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Math Revolution Approach (PS)

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New post 25 Jun 2017, 18:16
If n is the least common multiple of 18 and 60, which of the following can be the factor of n?

I. 24 II. 36 III. 45

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

==> You get 18=2(3^2) 60=(2^2)(3)(5), and since the least common multiple is the maximum value of the index, and you get n=(22)(32)(5).

Therefore, you get
I. 24=(2^3)(3) (X)
II. 36=(2^2)(3^2) (O)
III. 45=(3^2)(5) (O)

The answer is Ⅱ&Ⅲ, which is E.
Answer: E
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New post 25 Jun 2017, 18:20
(11+1/11)^2-(11-1/11)^2=?

A. 2
B. 3
C. 4
D. 5
E. 9


==> You get (11+1/11)^2-(11-1/11)^2=[(11+1/11)-(11-1/11)][(11+1/11)+(11-1/11)]= 2/11(22)=4.

The answer is C.
Answer: C
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New post 28 Jun 2017, 01:10
If p is the sum of all odd numbers greater than 0 but less than 50, and q is the sum of all even numbers greater than 0 but less than 50, what is the value of p-q?

A. -24
B. 0
C. 1
D. 24
E. 25

==> Since p=1+3+….+47+49, from q=2+4+…+46+48, the difference between 3+5+…+47+49 (part of p) and q=2+4+..+46+48 is 1 each, so there are 24. Since there is also +1 at the front of p, you get 24+1=25.

The answer is E.
Answer: E
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New post 29 Jun 2017, 03:00
If set A={a,b,c,d,e}, what is the number of subsets that must include only 3 elements?

A. 8
B. 10
C. 12
D. 15
E. 18

==> You get 5C3=5C2=(5)(4)/2!=10.

The answer is b.
Answer: B
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New post 30 Jun 2017, 01:03
When 2 dices are tossed, what is the probability that the 2 faced numbers have a difference of 3?

A.1/9
B. 2/9
C. 1/3
D. 4/9
E. 1/6

==> Numerator:(6,3), (5,2), (4,1), (3,6), (2,5), (1,4). Denominator:6*6. Thus, you get 6/6*6=1/6.

The answer is E.
Answer: E
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New post 02 Jul 2017, 18:12
If f(2x+3)=-6x, f(5)=?

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

==> From2x+3=5, you get x=1, and then you get f(5)=-6(1)=-6.

The answer is A.
Answer: A
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New post 02 Jul 2017, 18:14
If x=2y=4z for positive integers x, y, and z, which of the following can be the average (arithmetic mean) of x, y and 3z?

A. 15
B. 20
C. 25
D. 40
E. 47

==> You get x=4z and y=2z, and the average=(x+y+3z)/3=(4z+2z+3z)/3=3z, so it always needs to be the multiple of 3.

Therefore, the answer is A.
Answer: A
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New post 05 Jul 2017, 01:04
If $10,000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 5 year, in terms of dollars?

A. 10,000(1+ )^10
B. 10,000(1+0.08)^5
C. 10,000(1+0.08)
D. 10,000(1-0.08)^2
E. 10,000*1.08

==> if it is invested at 8 percent annual interest and is compounded semiannually, From
10,000(1+8%(1/2))^2*5= 10,000(1+)^10 the answer is A

Answer: A
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New post 06 Jul 2017, 01:25
3^11+3^12+3^13=?

A. 13(3^11)
B. 17(3^11)
C. 19(3^11)
D. 13(3^10)
E. 3^36

==> 3^11+3^12+3^13=(1+3+3^2)3^11=13(3^11)
Answer: A
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New post 07 Jul 2017, 01:10
3 robots can finish the same task in 6hrs, 7hrs, and 8hrs.What is the greatest part of the task that can be finished by two of these robots together in 1 hour?

A. 13/42
B. 11/42
C. 42/13
D. 42/11
E. 13/21

==> Assuming that A, B, and C finishes their tasks in 6hrs, 7hrs, and 8 hrs each, the work rate of A and B are good, and each finished 1/6 and 1/7,
so you get 1/6+1/7=13/42.

The answer is A.
Answer: A
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New post 09 Jul 2017, 18:27
√m^4=64 and m>0, what is the value of cubic root of m?

A. 1
B. 2
C. 4
D. 8
E. 16

==> You get √m^4=64=2^6, m^4=(2^6)^2=2^12. Then, you get m=(2^12)^1/4=2^3, and from 3√m=3√2^3=2, the answer is B.

Answer: B
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New post 09 Jul 2017, 18:31
What is the units digit of 248^20?

