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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.

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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.

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.
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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.
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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.
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What is the median of prices? 1) More than 1/2 of the prices are $1,500 or more than $1,500 2) More than 1/2 of the prices are $1,500 or less than $1,500

ANS: There are many variables in this case. Hence, there is high chance that E is the correct answer. Using 1) and 2), we can see that “more than 1/2 of the prices are $1,500 or more than $1,500” and “more than 1/2 of the prices are $1,500 or less than $1,500”. The overlapping price then will be $1,500. Thus, $1,500 becomes the median, and the correct answer is C.
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If Tom invest $x April at a constant monthly interest rate of y percent, what is the percent increase from April to October? 1) x=10,000 2) y=2

ANS: If we modify the original condition and the question, we get x--> x(1+y%)^6. Hence, for the percent increase, we only have to know the value of y. Thus, the correct answer is B.
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In the x-y plane, line K passes through (a,0) and (0,b). What is the slope of line K? 1) a/b=1 2) Line K passes through (1,2)

ANS: If we modify the original condition and the question, the slope of a line that passes through (a,0) and (0,b) is (0-b)/(a-0)=-b/a. Thus, the correct answer is A.
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ANS: If one of conditions is “number” and the other is “ratio”, the condition with “ratio” is the correct answer. Hence, the correct answer is A.
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ANS: If we modify the original condition and the question, the question becomes |a^b|=a^b? --> a^b≥0? --> a≥0?. Hence, the correct answer is A.
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