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Math Revolution Approach (PS)

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Re: Math Revolution Approach (PS) [#permalink] New post   14 Dec 2016, 01:30
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Which of the following is the approximation of \((4^4+8^6)/(4^8+16^8\))?

A. \(2^-^1^2\)
B. \(2^-^1^4\)
C. \(2^-^1^6\)
D. \(2^1^2\)
E. \(2^1^4\)

==> Because of the word “approximation”, you get \((4^4+8^6)/(4^8+16^8)= 8^6/16^8\).
Also, from \(8^6/16^8 =(2^3)^6/(2^4)^8=2^1^8/2^3^2=2^1^8^-^3^2=2^-^1^4\), the answer is B.

Answer: B
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Re: Math Revolution Approach (PS) [#permalink] New post   15 Dec 2016, 01:16
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In the x-y coordinate plane, the distance between (m, n) and (3, 4) is\(√26\). If m and n are integers, how many possible cases are there?
A. 5 B. 6 C. 7 D. 8 E. 9

==> From \((m-3)^2+(n-4)^2\)=(√26)2, you get (m-3, n-4)=(±1, ±5) or (±5, ±1), so there are total of 8 numbers. Therefore, the answer is D.

Answer: D
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Re: Math Revolution Approach (PS) [#permalink] New post   16 Dec 2016, 00:35
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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
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Re: Math Revolution Approach (PS) [#permalink] New post   18 Dec 2016, 18:21
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If n is an integer, which of the following must be an even number?

I. \(n^2+n\) II. \(n^2-n\) III. 2n

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

==> The multiple of two consecutive integers always becomes an even number that is a multiple of 2, because the multiple two consecutive integers always contain 2. Thus, I and II are the answers, and for III, 2n=even is always established, so it is also the answer.

Therefore, the answer is E.
Answer: E
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Re: Math Revolution Approach (PS) [#permalink] New post   18 Dec 2016, 18:24
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If 3 juniors from 8 juniors are selected at random to make a committee, how many cases are possible?
A. 8 B. 28 C. 35 D. 42 E. 56

==> From 8C3=(8)(7)(6)/3!=56, the answer is E. In general, if words such as “select”, “committee”, or “game” appear, use combination.
Answer: B
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Re: Math Revolution Approach (PS) [#permalink] New post   21 Dec 2016, 01:45
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A number of tournament games is represented as G(n) where n is the number of attendees and 2 attendees play a game such that G(n+1)=G(n)+n, G(2)=1. If the number of attendees is 10, what is the total number of games?
A. 20 B. 25 C. 30 D. 40 E. 45

==> For games, solve by use combination. It is usually less than 2 people, so you get 10C2=(10)(9)/2!=45.

The answer is E.
Answer: E
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Re: Math Revolution Approach (PS) [#permalink] New post   23 Dec 2016, 02:29
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For all positive integers m and n, the expression m △ n represents the remainder when m+n is divided by m-n. What is the value of
((19△9)△2) - (19△(9△2)) ?

(A) -8

(B) -6

(C) -4

(D) 4

(E) 6

Since m△n represents the remainder of m+n divided by m-n,
19△9 represents the remainder of (19+9) divided by (19-9), which is the remainder of 28 divided by 10. Then, from 28=10(2)+8, the remainder becomes 8, and thus 19△9=8.
8△2 represents the remainder of (8+2) divided by (8-2), which is the remainder of 10 divided by 6. Then, from 10=6(1)+4, the remainder becomes 4, and thus 8△2=4.
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Which of the following cannot be the factor of [#permalink] New post   25 Dec 2016, 18:39
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Which of the following cannot be the factor of \(x^4 + 10x^3 + 35x^2 + 50x + 24\)?

 
(A) x+1

(B) x+2

(C) x+3

(D) x+4

(E) x+5

In order to factorize \(x^4 + 10x^3 + 35x2 + 50x + 24\), you should do as shown below.
From \(x^4 + 10x^3 + 35x^2 + 50x + 24=(x+a)(x+b)(x+c)(x+d)\), if you expand this, you get \(x^4 + 10x^3 + 35x^2 + 50x + 24=x^4+………….+abcd\), which makes 24=abcd. In other words, a=1, b=2, c=3, d=4 all become factors of 24, but from x+5, 5 cannot be the factor of 24, and so you cannot factorize it.

Therefore, the answer is E.
Answer: E
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Math Revolution Approach (PS) [#permalink] New post   25 Dec 2016, 18:43
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John is collecting coins. If the amount he collected last year was 80% of the amount he collected this year, what is the percent increase of the coins that he collected from last year to this year?
 
(A) 10%

(B) 15%

(C) 20%

(D) 25%

(E) 33%

You get percent increase = (after−before)/before(100). If you assume the total number of coins collected this year as 100c, the number of coins collected from last year becomes 100c(80%)=80c. In other words, if 80c -> 100c,
Percent increase = (100c−80c)/80c(100) = 20c/80c(100)=25, so you get 25%.