A. 0
B. 2
C. 4
D. 6
E. 8

==>You get ~8^1=~8, ~8^2=~4, ~8^3=~2, ~8^4=~6, so the units digit becomes 8-->4-->2-->6-->8, and the index has a period of 4.
Thus, you get 248^20=(248^4)^5=(~6)^5=~6.

The answer is D.
Answer: D
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New post 12 Jul 2017, 01:14
If 10!/(10-r)!<1,000, what is the greatest possible value of r?

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

==>If you substitute r=1, 2, 3, 4.., for r=4, you get 10!/(10-4)!=10*9*8*7=5,040>1,000, and for r=3, you get 10!/(10-3)!=10*9*8=720<1,00.

Thus, the greatest possible value of r is r=3. The answer is C.
Answer: C
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New post 13 Jul 2017, 02:07
Attachment:
7.11.png
7.11.png [ 4.08 KiB | Viewed 545 times ]


A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through the center of the larger circle, what is the ratio of the area of the region shaded to the area of the larger circle?

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

==> Square of the ratio of the length=ratio of the area. The diameter of the smaller circle is equal to the radius of the larger circle, so the ratio of the length becomes 1:2. Then, the ratio of the area becomes 1^2:2^2=1:4. Thus, if the area of the smaller circle=k, the area of the larger circle=4k. Therefore, the area of the region shaded:the area of the larger circle=(4k-k):4k=3:4=¾.

The answer is C.
Answer: C
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New post 14 Jul 2017, 01:06
If x-2=√x+√2 , x=?

A. 3+2√2
B. 3-2√2
C. 3+√2
D. 3-√2
E. 2+2√3

==> You get x-2=√x+√2 , (√x-√2)(√x+√2)= √x+√2. If you divide √x+√2 on both sides, you get √x-√2=1, then √x=√2+1. Then, if you square both sides, you get x=(√2+1)^2=2+1+2√2 =3+2√2.

The answer is A.
Answer: A
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New post 16 Jul 2017, 18:46
An alarm of a certain clock rings every 15 minutes. If the clock’s alarm rings first at 12:00, when will the 15th alarm ring?

A. 14:30
B. 14:00
C. 14:30
D. 15:00
E. 15:30

==> Since the alarm rings every 15 minutes, it rings 4 times in an hour. Thus, the 15th alarm rings after 3 hours plus 3 times. Since 13th alarm is at 15:00, 15th alarm rings at 15:30.

Therefore, the answer is E.
Answer: E
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New post 16 Jul 2017, 18:48
If x>0, y<0, and a>b>0, then which of the following is (are) positive?
Ⅰ. ax+by Ⅱ. ax-by Ⅲ. by-ax

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


==> You getⅠ. ax+by a=2, b=x=1, y=-10, which is negative. (X)
From Ⅱ. ax-by by<0, you get –by>0 and ax>0, ax-by>0, hence it is always positive. (O)
From Ⅲ. by-ax a=2, b=1, x=1, y=-10, it is negative. (X)

Therefore, the answer is B.
Answer: B
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New post 19 Jul 2017, 02:01
For a positive integer x, the units digits of (x+2)^2 and (x+6)^2 are 9. What is the units digit of (x+3)^2?

A. 0
B. 2
C. 4
D. 6
E. 8

==>It needs to satisfy x=~1. Thus, you get ~3^2=~9 and ~7^2=~9. If you substitute X=~1, you get (x+3)^2=~4^2=~6.

The answer is D.
Answer: D
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New post 20 Jul 2017, 01:07
If the sum of all the even numbers from 1 to n(n: odd number) is 69*70, what is the value of n?

A. 135
B. 137
C. 139
D. 141
E. 143

==> If n=2m+1, the even numbers until 2m+1 becomes until 2m, and the sum of the even numbers is 2+4+…+2m=2(1+2+…m)=2m(m+1)/2=m(m+1). From m(m+1)=69*70, you get m=69, which becomes 2m+1=2(69)+1=139.

The answer is C.
Answer: C
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New post 21 Jul 2017, 01:07
When 8^101-8 is divided by 10, what is the remainder?

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

==> You get 8^101-8=8(8^100-1), and the units digit of ~8 becomes ~8^1=~8, ~8^2=~4, ~8^3=~2, ~8^4=~6. You get 8(8^100-1)=8{(8^4)^25-1}=8{(~6^25)-1}=8(~6-1)=8(~5)=~0, and the answer is A.

Answer: A
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Re: Math Revolution Approach (PS) &nbs [#permalink] 21 Jul 2017, 01:07

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