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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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25 May 2017, 00:14
Is a positive integer n a multiple of 6? 1) n is the product of the 4 consecutive integers 2) n is a multiple of 12 ==> In the original condition, there is 1 variable, and in order to match the number of variables to the number of equations, there must be 1 more equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), the product of consecutive 4 number is always the multiple of 24, hence yes, it is sufficient. For con 2), if it is a multiple of 12, it is also a multiple of 6, hence yes, it is sufficient. Therefore, D is the answer. Answer: D
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Math Revolution GMAT Instructor
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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28 May 2017, 22:51
Is x^2>y^2? 1) x>y 2) x>y ==> In the original condition, there are 2 variables (x,y), and in order to match the number of variables to the number of equations, there must be 2 variables. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from x>y≥0, it is x>0, so from x>y, it is x>y, which becomes x^2>y^2, hence yes, it is sufficient. The answer is C. However, this is an absolute value question, one of the key questions, so you apply CMT 4 (A: if you get C too easily, consider A or B). For con 1), you get (x,y)=(2,1) yes (2,3) no, hence not sufficient. For con 2), from x>y≥0, you get x>0, which becomes x>y, then x^2>y^2, it is always yes and sufficient. Therefore, the answer is B. Answer: B
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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01 Jun 2017, 17:00
If m and n are positive integers, is mn a multiple of 9? 1) m+n is a multiple of 3 2) mn is a multiple of 3 ==> In the original condition, there are 2 variables (m,n) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from the multiple of mn=3, it becomes a multiple of m or n=3. According to con 1), you always get a multiple of m=n=3, hence yes, it is sufficient. The answer is C. Answer: C
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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04 Jun 2017, 17:00
We define the average (harmonic mean) as the reciprocal of the average (arithmetic mean) of reciprocals. What is the average (harmonic mean) of 2, 3, and 6? A. 1/3 B. 1/2 C. 1 D. 2 E. 3 ==> If you find the average of the reciprocals, you get \(\frac{++}{3}=13\) . Since it is the reciprocal of that, the answer is E. Answer: E
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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08 Jun 2017, 17:45
Is xyz>0? 1) xy>0 2) yz>0 ==> In the original condition, there are 3 variables (x,y,z) and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), if x=y=z=1, yes, but if x=y=x=1, no, hence it is not sufficient. Therefore, the answer is E. Answer: E
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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11 Jun 2017, 17:31
Which of the following is the closest value of x such that \(x^{20}+x^2+0.0000019=0.09?\) A. 0.1 B. 0.01 C. 0.3 D. 0.03 E. 0.003 ==> From \(x^{20}+x^2+0.0000019=0.09, x^{20}\) and 0.0000019 are very close to 0, so you can ignore them, and the equation becomes \(x^2=0.09=0.3^2\). Thus, you get x=0.3. The answer is C. Answer: C
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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13 Jun 2017, 11:28
Hi, MathRevolution, just checking  do these patterns still hold true?



