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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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In addition, questions of the mistake type 4(A) related to method of approach to variables 1st account for considerable parts of scoring. C can also be the answer of the question below.

(ex 2)8^(s+3r)/4^(2s+5r)=?

1) s+r=3
2) 2s-r=6

In a case like this, when you modify the question, 2^(-s-r)=0? is derived. For 1), s+r=3, which is sufficient and the answer. is A.
This type of question is always at level of score 50-51.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8595
GMAT 1: 760 Q51 V42
GPA: 3.82
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1
You need to be extra careful on questions that involve the Common Mistake Type 4(B).

(ex 2) If x<0 and y<0, is x/y<1?
1) |x|<|y|
2) x>y

In the above question, we easily can find out that the condition 1) is sufficient. However, finding the condition 2) as the sufficient condition is not that easy. Hence, this is the Common Mistake Type 4(B) which states that we should consider the answer choice D if A or B seems too easily an answer. This type of question always appears in the score range between 50-51.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8595
GMAT 1: 760 Q51 V42
GPA: 3.82
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This is one of the most challenging types of the question that looks like a journal. This is a PS question that you should be familiar with.

It is well-known that the way to find out approximation value of a positive integer n’s square root is following;
1st approximation: select a positive integer "a" and n is divided by a.
2nd approximation: a positive integer n’s square root is the average (arithmetic mean) of a quotient and divisor.
What is the approximation positive integer n’s square root, in terms of a and n?
A. (a^2+n)/2a B. (a^2+n)/2 C. (a^2-n)/2a D. (a^2+n)/a E. (a^2+2n)/a
N=aQ, (a+Q)/2=(a+n/a)/2=(a^2+n)/2a

This type of questions looks very simple, but it is rather challenging. You should not underestimate the difficulty levels of PS questions (by the way this is a statistics problem).
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8595
GMAT 1: 760 Q51 V42
GPA: 3.82
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Be careful on probability questions.
2 men and 3 women are lined up in a row. What is the number of cases where they stand with each other in turn? (The number of cases in which men (or women) do not stand next to each other)
A. 12 B. 15 C. 18 D. 21 E. 24

Since, 3!*2!=12, the answer is A. This is a type of questions that appear in the 50-51 range.
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Math Revolution GMAT Instructor V
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Posts: 8595
GMAT 1: 760 Q51 V42
GPA: 3.82
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Also, there is a statistic question like below.
If the heights’ range of men is 14 inches and the heights’ range of women is 10 inches, what is combined heights’ range?
1) The shortest man is 3 inches shorter than the tallest woman.
2) The height of highest man is 72 inches.
There are 4 variables and 2 equations (14=MT-Ms, 10=WH-WS), in the original condition. In order to match the number of equations and the number of variables, we need 2 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer. Using the condition 1) and the condition 2), C is the answer. However, this is a statistic question, one of the key questions. Hence, we need to apply the Common Mistake Type 4(A). We can see the condition 1) is sufficient by itself, making A and correct answer. Be careful on this type of question.
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Math Revolution GMAT Instructor V
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Posts: 8595
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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.
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sarang1601 wrote:
MathRevolution can you please elaborate the solution B

Here is an answer to your question! Please refer to the attachment Attachments there some difficult- in the xy plane.jpg [ 1.8 MiB | Viewed 1678 times ]

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Math Revolution GMAT Instructor V
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Posts: 8595
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8595
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 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.
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MathRevolution wrote:
From con 2), the units digit of 7^(4m+2) is always 4.

I don't know what con 2) is, but the units digit of an odd integer can never be 4.

7^(4m+2) always has a digits unit of 9.

