown above, the answer is D.
Answer: D
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