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Math Revolution GMAT Instructor
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GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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27 Jan 2019, 17:31
[ Math Revolution GMAT math practice question] If y=x1+x+1, then y=? 1) x>1 2) x<1 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. There are three ranges of values of x to consider. If x > 1, then y =  x – 1  +  x + 1  = x – 1 + x + 1 = 2x and we don’t have a unique value of y. If 1 ≤ x ≤ 1, then y =  x – 1  +  x + 1  =  ( x – 1 ) + x + 1 = 2 and we have a unique value of y. If x < 1, then y =  x – 1  +  x + 1  = ( x – 1 ) – ( x + 1 ) = 2x and we don’t have a unique value of y. Asking for the value of y is equivalent asking if 1 ≤ x ≤ 1. Both conditions yield the inequality 1 < x < 1, when applied together. Therefore, both conditions are sufficient, when taken together. In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient. Therefore, C is the answer. Answer: C
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 9022
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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29 Jan 2019, 20:44
[ Math Revolution GMAT math practice question] m+n=? 1) (4^m)(2^n)=16 2) (2^{2m})(4^n)=64 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Condition 2) is equivalent to m + n = 3 as shown below: (2^{2m})(4^n)=64 => (2^{2m})(2^{2n})=2^6 => 2^{2m+2n}=2^6 => 2m+2n = 6 => m + n = 3 Condition 2) is sufficient. Condition 1) (4^m)(2^n)=16 => (2^{2m})(2^n)=2^4 => 2^{2m+n}=2^4 => 2m+n = 4 If m = 1 and n =2, then m + n = 3. If m = 0 and n = 4, then m + n = 4. Since it does not yield a unique solution, condition 1) is not sufficient. Therefore, the answer is B. Answer: B
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Math Revolution GMAT Instructor
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GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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31 Jan 2019, 16:31
[ Math Revolution GMAT math practice question] What is the measure of each interior angle of a regular decagon? A. 72° B. 108° C. 120° D. 135° E. 144° => The sum of all interior angles of ngon is (n2)*180°. A decagon is a 10gon. The sum of all interior angles is (102)* 180° = 8*180°. And each interior angle of a regular decagon has measure 8*180° / 10 = 8*18° = 144°. Therefore, the answer is E. Answer: E
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Math Revolution GMAT Instructor
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GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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04 Feb 2019, 20:14
[GMAT math practice question] If operation # represents one of addition, subtraction, multiplication, and division, what is the value of 0#1? 1) 2#1 = 2 2) 4#2 = 2 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The operation is considered as a variable. Since we have 1 variable and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first. Condition 1) Since 2#1 = 2, # is one of the operations, multiplication and division. If # is the multiplication operation, then 0#1 = 0. If # is the division operation, then 0#1 = 0. Since condition 1) yields a unique solution, it is sufficient. Condition 2) Since 4#2 = 2, # is one of the operations, subtraction and division. If # is the subtraction operation, then 0#1 = 1. If # is the division operation, then 0#1 = 0. Since condition 2) doesn’t yield a unique solution, it is not sufficient. Therefore, A is the answer. Answer: A
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Math Revolution GMAT Instructor
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GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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07 Feb 2019, 17:30
[GMAT math practice question] What is the value of (2^8 + 2^9 + 2^{10} + 2^{11}) / 32? A. 80 B. 96 C. 100 D. 120 E. 160 => (2^8 + 2^9 + 2^{10} + 2^{11}) / 32 = (2^8 + 2^82^1 + 2^82^2 + 2^82^3) / 2^5 = 2^8(1 + 2^1 + 2^2 + 2^3) / 2^5 = 2^3(1+2+4+8) = 8*15 = 120 Therefore, the answer is D. Answer: D
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Math Revolution GMAT Instructor
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Posts: 9022
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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10 Feb 2019, 17:19
[GMAT math practice question] If a>b>c>d>0, is d<4? 1) 1/c + 1/d > 1/2 2) (1/a)+(1/b)+(1/c)+(1/d)=1 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. The original condition a>b>c>d>0 is equivalent to 0 < 1/a < 1/b < 1/c < 1/d. The question asks if d < 4. This is equivalent to asking if 1/d > 1/4. By condition 1, 1/d > 1/4 since 1/c < 1/d. So, d < 4. Condition 1) is sufficient. Condition 2) Since 0 < 1/a < 1/b < 1/c < 1/d and (1/a)+(1/b)+(1/c)+(1/d)=1, we have 1/a<1/d, 1/b<1/d, 1/c<1/d and 1/a +1/b + 1/c + 1/d < 1/d +1/d +1/d + 1/d = 4/d. Therefore, 1 < 4/d and d < 4. Condition 2) is sufficient. Therefore, D is the answer. Answer: D Note: This question is a CMT4(B) question: condition 1) is easy to work with and condition 2) is hard. For CMT4(B) questions, D is most likely to be the answer.