Posted from my mobile device
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Stuck in the 600's and want to score 700+ on the GMAT?
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$90/hour as of August 2019. I am not accepting any more students for the Fall 2019 application cycle, but if you are planning to apply in 2020, feel free to reach out! http://www.facebook.com/HanoiGMATtutor HanoiGMATTutor@gmail.com Math Revolution GMAT Instructor V Joined: 16 Aug 2015 Posts: 8595 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 1 Are the median and the average (arithmetic mean) of m, n, and k are the same? 1) n is the average (arithmetic mean) of m, n, and k 2) m+n<k This is a common mistake type 4(A) question in which both C and A can be an answer. The correct answer is A. _________________ Math Revolution GMAT Instructor V Joined: 16 Aug 2015 Posts: 8595 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 1 This is a 50-51 level question (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. _________________ Math Revolution GMAT Instructor V Joined: 16 Aug 2015 Posts: 8595 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 1 sairam595 wrote: MathRevolution wrote: 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. Please elaborate how to solve above question Here is an answer to your question! Attachments 1-st.jpg [ 2.24 MiB | Viewed 1183 times ] _________________ Math Revolution GMAT Instructor V Joined: 16 Aug 2015 Posts: 8595 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 1 Please be careful on Common mistake type 4(B) questions. When p, s, and t are positive integers, is p a factor of st? 1) p is a factor of s 2) t is a multiple of p There are 2 variabes in the original condition. Hence, there is a high chance that C is the correct answer. Using con 1) & 2), C is the correct answer. However, since this is one of key questions, we can apply the common mistake type 4(B). Then, we get 1)=2). The answer is always yes and the condition is sufficient. Hence, the correct answer is D. _________________ Math Revolution GMAT Instructor V Joined: 16 Aug 2015 Posts: 8595 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 1 NandishSS wrote: MathRevolution wrote: This is a 50-51 level question (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. MathRevolution Could pls elaborate this que how the ans is D 1) if a certain number is 1, the greatest common divisor is always 1 2) in case of consecutive numbers, the greatest common divisor is also 1. Hence, the conditions are sufficient, and the correct answer is D. _________________ Senior Manager  S Joined: 24 Jun 2016 Posts: 344 GMAT 1: 770 Q60 V60 GPA: 4 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 1 MathRevolution wrote: If you change the original condition and the prolem, you all ways get the remainder of 1 if you divide 100x by 11 regardless of the value of x. Thus, you only need to know y. Therefore, the answer is . This is a typical 5051 level problem. (CMT 4(A)) Answer: A Your answer is wrong. If x = 0, the remainder in the division of 100x by 11 is 0, and if x = 3, the remainder is 3. Not the first time you've posted a wrong solution in this thread though. Posted from my mobile device _________________ Stuck in the 600's and want to score 700+ on the GMAT? If this describes you, we should talk. I specialize in getting motivated students into the 700's.$90/hour as of August 2019. I am not accepting any more students for the Fall 2019 application cycle, but if you are planning to apply in 2020, feel free to reach out!

HanoiGMATTutor@gmail.com
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MathRevolution wrote:
Below is 50-51 level question
The product of the units digit, tens digit, and hundreds digit of a positive 3-digit integer n less than 500 is 15, what is the value of n?
1) n>350
2) The sum of the units digit, tens digit, and hundreds digit of a positive 3-digit integer n is 8.
There are 3 variables in the original condition and 1 equation. Hence, there is a high chance that C is the correct answer. Since this is a key question, one of integer questions, we need to apply the CMT 4(A). Hence, using con 1), we get n=351. The condition is sufficient and the correct answer is A.

Wait hold on. If the 3 digits are 1, 3, and 5, how is it possible that their sum is 8?

This is a terribly written question.
_________________
Stuck in the 600's and want to score 700+ on the GMAT?
If this describes you, we should talk. I specialize in getting motivated students into the 700's.

\$90/hour as of August 2019. I am not accepting any more students for the Fall 2019 application cycle, but if you are planning to apply in 2020, feel free to reach out!

HanoiGMATTutor@gmail.com
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8595
GMAT 1: 760 Q51 V42
GPA: 3.82
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What is the difference between the circumferences of 2 circles such that the diameters of the circles are 10 and 11?

A. $$\frac{π}{2}$$
B. $$π$$
C. $$\frac{3π}{2}$$
D. $$2π$$
E. $$\frac{5π}{2}$$

==> The circumference of a circle is πd, thus $$π(11-10)= π$$. Therefore, the answer is B.
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Math Revolution GMAT Instructor V
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Posts: 8595
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1
xy=?
1) y=x-1
2) y^2=-|x-1|

==> a^2+b^2=0 or |a|+|b|=0 is satisfied by a=b=0 only. Thus, according to the same logic, a^2+|b|=0 also must be a=b=0. Then, you get 2) y^2=-|x-1|, y^2+|x-1|=0, which is y=0 and x=1.

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Which of the following is the closest to 11*10^20–9*10^10?

A. 10^2 B. 10^7 C. 10^10 D. 10^20 E. 10^21

=>9*10^10 is a relatively small number compared with 11*10^20.
11*10^20–9*10^10 is approximate to 11*10^20, which is similar to 10^21.

Ans: E
_________________ Re: The Ultimate Q51 Guide [Expert Level]   [#permalink] 29 Aug 2017, 00:49

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# The Ultimate Q51 Guide [Expert Level]

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