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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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.

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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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

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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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If ab≠0, is |a^b|=a^b?
1) |a|=a
2) |b|=b

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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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.

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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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

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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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
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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#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
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

Hence, the correct answer is D.
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Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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 _________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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

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What GMAT club tags would be included in "Integer Properties?" Divisibility and multiples... what else?
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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If |a+1|=|b-1|, a+b=?
1) a>b
2) a=b-1

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).
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8268
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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.
_________________ Re: The Ultimate Q51 Guide [Expert Level]   [#permalink] 25 Jul 2016, 19:45

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# The Ultimate Q51 Guide [Expert Level]

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