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Math Revolution GMAT Instructor
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GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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13 Feb 2019, 17:23
[GMAT math practice question] What is the number of the xintercepts of y=x^43x^3+2x^2? A. one B. two C. three D. four E. five => y = x^43x^3+2x^2 => y = x^2(x^23x+2) => y = x^2(x1)(z2) The xintercepts occur when y = 0. This occurs when x = 0, x = 1 and x = 2. There are three xintercepts. Therefore, the answer is C. Answer: C
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 9022
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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14 Feb 2019, 17:30
[GMAT math practice question] We define the harmonic mean of a set of numbers as the reciprocal of the average (arithmetic mean) of the reciprocals of the numbers. What is the harmonic mean of 20 and 30? A. 22 B. 24 C. 25 D. 26 E. 28 => 1 / { ( 1/20 + 1/30 ) / 2 } = 1 / { ( 3/60 + 2/60 ) / 2 } = 1 / { (5/60) / 2 } = 1 / { 5 / 120 } = 120 / 5 = 24. Therefore, the answer is B. Answer: B
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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17 Feb 2019, 17:42
[GMAT math practice question] Is 3(ab)>0? 1) a^3>b^3 2) a>b => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Asking if 3(ab)>0 is equivalent to asking if a – b > 0, or, equivalently, if a > b. Thus, condition 2) is sufficient. Condition 1) a^3>b^3 => a^3b^3 > 0 => (ab)(a^2+ab+b^2) > 0 => a  b > 0 since a^2+ab+b^2 > 0 => a > b Thus, condition 1) is sufficient too. Therefore, D is the answer. Answer: D FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
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Math Revolution GMAT Instructor
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GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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18 Feb 2019, 17:37
[GMAT math practice question] Is a<1? 1) a^2<1 2) 1/(1a^2)>0 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. a<1 => a^2 < 1 => a^2 < 1 => a^21 < 0 => (a+1)(a1) < 0 => 1 < a < 1 Condition 1) is sufficient, since it is equivalent to the question. Condition 2) 1/(1a^2) > 0 => (1a^2) > 0 => a^21 < 0 => (a+1)(a1) < 0 => 1 < a < 1 Thus, condition 2) is sufficient, since it is also equivalent to the question. Therefore, the answer is D. Answer: D FYI: Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
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Math Revolution GMAT Instructor
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GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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20 Feb 2019, 17:28
[GMAT math practice question] Which of the following expressions is equal to 2^{32}2^{31}2^{30}? A. 3*2^{29} B. 5*2^{29} C. 2^{30} D. 3*2^{30} E. 2^{31} => 2^{32}2^{31}2^{30}? = (2^2)(2^{30}) (2^1)(2^{30})2^{30} = 4(2^{30}) 2(2^{30})2^{30} = (421)(2^{30}) =1(2^{30})=2^{30} Therefore, the answer is C. Answer: C
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Math Revolution GMAT Instructor
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GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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24 Feb 2019, 17:29
If the median of 5 positive integers is 10, is their average (arithmetic mean) greater than 10? 1) The largest number is 40 2) The smallest number is 1 Answer: A Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Suppose the numbers satisfy a ≤ b ≤ 10 ≤ c ≤ d. The question asks if ( a + b + 10 + c + d ) / 5 > 10 or a + b + c + d + 10 > 50. This is equivalent to the inequality, a + b + c + d > 40. If a question includes the words “greater than”, then it asks us to look for a minimum. Since a, b c, and d are positive, and d = 40 by condition 1), we must have a + b + c + d > 40. Condition 1) is sufficient. Condition 2) If a = 1, b = 2, c = 11, and d = 40, then a + b + c + d > 40, and the answer is ‘yes’. If a = 1, b = 2, c = 11, and d = 12, then a + b + c + d < 40, and the answer is ‘no’. Thus, condition 2) is not sufficient since it does not yield a unique solution. Therefore, A is the answer.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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25 Feb 2019, 23:19
f(x)=x^2n+x^n+1, where n is an integer. Is f(x)=1? 1) x=1 2) n is a multiple of 5. Answer: E Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. f(x)=1 ⇔ x^2n+x^n+1=1 ⇔ x^2n+x^n=0 ⇔ x^n(x^n +1)=0 ⇔ xn= 0 or xn =1 ⇔ ( x = 0 ) or ( x = 1 and n is odd ) Conditions 1) and 2) If x = 1 and n = 5, then f(x) = (1)10 + (1)5 + 1 = 1 + (1) + 1 = 1 and the answer is ‘yes’. If x = 1 and n = 10, then f(x) = (1)20 + (1)10 + 1 = 1 + 1 + 1 = 1 and the answer is ‘no’. Thus, both conditions together are not sufficient, since they do not yield a unique solution. Therefore, E is the answer.
