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# Math Revolution Approach (PS)

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6832
GMAT 1: 760 Q51 V42
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Re: Math Revolution Approach (PS)  [#permalink]

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14 Dec 2016, 00:30
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.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6832 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (PS) [#permalink] ### Show Tags 15 Dec 2016, 00:16 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6832
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GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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15 Dec 2016, 23:35
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.

_________________

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6832 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (PS) [#permalink] ### Show Tags 18 Dec 2016, 17:21 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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18 Dec 2016, 17:24
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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6832 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (PS) [#permalink] ### Show Tags 21 Dec 2016, 00:45 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6832
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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23 Dec 2016, 01:29
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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6832 GMAT 1: 760 Q51 V42 GPA: 3.82 Which of the following cannot be the factor of [#permalink] ### Show Tags 25 Dec 2016, 17:39 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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25 Dec 2016, 17:43
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%.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6832 GMAT 1: 760 Q51 V42 GPA: 3.82 Math Revolution Approach (PS) [#permalink] ### Show Tags 31 Dec 2016, 00:50 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6832
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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31 Dec 2016, 00:52
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%,

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6832 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (PS) [#permalink] ### Show Tags 31 Dec 2016, 00:55 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6832
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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01 Jan 2017, 17:36
[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.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6832 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (PS) [#permalink] ### Show Tags 01 Jan 2017, 22:57 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6832
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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04 Jan 2017, 17:57
Which of the following is equal to $$1/(√3−√2)^2$$?

A) 1

B) 5

C) √6

D) 5 - √6

E) 5 + 2√6

$$1/((√3−√2)^2)=1/(3+2−2√3 √2)=1/(5−2√6)*((5+2√6))/((5−2√6)(5+2√6))=((5+2√6))/(5^2−〖(2√(6))〗^2 )=((5+2√6))/(25−24)=5+√6$$

_________________

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 26 Oct 2016 Posts: 636 Location: United States Concentration: Marketing, International Business Schools: HBS '19 GMAT 1: 770 Q51 V44 GPA: 4 WE: Education (Education) Re: Math Revolution Approach (PS) [#permalink] ### Show Tags 04 Jan 2017, 18:09 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 _________________ Thanks & Regards, Anaira Mitch Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6832 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (PS) [#permalink] ### Show Tags 05 Jan 2017, 04:44 1 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: Math Revolution Approach (PS)  [#permalink]

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06 Jan 2017, 01:43
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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6832
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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08 Jan 2017, 17:11
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=$$1-(1-0.02)^6$$.

_________________

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6832 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (PS) [#permalink] ### Show Tags 08 Jan 2017, 17:12 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: Math Revolution Approach (PS) &nbs [#permalink] 08 Jan 2017, 17:12

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# Math Revolution Approach (PS)

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