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There are questions that combine common mistake types 3 and 4. Below is a question type that frequently appears in the current GMAT test. This is a 50-51 level question that includes the common mistake type 4(B). You have to be strong at these types of questions. In order to solve it, you have to know the relationship between Variable Approach Method and the common mistake type.

(ex 1) 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

This is a typical common mistake type question that makes C and A both the answers. Answer:A
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Geometry question like below is also very challenging. (ex 2) 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

Question like above has one condition as a number and the other as a ratio. Then, the condition with ratio becomes the answer, making A the correct answer. This is a 50-51 level question. Answer: A
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Be careful on a question that involves common mistake type 4(A) like below. These questions often involve integers. (ex 3) There are 7 consecutive integers. How many multiples of 6 are in the 7 numbers? 1) The median of the 7 numbers is a multiple of 6 2) The average (arithmetic mean) of the 7 numbers is 12

Answer: D Consecutive integers questions are also 50-51 level questions. Also ,these are common mistake type 4(B) questions.
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Below is another 50-51 level question. For 2-by-2 question, if a percentage appears, then that condition is sufficient (This is only true when the question is in %).

As you can see, this is a 2-by-2 question, and the question is in %. Since the condition 1) and 2) each has one percentage, there are 3 percentages. Hence, the correct answer is D. This is a very challenging 50-51 question. Answer: D

There are some difficult PS questions that appear as 50-51 level questions. In the x- y plane, there are 4 points (0,0), (0,4), (6,4), and (6,0). If these 4 points makes a rectangle, what is the probability that x+y<4? A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 2/5 Answer: B If we draw conditions on coordinates, the correct answer is B.
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Also, Is x<3? 1) 0.025(10x)<25 2) 0.025(102x)<250,000 Answer: A

This is a question involving inclusion relationships. If the range of the question includes the range of the condition, then the condition is sufficient. In this case, A is the correct answer. (Since there is 1 variable, there is high chance that D is the correct answer. Hence, we should use the condition 1) and the condition 2) separately.
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Below is 50-51 question type. If the average (arithmetic mean) height of John, Tom and Sue is 1.70m, what is the median height of them? 1) The height of Tom is 1.65m. 2) The height of Sue is 1.70m. Answer: B

There are 3 variables (J,T,S) and 1 equation (J+T+S=5.1) in the original condition. In order to match the number of variables to the number of equations, we need 2 equations. Hence there is high chance that C is the correct answer. Using the condition 1) and the condition 2), C can be the answer. However, since this is statistics question, we need to apply common mistake type 4(A). The condition 2) always gives us median=1.7. Hence, the correct answer is B.
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If x and y are integers, is xy an even? 1) x+3 is an even 2) y-3 is an odd Answer: B

This is a recent 50-51 level question type. As you can see, this is one of common mistake type 4(A) question in which both C and B can be the answer.
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If ab≠0, is |a^b|=a^b? 1) |a|=a 2) |b|=b Answer: A

The above question can have 2 answers – C and A. For such questions, A becomes the correct answer. This is common mistake type 4(A) question.
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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. A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? 1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median. 2) The sum of the 3 numbers is equal to 3 times median of the 3 numbers.

If we assume the original condition as a<M<b. Then, the question becomes (a+M+b)/3=M?. Then, a+M+b=3M?. This is same as the condition 2), hence it is sufficient. Condition 1), b-a=2(b-M), is also yes. Hence, according to the common mistake type 4(B), the correct answer is D.
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Sometimes geometry question can be a high level question A larger cube has 27 cubic inch as a volume and in the cube there are 27 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 27 smaller cubes and the surface area of the larger cube, in square inch? A. 54 B. 64 C. 81 D. 108 E. 120 Since 6*27-6*9=108, the correct answer is D. This is always a type of 50-51 level question.
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Please be careful on common mistake type 4(A) question. Integer questions often appear as common mistake type 4(A) questions. The product of the units digit, tens digit, and hundreds digit of a positive 3-digit integer n is 54, what is the value of n? 1) n>950 2) The sum of the units digit, tens digit, and hundreds digit of a positive 3-digit integer n is 16.

Answer: A There are 3 variables and 1 equation. Hence, there is high chance that C is the correct answer. However, we have to consider common mistake type 4(A) because it is integer question. Since the condition 1) gives us n=961, it is sufficient alone. So, the correct answer is A.
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In a certain school, 40% of all the students are boys. What percent of all the students take Biology? 1) All the students are 4,000 2) 10% of the girl students and 15% of the boy students take Biology For a question like above, there are number and ratio. There is not exceptional case to this type of questions. In case of 2-by-2 questions, when % appears 3 times, that condition is sufficient (only when the question asks for %). Girls Boys Bio NOT Bio This is 2-by-2 and the question is asking %. Since the condition 2) has 2 % and there are 3 %, the correct answer is B. This is a very difficult question. Answer: B
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Also, this is a challenging question. n and k are positive integers. If n=(22)(3)(53)/15k, is n<k? 1) n<10 2) k>4 Answer: A

If we modify the original condition and the question, we get n=100/k. This means k=100/n. If we substitute, we get n<100/n?, n^2<100?. Hence n<10?. So, the correct answer is A.
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Below is also 50-51 question. When x and y are integers, x^3y^4=z, x=? 1) z=2,000 2) y=2 Answer: A There are 3 variables (x,y,z) and 1 equation (x^3y^4=z) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Hence, there is high chance that C is the answer. Using 1) and 2), C can be the answer. However, if we apply common mistake type (4A), as this is an integer question – a key question, we get x=5 and y=2. The condition 1) is sufficient and 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 Answer: D Above is also a 50-51 level question. If Range=0, Max=mean, or min=mean, SD=0. In case of this question, (DS) mean=43. 1) min=43=mean 2) Max=43=mean

Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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28 Jun 2016, 07:31

MathRevolution wrote:

In addition, the mistake type 4(A) questions related to our life are given at level of score 50-51. In a case of the question below, the answer is A if you modify the question.

(ex 3) Machine X is taken 30 minutes for preparing to work and machine Y is taken 20 minutes for warming up before driving machines. The work rate of machine X is 40 parts per 1 minute and machine Y is 30 parts per 1 minute. Is the total time taken to work including preparing time of machine X smaller than that of machine Y?

1) The total task is more than 1,200 parts. 2) The total task is less than 1,800 parts.

Therefore, when you face with questions related to real life, approach them very cautiously.

MathRevolution Could you please post detailed solution for the problems,which you have been posting
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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(B). 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) If s, p, t are there such that s<p<t, is the average (arithmetic mean) of s and t equal to 4p? 1) The average (arithmetic mean) of s, p, and t is equal to three times the median of them 2) s+t=8p This is a common mistake type question in which both C and D can be the answer. This is 50-51 level question. If we modify the original condition and the question, we get (s+t)/2=4p? s+t=8p?. Hence, 2) is sufficient and in case of con 1), we get (s+p+t)/3=3p, s+p+t=9p, s+t=8p. Since 1)=2), the correct answer is D.
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