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Math Revolution GMAT Instructor
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Re: Math Revolution Approach (PS)
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07 Sep 2018, 01:20
[ Math Revolution GMAT math practice question] If r is a positive integer, n=r^3 and 4,14, and 27 are factors of n, which of the following must be a factor of n? A. 16 B. 32 C. 36 D. 48 E. 64 => Since 4 = 2^2,14 = 2*7, 27 = 3^3 are factors of n and n is a perfect cube, the smallest possible value of n is 2^3*3^3*7^3. When n = 2^3*3^3*7^3, 16 = 2^4, 32 = 2^5, 48=2^4*3 and 64 = 2^6 can’t be factors of n. The only answer choice that is a factor of n is 36 = 2^2*3^2. Therefore, the answer is C. Answer: C
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6227
GPA: 3.82

Re: Math Revolution Approach (PS)
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09 Sep 2018, 18:28
[ Math Revolution GMAT math practice question] What is the sum of roots of the equation x^2 – 40x + 399 = 0? A. 19 B. 20 C. 21 D. 40 E. 399 => Let p and q be the roots of the equation x^2 – 40x + 399 = 0. Then x^2 – 40x + 399 = (xp)(xq) = x^2 – (p+q)x + pq. Equating coefficients gives p + q = 40 from the coefficient of x. Therefore, the answer is D. Answer: D
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6227
GPA: 3.82

Re: Math Revolution Approach (PS)
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09 Sep 2018, 18:29
[ Math Revolution GMAT math practice question] If n is the greatest positive integer for which 5^n is a factor of 50!, what is the value of n? A. 10 B. 11 C. 12 D. 13 E. 14 => 50! = 1*2*…*5*…*10*…*15*…*20*…*25*…*30*…*35*…*40*…*45*…*50 =1*2*…*(5)…*(2*5)*…*(3*5)*…*(4*5)*…*(52)*…*(6*5)*…*(7*5)*…*(8*5)*…*(9*5)*…*(2*5^2) Since 5 is a prime number, no further factors of 5 appear in the prime factorization of 50!. The number of 5s in the above expansion of 50! is 12. Therefore, the answer is C. Answer: C
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6227
GPA: 3.82

Re: Math Revolution Approach (PS)
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12 Sep 2018, 02:43
[ Math Revolution GMAT math practice question] If 5^{m2}2^{m+2} is an ndigit integer, where m is an integer greater than 2, what is the value of n, in terms of m? A. n=m4 B. n=m2 C. n=m1 D. n=m E. n=2m => 5^{m2}2^{m+2} = 5^{m2}2^{m2+4} = 5^{m2}2^{m2}*2^4 = (5*2)^{m2}*2^4= (10)^{m2}*2^4 = 16*(10)^{m2} = 16*(100…0)= 1600…0 with m2 0’s. 10^{m2} has m2 digits that are 0 and 16*(10)^{m2} has digits including 1, 6 and m2 digits that are 0. Thus, 16*(10)^{m2} has m – 2 + m = m digits. Therefore, D is the answer. Answer: D
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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 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: 6227
GPA: 3.82

Re: Math Revolution Approach (PS)
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13 Sep 2018, 01:37
[ Math Revolution GMAT math practice question] What is the value of 22C 19? A. 770 B. 1540 C. 3080 D. 4620 E. 6160 => Since nCnr = nCr, 22C 19 = 22C 3 = (22*21*20)/(1*2*3) = 11*7*20 = 1540. Therefore, the answer is B. Answer: B
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Math Revolution GMAT Instructor
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Posts: 6227
GPA: 3.82

Re: Math Revolution Approach (PS)
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14 Sep 2018, 00:40
[ Math Revolution GMAT math practice question] If the interior angles of a triangle are in the ratio 3 to 4 to 5, what is the measure of the largest angle? A. 30 B. 45 C. 60 D. 75 E. 90 => Let x, y and z be interior angles of the triangle. Since x:y:z = 3:4:5, we can write x = 3k, y = 4k and z = 5k. Since the interior angles of the triangle add to 180, x + y + z = 3k + 4k + 5k = 12k = 180, and so k = 180/12 = 15. Therefore, the largest angle of the triangle is z = 5k = 5(15) = 75. Therefore, the answer is D. Answer: D
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6227
GPA: 3.82

