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This is also a type of question related to common mistake type 4(A) When 25 integers are there such that their average (arithmetic mean) is 100, is their median equal to 100? 1) They are consecutive 2) The average (arithmetic mean) of the greatest number and the smallest number of them is 100 There are 2 variables in the question. Hence, C can be the answer. Yet, since this is an integer question, we have to apply common mistake type 4(A). Hence, this makes A the answer.
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This is also a 50-51 level question and is related to the common mistake type 4(A) When 25 integers are there such that their average (arithmetic mean) is 100, is their median equal to 100? 1) They are consecutive 2) The average (arithmetic mean) of the greatest number and the smallest number of them is 100

There are 2 variables in the question. Hence, C could be the answer. However, since this is an integer question, we have to apply the common mistake type 4(A). Then, we can see that A is the correct answer.
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Below is a type of common mistake type 4(A) questions. Many integer questions are related to this mistake type. (ex 3) If x is integer and |x|+x<4, what is the value of x? 1) x>0 2) x<-2 If we modify the original condition and the question, we get 2x<4, x<0 when x>0. Since x<0 is always true, we get x<2. Since there is one variable (x), there is a high chance that D is the correct answer. In case of con 1), as 0<x<2, x=1. The answer is unique and the condition is sufficient. In case of con 2), since x<-2, the answer is not unique and the condition is not sufficient. Hence, the correct answer is A.
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A Geometry question can be difficult as well (ex 6) A rectangular iron plate is 12 feet by 8 feet. We can make a right circular cylinder by rolling the length side of the plate or the width side of the plate. If the cylinder’s volume is at its greatest, which one of the length or the width of the iron plate is the circumference of the cylinder and what is the difference between 2 volumes of cylinders made by rolling? A. the circumference is 8, the difference is 54/π B. the circumference is 8, the difference is 96/π C. the circumference is 12, the difference is 84/π D. the circumference is 12, the difference is 96/π E. the circumference is 12, the difference is 86/π ==> As the number increases fast when it is squared, the volume increases faster when it is being rolled at 12-inches side. Hence, from 2πr=12, we get r=6/π. Hence, π(6/π)2(8)=288/π. The volume of the cylinder rolled at the 8-inches side is – from 2πr=8, we get r=4/π – π(4/π)2(12)=192/π. The difference is 288/π-192/π=96/π. Hence, the correct answer is D. Answer: D
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If x and y are integers, is x+y an even? 1) x-y is an even 2) y is an odd Above question is also a 50-51 level question. Both C and A can be correct. Hence, this is a typical common mistake type 4(A) question. Answer: A
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As always, questions combined with the mistake type 3 and 4 are given. Let's have a look at the example below. This is a very recent question, which also belongs to the mistake type 4(A). This question is on the level of score 50-51. You should be able to tackle a question like this. In addition, you should be aware of relation between approach method to variables and the mistake types. (ex 1) (integer) If x and y are integers, is xy an even? 1) y=4x 2) x=odd Both C and A can be answers. This is a 50-51 level question. From con 1), y=4x is always even. Hence, the condition is sufficient and the answer is A. Answer: A
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What is the median number of cloths sold in the last 11 days? 1) 30 cloths are sold every day in the last 6 days 2) The total number of cloths sold was 400 in the last 11 days.

This is a typical common mistake type 4(A) question. The answer can either be C or A. The final correct answer is A. Answer: A
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Is a>b? 1) a>|b| 2) |a|>b This is a common mistake type 4(A) question in which both C and A can be an answer. We apply the common mistake type 4(A) because this is an absolute question, which is one of key questions. In other words, in case of con 1), from a>|b|≥b, we get a>b. Hence, the answer is yes and the condition is sufficient. Thus, the correct answer is A.
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Below is common mistake type 4(B) question. If x and y are integers, is x2+xy an even? 1) x=even 2) y=odd There are 2 variables in the original condition. Hence, there is a high chance that C is the correct answer. From 1) and 2), C is certainly an answer. However, since it is one of key questions, we should apply the common mistake type 4(A). We can see that con 1) gives the answer that is ‘yes’ too easily because x(x+y)=even(x+y)=even. However, since con 2) is difficult, we should apply the common mistake type 4(B). Then, the correct answer is D.
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There are many difficult PS questions nowadays. (ex 5) *(integer) 40,195*26*10,082 is approximation of which of the followings? A. 108 B. 109 C. 1010 D. 1011 E. 1012 40,000*25*10,00=1010. Hence, the correct answer is C
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If m, n are positive integers, what is the unit digit of 7^(4m+2)+n? 1) m=1 2) n=2 Since there are 2 variables in the original condition, there is a high chance that C is the correct answer. Even though C is the correct answer, we have to apply the common mistake type 4(A) because it is one of key questions, integer question. From con 2), the units digit of 7^(4m+2) is always 4. Hence, we only have to know the value of n. Thus, the condition is sufficient and the correct answer is B.
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Since there are 2 variables and 1 equation in the original condition, there is a high chance that D is the correct answer. The correct answer indeed is D according to the common mistake type 4(B).
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As always, questions combined with the mistake type 3 and 4 are given. Let's have a look at the example below. This is a very recent question, which also belongs to the mistake type 4(A). This question is on the level of score 50-51. You should be able to tackle a question like this. In addition, you should be aware of relation between approach method to variables and the mistake types. (ex 1) (integer) If m is an integer, is m an even? 1) m/2=integer 2) m=-m Both C and D can be an answer. Applying the common mistake type 4(B), the correct answer is D.
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Becareful on the common mistake type 4(B) If x and y are integers, is xy an even? 1) x=even 2) y=odd There are 2 variables in the original condition and there is a high chance that C is the correct answer. Using 1) and 2), C is the correct answer. However, since this is one of key questions, con 1) is always yes. The condition is sufficient and the correct answer is A.
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This is a difficult inequality question. (ex 6) *(inequality) If 0.01<a<0.02, 5,000<b<10,000, which of the following can be the value of (1/a2)+(1/b2)? A. 0.2 B. 0.5 C. 750 D. 525 E. 7250

(ex 7) *(integer) What is the greatest common divisor of positive integers n and m? 1) n=1 2) m=n+1 There are 2 variables in the original condition (m, n). 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. Using 1) and 2), C is the correct answer. However, we have to utilize the common mistake type 4(B) since it is an integer question. The correct answer is D.
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