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# Math Revolution Approach (DS)

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: Math Revolution Approach (DS)  [#permalink]

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26 Feb 2017, 21:33
Is a=b?

1) $$a^2=b^2$$
2) $$a=2$$

==> 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 a=2, you get $$b^2=2^2=4$$, then b=±2. Thus, (a,b)=(2,2) yes but (a,b)=(2,-2) no, hence it is not sufficient.

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"Only $99 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: 6020 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (DS) [#permalink] ### Show Tags 02 Mar 2017, 01:38 If mn≠0, what is the value of $$\frac{m+1}{m}-\frac{n+1}{n}$$? 1) m=n 2) m=1 ==> If you modify the original condition and the question, you get $$\frac{m+1}{m}-\frac{n+1}{n}=\frac{n(m+1)-m(n+1)}{mn}= \frac{nm+n-mn-m}{mn}=\frac{n-m}{mn}=?$$. Then, for con 1), m=n, so n-mmn=0, hence it is unique and sufficient. 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$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6020
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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03 Mar 2017, 01:12
If a, b, and c are integers, is abc an even?

1) a+b is an even
2) b+c is an even

==> 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 (a,b,c)=(1,1,1), you get a+b+c=1+1+1=3=odd, so no, but if (a,b,c)=(2,2,2), you get a+b+c=2+2+2=6=even, so yes, hence it is not sufficient.

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"Only $99 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: 6020 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (DS) [#permalink] ### Show Tags 08 Mar 2017, 01:13 What is the perimeter of a certain right triangle? 1) The hypotenuse’s length is 10 2) The triangle’s area is 24 ==> In the original condition, for a right triangle, there are 2 variables (2 legs) 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 6:8:10 and the perimeter of the right triangle becomes 6+8+10=24, hence unique and sufficient. Therefore, the answer is C. 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$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6020
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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09 Mar 2017, 02:39
Is a positive integer n greater than 1 divisible by 2?

1) 24/n is an integer
2) 32/n is an integer

==> In the original condition, there is 1 variable (n) 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. For con 1), n=2 yes, but n=3 no, hence it is not sufficient.
For con 2), from $$32=2^5$$, n always has 2 as its factor, hence yes, it is sufficient.

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"Only $99 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: 6020 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (DS) [#permalink] ### Show Tags 10 Mar 2017, 03:12 If the average (arithmetic mean) of set A is 10,000 and the average (arithmetic mean) of set B is 10,000, what is the range of set A and set B combined? 1) The range of set A is 6,000 2) The range of set B is 3,000 ==> If you modify the original condition and the question, from range= Max-min, you get set A: Ra =Ma-ma and set B: Rb=Mb-mb. Then, there are 6 variables and 2 equations, and in order to match the number of variables to the number of equations, there must be 4 more 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), the answer becomes E as well. Also, there is no relationship between the average and the range, and thus the answer is definitely 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$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6020
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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12 Mar 2017, 18:44
Is a positive integer x a factor of 12?

1) 3x is a factor of 48
2) 2x is a factor of 12

==> In the original condition, there is 1 variable (x) 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), “3x is a factor of 48” becomes “x is a factor of 16”, and x=2 yes but x=8 no, hence it is not sufficient.
For con 2), “2x is a factor of 12” becomes “x is a factor of 6”, hence it is always yes and sufficient.

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"Only $99 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: 6020 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (DS) [#permalink] ### Show Tags 12 Mar 2017, 18:48 There are 30 consecutive integers. What is the sum of the integers? 1) The sum of the smallest integer and the greatest integer is -1 2) The greatest integer is 14. ==> In the original condition, there is 1 variable (n, n+1, n+2,……n+29), 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. For con 1), you get -15~14, so the sum=-15, hence unique and sufficient. For con 2), you also get -15~14, so the sum=-15, hence unique and sufficient. Thus, con 1) = con 2). 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$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6020
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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15 Mar 2017, 02:09
Is a positive integer n a multiple of 12

1) n is a multiple of 6
2) n is a multiple of 24

==> In the original condition, there is 1 variable (n) 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. For remainder questions, you always use direct substitution.
For con 1), n=6 no, n=12 yes, hence not sufficient.
For con 2), n=24,48,…, hence it is always yes and sufficient.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 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: 6020 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (DS) [#permalink] ### Show Tags 16 Mar 2017, 01:24 Is x>y>z? 1) x>y 2) y>z ==> 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), from x>y>z, it is always yes and sufficient. Therefore, the answer is C. 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$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6020
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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19 Mar 2017, 17:58
n=?

