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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82

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x+y=?

ANS:We can modify the original condition and the question. If line A and line D are parallel, x+y=180. However, since conditions do not state that line A and line D are parallel to each other, the correct answer is E.
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_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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1
If a and b are non-negative integers, ab=?
1) 9^a=3^b
2) 5^a=2^b

ANS: From the original condition, there are 2 variables. Hence, there is a high chance that C is the correct answer. However, since this is an integer question, one of key questions, we should apply the common mistake type 4(A). From con 1), we get 2a=b. The answer is not unique and the condition is not sufficient. In case of con 2), we get a=b=0. The answer is unique and the condition is sufficient. Hence, the correct answer is B.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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1
If x, y are positive integers, what is the remainder when 2^(8x+y) is divided by 5?
1) x=1
2) y=2

ANS: From the original condition, there are 2 variables (x and y). In order to match the number of variables and the number of equations, we need 2 equations. Hence, there is a high chance that C is the correct answer. However, even though C is indeed the correct answer, since it is an integer question, one of the key questions, we have to apply the common mistake type 4(A). From the condition 2), the remainder of 2^(8x+y) is always 4. Hence, it is sufficient and the correct answer is B.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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1
What is the perimeter of a certain right triangle?

1) The hypotenuse’s length is 5
2) The triangle’s area is 4.5

ANS: From the original condition, we can see that the number of variables is 2. Hence, the number of equations we need is 2 as well. The correct answer is C
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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1
Is m/n>0?
1) m+n>0
2) mn>0
==> If you change the original condition and problems, in the case of sign of inequality, squaring is the most important thing because squaring never changes the direction of the sign of inequality even if it’s divided or multiplied since any number squared is a positive number. Hence, if you multiply n^2 by both sides, you get n2(m/n)>n2*0? --> mn>0?. Therefore, the answer is B.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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1
If n and mare positive integers, is n^m+2n divisible by 3?

1)m=3
2)n=1

==>In the original condition, there are 2 variables, and C is the answer. However, 1) and 2) each becomes yes, so D is the answer, a common CMT 4(B). Especially in the case of 1), if you substitute m=3, you get n^3+2n=n^3-n+3n=(n-1)n(n+1)+3n. Here, (n-1)n(n+1) is the multiple of three consecutive integers, and you always get the multiples of 6, hence yes each time.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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1
The question below is also a 5051-level question, a typical integer question.

When a positive integer n has 6 different factors, n=?
1) n has 2 prime factors
2) n<18

==> In the original condition, in case of standard deviation questions, there is 1(n) variable, and therefore D is most likely to become the answer.

In case of con 1), you get $$n=2^23^1, 2^13^2,$$ hence it is not unique and not sufficient.
In case of con 2), you get only $$n=2^23^1$$, hence it is unique and sufficient.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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In a certain school, teachers who lecture English and Spanish are there. If 2 teachers are selected randomly, what is the probability that at least one teacher selected lectures Spanish?
1) The ratio of Spanish teachers’ number to English teachers’ number is 3 to 1.
2) The sum of Spanish teachers’ number and English teachers’ number is less than 20.

If we modify the original condition and the question, there are two variables (E and S). In order to match the number of variables and the number of equations, we need 2 equations. Hence, there is high chance that the correct answer is C. Using the condition 1) and the condition 2), since (E,S)=(2,6),(3,9),(4,12), the answer is not unique and the conditions are not sufficient. Thus, the correct answer is E.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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n and k are positive integers. If n=(2^2)(3)(5^3)/15k, is n<k?
1) n<10
2) k>4

ANS: If we modify the original condition and the question, we get n=100/k, k=100/n. If we substitute this into n<k?, the question becomes n<100/n?, n2<100=102?, n<10?. Hence, the correct answer is A.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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Is x-intercept of y=ax+b greater than 0?
1) ab<0
2) a+b<0