Therefore, the answer is D.
Answer: D
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Math Revolution Approach (PS) [#permalink] New post   31 Dec 2016, 01:50
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If (3-√10)x=-1, x=?
A. 3-√10 B. 3-2√5 C. 3+√10 D. 3-√5 E. 3+√5

==> (3-√10)x=-1, (√10-3)x=1, x=1/(√10-3) = (√10+3)/(√10-3)(√10+3)
= (√10+3)/(10-9)= √10+3

Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   31 Dec 2016, 01:52
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In a certain class, 70% of the students learn Physics and 65% of the students learn Chemistry. What is the smallest percentage of those who learn both French and Spanish?
A. 25% B. 30% C. 35% D. 40% E. 45%


==> You get 70%+65%=135% and 135%-100%=35%,

so the answer is C.
Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   31 Dec 2016, 01:55
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If a sequence Sn, where n is a positive integer, has a property that Sn+1=1/Sn and S1=3, what is the value of S1002?

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

==> S2=1/S1=1/3, S3=1/S2=3,….. therefore Sodd=3 and Seven=1/3, S1002=1/3

Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   01 Jan 2017, 18:36
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[x] is the greatest integer less than or equal to x. If [x]=3, then [x/4]=?

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

==> You get [x]=round down. In other words, you get [1.1]=1. Then, from [x]=3, you get 3≤x<4, and if you divide it by 4, you get 3/4≤x<1, which becomes [3/4≤x<1]=0.

Therefore, the answer is C.
Answer: C
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Re: Math Revolution Approach (PS) [#permalink] New post   01 Jan 2017, 23:57
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If the units digits of \(n^3^9\) is 3, which of the following can be the value of the positive integer n?
A. 21 B. 23 C. 25 D. 67 E. 59

==> Generally, the units digits have a period of 4 square. Then, you get \(~7^1=~7, ~7^2=~9, ~7^3=~3, and ~7^4=~1\), which becomes \(n^3^9=n^4^(^9^)^+^3=n^3\), so the correct answer is the one that has units digit as 7.

The answer is D.
Answer: D
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Re: Math Revolution Approach (PS) [#permalink] New post   04 Jan 2017, 18:57
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Which of the following is equal to \(1/(√3−√2)^2\)?

A) 1

B) 5

C) √6

D) 5 - √6

E) 5 + 2√6

\(1/((√3−√2)^2)=1/(3+2−2√3 √2)=1/(5−2√6)*((5+2√6))/((5−2√6)(5+2√6))=((5+2√6))/(5^2−〖(2√(6))〗^2 )=((5+2√6))/(25−24)=5+√6\)
The answer is E.

Answer: E
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Re: Math Revolution Approach (PS) [#permalink] New post   04 Jan 2017, 19:09
Hello,

Is it possible to apply variable approach on below problem?

Eight women of eight different heights are to pose for a photo in two rows of four. Each woman in the second
row must stand directly behind a shorter woman in the first row. In addition, all of the women in each row
must be arranged in order of increasing height from left to right. Assuming that these restrictions are fully
adhered to, in how many different ways can the women pose?
(A) 2 (B) 14 (C) 15 (D) 16 (E) 18
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Re: Math Revolution Approach (PS) [#permalink] New post   05 Jan 2017, 05:44
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The function f is defined by \(f(x) = - k/x^2\) for all nonzero numbers x (k is constant). If f(2) = 1/4, then f(1/2) =?


A) 4

B) 1/4

C) - 1/4

D) -4

E) -2

=>If f(x)=-k/x2, f(2)=-k/22=-k/4=1/4, then k=-1. If so, f(x)=-(-1)/x2=1/x2, then f(1/2)=1/(1/2)2=4
The answer is A.

Answer: A
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Re: Math Revolution Approach (PS) [#permalink] New post   06 Jan 2017, 02:43
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John invests $10,000 at the monthly constant compounded rate of annually 11 percent. After t years, what is the amount including interest?

A. \($10,000(1+0.11/12)^t\)
B. \($10,000(1+0.11/12)^1^2^t\)
C. \($10,000(1+0.11)^1^2^t\)
D. \($10,000(1+0.11)^t\)
E. \($10,000(0.11/12)^1^2^t\)

==> \($10,000(1+0.11/12)^1^2^t\) becomes the answer, because 11% of yearly compound interest rate is divided by month, and the amount including the interest in t years.

Hence, the answer is B.
Answer: B
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Re: Math Revolution Approach (PS) [#permalink] New post   08 Jan 2017, 18:11
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In a certain factory, the production line which produces the bags has the probability that a bag selected at random is defective is 0.02. If 6 bags are selected at random, what is the probability that at least one bag is defective?

A. \(0.02^6\)

B. \((0.02)(0.98)^6\)

C. \(1-(0.02)^6\)

D. \(0.98^6\)

E. \(1-(0.98)^6\)

==> probability that at least one bag is defective=1-probability that all bags are not defective=\(1-(1-0.02)^6\).

Hence, the answer is E.
Answer: E
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Re: Math Revolution Approach (PS) [#permalink] New post   08 Jan 2017, 18:12
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Which of the following points is reflect to y=-x at (-2,1)?
A. (-1, 2) B. (1,-2) C. (2,1) D. (2,-1) E. (1,2)

==> You can figure out a point reflecting to y=-x by substituting –y to x-coordinate and –x to y-coordinate. Then, (-2,1) --> (-1, -(-2))=(-1,2) is derived.

Hence, the answer is A.
Answer: A
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