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Math Revolution GMAT Instructor
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GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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27 Feb 2019, 04:09
The squares of two consecutive positive integers differ by 55. What is the smaller of the two integers? A. 27 B. 29 C. 30 D. 32 E. 35 Answer: A Let the two consecutive positive integers be n and n+1. Then (n+1)^2 – n^2 = 55, so 2n+1 = 55. It follows that 2n = 54 and n = 27. Therefore, the answer is A.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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28 Feb 2019, 20:49
[GMAT math practice question] What is the greatest positive threedigit number that is divisible by 2, 3, 4, 5, 6 and 7? A. 120 B. 140 C. 210 D. 420 E. 840 => The question asks for the value of the greatest positive threedigit multiple of lcm(2,3,4,5,6,7), where lcm(2,3,4,5,6,7) is the least common multiple of 2, 3, 4, 5, 6 and 7. lcm(2,3,4,5,6,7) = 22*3*5*7 = 420. There are two positive threedigit integers that are multiples of 420: 420 and 840. The greatest positive threedigit number that is a multiple of 420 is 840. Therefore, the answer is E. Answer: E
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Math Revolution GMAT Instructor
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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03 Mar 2019, 17:37
[GMAT math practice question] If n is an integer, is (n+1)(n+2)(n+3) divisible by 12? 1) n is an even number. 2) n is a multiple of 4. => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Since n+1, n+2 and n+3 are three consecutive integers, (n+1)(n+2)(n+3) is a multiple of 3. Condition 2) tells us that n+1 and n+3 are odd integers, and n+2 is an even number which is not a multiple of 4. Thus, (n+1)(n+2)(n+3) is not a multiple of 4. CMT(Common Mistake Type 1) states “no” is also an answer and a condition giving rise to the unique answer “no” is sufficient. Thus, condition 2) is sufficient. Condition 1) If n = 2, then (n+1)(n+2)(n+3) = 3*4*5 = 60 is a multiple of 12 and the answer is “yes”. If n = 4, then (n+1)(n+2)(n+3) = 5*6*7 = 210 is not a multiple of 12 and the answer is “no”. Thus, condition 1) is not sufficient, since it does not yield a unique solution. Therefore, B is the answer. Answer: B
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Math Revolution GMAT Instructor
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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06 Mar 2019, 17:27
[GMAT math practice question] A is the set of 6digit positive integers whose first three digits are same as their last three digits, written in the same order. Which of the following numbers must be a factor of every number in the set A? A. 7 B. 11 C. 17 D. 19 E. 23 => Each number n in the set A is an integer of the form “xyz,xyz”. So, n = 10^5x + 10^4y + 10^3z + 10^2x + 10y + z = 10^3(10^2x + 10y + z) + (10^2x + 10y + z ) = 1000(10^2x + 10y + z) + (10^2x + 10y + z ) = 1001(10^2x + 10y + z ) = 11*91(10^2x + 10y + z ) Thus, n is a multiple of 11. Therefore, B is the answer. Answer: B
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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10 Mar 2019, 17:25
[GMAT math practice question] Is a triangle, with one side of length 12, inscribed in a circle a right triangle? 1) The area of the circle is 36π. 2) The circumference of the circle is 12π. => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Attachment:
3.8.png [ 7.42 KiB  Viewed 407 times ]
If a side of a triangle is the diameter of its circumscribed circle, then the triangle is a right triangle. Condition 1) A circle with area 36π has radius 6 and diameter 12. So, the answer is ‘yes’ and condition 1) is sufficient. Condition 2) A circle with circumference 12π has diameter 12. So, the answer is ‘yes’ and condition 2) is sufficient. Therefore, D is the answer. Answer: D Note that if conditions 1) and 2) yield the same information, Tip 1 of the VA method tells us that D is most likely to be the answer.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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13 Mar 2019, 17:27
[GMAT math practice question] If x and y are positive integers and (xy)^2+y^2=25, which of the following could be the value of x? A. 6 B. 7 C. 8 D. 9 E. 10 => The possible values of the pair (xy,y), with x and y positive, are (0,5), (3,4), (3,4), (4,3) and (4,3). So, (x,y) = (5,5), (7,4), (1,4), (7,3) or (1,3). Thus, x could be 5, 7 or 1. Therefore, B is the answer. Answer: B
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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17 Mar 2019, 17:23
[GMAT math practice question] If x and y are positive integers, x/y=? 1) 2^{x+y}3^{xy}=72 2) 2^x3^y=12 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Condition 2) tells us that 2^x3^y=12 = 2^23^1 and x = 2, y = 1. Thus x/y = 2/1 = 2, and condition 2) is sufficient. Condition 1) 2^{x+y}3^{xy}=72 = 2^33^2 yields the equations x+y=3 and xy=2. So, x = 1 and y = 2, or x =2 and y = 1. Thus, x/y = 1/2 or x/y = 2/1 = 2. Condition 1) is not sufficient since it does not yield a unique solution. Therefore, B is the answer. Answer: B
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