ANS: If we modify the original condition and the question, the question becomes x-integercept=-b/a>0?, b/a<0?. If we multiply a^2, since it is a positive number, the sign of inequality does not change. Hence, it becomes ab>0?. So, since the condition 1) states ab<0, the answer is yes and the condition is sufficient. Hence, the correct answer is A.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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If the average (arithmetic mean) of 9 numbers is 43, what is the standard deviation of them?
1) The smallest number of them is 43
2) The greatest number of them is 43

ANS: This is a recent trend question type. If range=M-m=0, mean=Max, or mean=min, then SD=0.
Condition 1) gives us mean=min, SD=0
Condition 2) also gives us mean=Max, SD=0. Hence, the correct answer is D.
- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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Is x^2-y^2>x+y?
1) x<y
2) x+y<0

ANS: We can modify the original condition and the question. Then, the question becomes x^2-y^2>x+y? (x-y)(x+y)-(x+y)>0?, (x-y-1)(x+y)>0?. Then, since there are 2 variables, there is high chance that C is the correct answer. Using the condition 1) and the condition 2), the answer is always yes and the conditions are sufficient. Hence, the correct answer is C.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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At least 10 cars have tinting window and fog light. 40% cars which have tinting windows also have fog light, is the number of the cars with tinting windows larger than that of the cars with the fog light?
1) 80% cars which have fog light also have tinting windows
2) 52 cars have tinting windows or fog light or both

ANS: If we were to solve this question with our trick, we should observe if one of conditions include ratio. If one of conditions contains ratio, then the condition with ratio has 90% of chance to become the answer. Since the condition 1) has ratio, the correct answer is A.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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If m, n are positive integers, what is the value of mn?
1) m/n=7/15
2) The greatest common divisor of m and n is 3

ANS: There are 2 variables in the original condition. Hence, there is high chance that C is the correct answer. Using both the condition 1) and the condition 2), we get m=(7)(3) and n=(15)(3). Thus, the correct answer is C.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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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=2b
2) a=6

ANS: We can modify the original condition and the question. When the question asks about the x-intercept, we need to find the value of x when y=0. Then, if we substitute y=0, from x/a=1, we get x=a. Hence, we all need to know the value of a. Since the condition 2) states a=6, the condition is sufficient. Thus, the correct answer is B.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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If P, Q, R are integers greater 1, have P and R common factors other than 1?
1) P and Q have common factors other than 1
2) Q and R have common factors other than 1

ANS: Since the original condition has 3 variables, we need 3 equations in order to match the number of equations and the number of variables. Thus, the correct answer is E.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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If 2-digit positive integer n is 12 times of the tens digit of n, what is the value of n?
1) The tens digit of n is 3.
2) The sum of the tens digit and the units digit of n is 9.

There are 3 variables (n, a, b) and 1 equation (10a+b=12a) in the original condition. Since we need 1 more equation, the correct answer is D.

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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Is (r^2)x>0?
1) r^5=1
2) x>0

ANS: There are two variables (r and x) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Hence, the correct answer is C.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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A circle has the same area as a rectangle. What is the circumference of the circle?
1) The perimeter of the rectangle is 18
2) The area of the rectangle is 20

ANS: We can modify the original condition and the question. The area of the circle and the area of the rectangle are same. Hence, since it is asking for the circumference of the circle, we only have to know the area of the circle (which is same as the area of the rectangle). So, the correct answer is B.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8123
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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There are 3 integers, a, b, and c in that order. Are these integers consecutive?
1) a=c-2
2) b>a

We can modify the original condition and the question. In order for integers to be consecutive, they need to be a, b(=a+1), c(=a+2). Hence, the difference between c and a needs to be 2. Thus, the answer is yes for the condition 1). The correct answer is A.
_________________ Re: Math Revolution Approach (DS)   [#permalink] 26 Jun 2016, 18:19

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# Math Revolution Approach (DS)

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