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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14 Jun 2017, 17:14
If f(x)=ax²+bx+c, for all x is f(x)<0? 1) b²4ac<0 2) a<0 ==> In the original condition, there are 3 variables (a, b, c) and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), if discriminant =b24ac<0, it doesn’t meet with the xaxis, and if a<0, you always get f(x)<0, hence yes, it is sufficient. Therefore, the answer is C. Answer: C
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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18 Jun 2017, 17:05
When a positive integer n is divided by 13, what is the remainder? 1) n+1 is divisible by 13 2) n+14 is divisible by 13 ==> In the original condition, there is 1 variable, and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. By solving con 1) and con 2), you get con 1) = con 2), and you use direct substitution for the rest, so you get n=12,25,38,… When you divide by 13, the remainder always becomes 12, hence it is unique and sufficient. The answer is D. Answer: D
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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20 Jun 2017, 18:53
If the sum of the first 50 even numbers is 2,550, what is the sum of the first 50 odd numbers? A. 1,275 B. 2,550 C. 2,500 D. 2,600 E. 3,000 ==> You get 2+4+…..+98+100=2,550, then 1+3+….+97+99=?. If you compare each numbers, 1 is 1 less than 2, 3 is 1 less than 4, 97 is 1 less than 98, and 99 is 1 less than 100. Since there are 50 numbers in total, it is 50 less than 2,550. Therefore, the answer is C. Answer: C
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Math Revolution GMAT Instructor
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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22 Jun 2017, 17:42
Is ab(ab)>0? 1) a<b 2) a>0 and b>0 ==> If you modify the original condition and the question, what satisfies ab>ab? must be ab<0. Therefore, the answer is A. Answer: A
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Math Revolution GMAT Instructor
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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26 Jun 2017, 16:52
ab=? 1) a+b=10 2) a2b2=20 ==> In the original condition, there are 2 variables (a,b) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), you get a^2b^2=a+bab=20, 10ab=20, ab=2. The answer is C. Answer: C
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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28 Jun 2017, 15:51
Is a<b? 1) a<0 2) b<1 ==> In the original condition, there are 2 variables (a, b) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from 1<b<1, if a=0.1 and b=0.2, no, but if b=0.1 and a=0.1, yes. Hence, 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 [#permalink]
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03 Jul 2017, 17:04
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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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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04 Jul 2017, 17:08
If x and y are integers, what are the values of x and y? 1) 2^x3^y=16/27 2) x+y=1 ==> For con 1), you get 2^x*3^y=16/27=2^4*3^3, then x=4 and y=3. Therefore, the answer is A. In other words, it is CMT 4(A), in which A and C are both the answers. In the original condition, there are 2 variables, so the answer is C, but since it is an integer question, you apply CMT 4(A) and get the final answer as A. This is a 4950 level question. Answer: A
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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06 Jul 2017, 17:27
If x and y are positive integers and y(2^x)=24, x=? 1) x 2 2) y is even ==> In the original condition, there are 2 variables (a,b), and in order to match the number of variables to the number of equations there must be 2 equations as well. Since there is 1 for con 1) and 1 for con 2) C is most likely to be the answer. By solving con 1) and con 2), you get 24=6(2^2). The answer is C.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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09 Jul 2017, 17:32
When x+y is integer, is y an integer? 1) x is an integer. 2) x+2y is an integer. ==> In the original condition, there are 2 variables (x,y) and 1 equation (x+y=integer). In order to match the number of variables to the number of equations, there must be 1 more equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), from x=integer and x+y=integer, integer+y=integer, you get y=integer, which is yes and sufficient. For con 2), from x+2y=x+y+y=integer, integer+y=integer, you get y=integer, which is also yes and sufficient. Therefore, the answer is D. Answer: D
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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10 Jul 2017, 16:54
If mr≠0, m/r=? 1) (m+r)/r=3 2) r/(m+r)=1/3 ==> In the original condition, there are 2 variables (m,r) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), you get con 1) = con 2), so from m/r+1=3, you get m/r=2, hence it is unique and sufficient. Therefore, the answer is D. Answer: D
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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12 Jul 2017, 18:07
Is x^3y^2z<0? 1) x^2y<0 2) yz<0 ==> If you modify the original condition and the question, when xyz≠0, you get xz<0?. There are 3 variables (x,y,z), and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), you get x^2y<0, y<0 and yz<0, z>0. Since x is unknown, it is not sufficient. Therefore, the answer is E. Answer: E
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]
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16 Jul 2017, 17:49
If x>0, y<0, and a>b>0, then which of the following is (are) positive? Ⅰ. ax+by Ⅱ. axby Ⅲ. byax 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. axby by<0, you get –by>0 and ax>0, axby>0, hence it is always positive. (O) From Ⅲ. byax a=2, b=1, x=1, y=10, it is negative. (X) Therefore, the answer is B. Answer: B
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