1) twice n equals to n+1
2) n times n equals to n

==> In the original condition, there is 1 variable (n) 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.
For con 1), from 2n=n+1, you get n=1, hence sufficient.
For con 2), from $$n^2=n$$ and $$n^2-n=0$$, n(n-1)=0, you get n=0,1, hence it is not unique and not sufficient.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 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: 6020 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (DS) [#permalink] ### Show Tags 19 Mar 2017, 17:59 Is a positive integer x a factor of 24? 1) 3x is a factor of 48 2) 2x is a factor of 24 ==> In the original condition, there is 1 variable (x) 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. For con 1), x is a factor of 16, so x=8 yes, x=16 no, hence not sufficient. For con 2), x is a factor of 12, so it is always yes, hence sufficient. Therefore, 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$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6020
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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20 Mar 2017, 03:40
If x and y are integers greater than 1 and x>y, what are the values of x and y?
1) x+y=13
2) xy=22

==> 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 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 x=11 and y=2, hence it is unique and sufficient. The answer is c. However, this is an integer question, one of the key questions, so you apply CMT 4(A).
For con 1), from (x,y)=(11,2),(10,3), it is not unique and not sufficient.
For con 2), you only get (x,y)=(2,11), hence it is unique.

Therefore, the answer is B, not C.
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"Only $99 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: 6020 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (DS) [#permalink] ### Show Tags 22 Mar 2017, 02:48 In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-intercept of line K? 1) a=b 2) a=1 ==> If you modify the original condition and the question, the x-intercept is the value of x when y=0, hence from (x/a)=1, you get x=a, so you only need to find a. Therefore, 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$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6020
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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23 Mar 2017, 01:21
Is wp+st>0?
1) ws+pt>0
2) wt+ps>0

==> In the original condition, there are 4 variables (w,p,s,t) and in order to match the number of variables to the number of equations, there must be 4 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 (w,s,p,t)=(1,1,1,1) yes, but (w,s,p,t)=(3,-1,-4,-1) no, hence it is not sufficient.

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"Only $99 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: 6020 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (DS) [#permalink] ### Show Tags 24 Mar 2017, 03:53 How much is the total price of the 3 products? 1) The sum of any two prices of these 3 products is$8,000
2) At least one of them is 4,000

==> In the original condition, there are 3 variables, 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), the price of each 3 products becomes $4,000, hence it is unique and sufficient. This is an inequality 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), the price of each 3 products always becomes$4,000, hence it is unique and sufficient. For con 2), it is unknown, hence it is not sufficient.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 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: 6020 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (DS) [#permalink] ### Show Tags 26 Mar 2017, 18:30 m=? 1) 5 is a factor of m 2) m is a prime number ==> In the original condition, there is 1 variable (m) 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. For con 1), from m=5,10…, it is not unique and not sufficient. For con 2), from m=5,7…, it is not unique and not sufficient. By solving con 1) and con 2), you get m=5, hence it is unique and sufficient. Therefore, the answer is C. 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$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6020
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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26 Mar 2017, 18:31
is an integer n even?

1) n(n+2)=even
2) n(n+3)=even

==> In the original condition, there is 1 variable (n) 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.

For con 1), in order to get n(n+2)=even, you get n=even, hence yes, it is sufficient.
For con 2), n=2 yes, but x=3 no, hence it is not sufficient.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 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: 6020 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution Approach (DS) [#permalink] ### Show Tags 29 Mar 2017, 01:44 When a positive integer $$m^2$$ is divided by 4, what is the remainder? 1) When m is divided by 3, the remainder is 1 2) When m is divided by 2, the remainder is 1 ==> In the original condition, there is 1 variable (m) 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. For remainder questions, it is best to use direct substitution. For con 1), if you substitute from m=3p+1=1,4,7…, from m=1, 1^2=1=4(0)+1, the remainder=1, and if m=4, from 4^2=16=4(4)+0, the remainder=0, hence it is not unique and not sufficient. For con 2), from m=2q+1=1,3,5,7,…, you get m2=1,9,25,49.., and the remainder divided by 4 always becomes 1, hence it is unique and sufficient. Therefore, 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$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6020
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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30 Mar 2017, 02:16
Is x<1<y?

1) x<√x<y
2) x<√y<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 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 x<√x, you get 0<x<1, and from √y<y, you get y>1. Then, you get x<1<y, hence always yes.

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Re: Math Revolution Approach (DS) &nbs [#permalink] 30 Mar 2017, 02:16

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