Re: Math Revolution Approach (PS)
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16 Sep 2018, 18:33
[ Math Revolution GMAT math practice question] (1^2+2^2+3^3+…+20^2) / (1+2+3+ …+20)=? A. 41/3 B. 41/6 C. 41 D. 210 E. 420 => Now, 1^2 + 2^2 + 3^2 + … + n^2 = n(n+1)(2n+1)/6 and 1 + 2 + 3 + … + n = n(n+1)/2. So, (1^2+2^2+3^3+…+20^2) / (1+2+3+ …+20) = ( 20*21*41/6 ) / ( 20*21/2 ) = (41/6) / (1/2) = 41/3 Therefore, the answer is A. Answer: A
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Math Revolution GMAT Instructor
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Posts: 6227
GPA: 3.82

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16 Sep 2018, 18:35
[ Math Revolution GMAT math practice question] If 1/n(n+1) = 1/n – 1/(n+1), then what is the value of 1/(1*2) + 1/(2*3) + 1/(3*4) + … + 1/(99*100) A. 1/100 B. 1/50 C. 49/50 D. 99/100 E. 1/2 => 1/(1*2) + 1/(2*3) + 1/(3*4) + … + 1/(99*100) = (1/1 – 1/2) + (1/2 – 1/3) + (1/3 – 1/4) + … + (1/99 – 1/100) = 1/1 – 1/100 = 1 – 1/100 = 99/100 after cancellation of the inner terms. Therefore, the answer is D. Answer: D
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6227
GPA: 3.82

Re: Math Revolution Approach (PS)
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19 Sep 2018, 02:13
[ Math Revolution GMAT math practice question] x^4+12x^3+49x^2+78x+40 can be factored as a product of four linear polynomials with integer coefficients. Which of following cannot be a factor of x^4+12x^3+49x^2+78x+40? A. x+1 B. x+2 C. x+3 D. x+4 E. x+5 => Assume x^4+px^3+qx^2+rx+s = (x+a)(x+b)(x+c)(x+d). Then, s = abcd. The constant terms a, b, c and d of the linear factors are factors of the constant term s of the original polynomial. Since 3 is not a factor of 40, x + 3 cannot be a factor of the original polynomial x^4+12x^3+49x^2+78x+40. Therefore, C is the answer. Answer: C
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6227
GPA: 3.82

Re: Math Revolution Approach (PS)
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20 Sep 2018, 02:02
[ Math Revolution GMAT math practice question] Which of the following functions satisfies f(a+b)=f(a)f(b) for all positive numbers a, b ? A. f(x)=x+1 B. f(x)=x^2+1 C. f(x)=√x D. f(x)=1/x E. f(x)=2^x => A. f(1) = 2, f(2) = 3, f(1)f(2) = 6, but f(1+2) = f(3) = 4. Choice A is incorrect. B. f(2) = 5, f(3) = 10, f(2)f(3) = 50, but f(2+3) = f(5) = 26. Choice B is incorrect. C. f(9) = 3, f(16) = 4, f(9)f(16) = 12, but f(9+16) = f(25) = 5. Choice C is incorrect. D. f(1) = 1, f(2) = 1/2, f(1)f(2) = 1/2, but f(1+2) = f(3) = 1/3. Choice D is incorrect. E. Let a,b > 0. Then f(a+b) = 2^{a+b} = 2^a2^b = f(a)f(b). Choice E is correct. Therefore, the answer is E. Answer: E
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Re: Math Revolution Approach (PS)
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21 Sep 2018, 01:25
[ Math Revolution GMAT math practice question] √32+3√2+5+√3+1√2=? A. 0 B. 2√2 C. 2√3 D. 9 E. 11 => A=A when A>0, 0=0, and A=A when A<0 Since √32 < 0, we have √32 = (√32). Since 3√2 > 0, we have 3√2 = 3√2. Since 5+√3 > 0, we have 5+√3 = 5+√3 Since 1√2 < 0, we have 1√2 = (1√2) So, √32+3√2+5+√3+1√2= (√32) +(3√2) + (5+√3) (1√2) = √3+2 + 3√2 + 5+√3 – 1 +√2 = 9. Therefore, the answer is D. Answer: D
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