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If 10!/(10-r)!<1,000, what is the greatest possible value of r?

A. 1 B. 2 C. 3 D. 4 E. 5

==>If you substitute r=1, 2, 3, 4.., for r=4, you get 10!/(10-4)!=10*9*8*7=5,040>1,000, and for r=3, you get 10!/(10-3)!=10*9*8=720<1,00. Thus, the greatest possible value of r is r=3.

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

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13 Jul 2017, 08:18

MathRevolution wrote:

As always, the more advanced questions combined with the mistake type 3 and 4 are frequently given on GMAT Math. Let's have a look at the question below, which is a current question. This question is also the mistake type 4(A), which is on the level of score 50-51. You have to be very confident with questions like this. You have to know the relation between approach method to variables and the mistake types. In particular, questions including number and ratio are frequently given, in which ratio is always an answer. The question below also contains 1) ratio and 2) number and the answer is A as well.

(ex 1) A certain store, books are sold. Books are hard cover or soft cover and hard cover books sold $10 each and soft cover books sold $6. Is the number of hard cover books sold greater than that of soft cover books sold? 1) The average price sold of total books is $9 2) The number of hard cover books sold is 100

Answer: A

MathRevolution What is mistake type 2? Can you name the other mistake types also?

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

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13 Jul 2017, 08:35

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.

Ans. A? Is there any shortcut to reach ans. for this ques?

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

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13 Jul 2017, 08:43

MathRevolution wrote:

As always, questions combined with the mistake type 3 and 4 are evolving and often given. The below question is recent, which also belongs to the mistake type 4(A) at level of score 50-51. You should be able to solve this type of question and know the relation between method of approach to variables and the mistake types.

(ex 1) If x and y are different prime numbers, and n is a positive integer, what is the factors’ number of x(y^n)?

1) xy=21 2) n=2

Answer: B

The answer is C but also B, which is a typical question at level of score 50-51. You have to be strong with a question like this. Be cautious on integer or statistics questions, which make C the answer. Especially, be aware of the word "different" when questions with factor or prime factors are given.

The ans should be B. Why did you write C? Would you plz explain?

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

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13 Jul 2017, 09:20

MathRevolution wrote:

As always, more developed questions combined with the mistake types 3 and 4 appear on GMAT. Look at the question below. This is a very recent one, which also belongs to the mistake type 4(A) at level of score 50-51. You should be able to tackle this type of question. Be aware of a relation between the method of approach to variable and the mistake types.

(ex 1) What is the median of 5 numbers? 1) They have 5 and 15 2) 3 of them are 10 each

Answer: B

In this question, the answer is C but also B, which is a typical question at level of 50-51. You have to be strong with this type of question. Focus on integer or statistics questions that make C the answer.

Hello! I can't understand what do you mean by "the answer is C but also B" I think B is the answer because if we know that the frequency of occurance of number 10 is 3 times in a set of 5 numbers then the remaining numbers do not matter. Whether the numbers are >10 or < 10 the median will be 10 & hence B is the answer. Please correct me if I am wrong
_________________

If you appreciate my post then please click +1Kudos

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

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13 Jul 2017, 09:23

MathRevolution wrote:

How to Improve GMAT Quant from Q49 to a Perfect Q51

A lot of people on the forum are not happy with their 79th percentile Q49 scores. These are good scores but understandably some just need a higher one to beat their competition. This guide is designed to be a comprehensive overview for very serious test-takers (those with Q49 already) who are looking to get to the elusive Q51. Important: You only have one shot at the Q51 on your test. You will face a handful of elite questions and you need to be ready to face them. Here is a detailed inventory of the tough Q51 question types, concepts, and tips how to handle them. For the overview of what question types appear on the GMAT, see this post: http://gmatclub.com/forum/overview-of-g ... 11809.html

1. Do I have to get ALL Quant questions right to Q51?

Answer: not all but you have to get to hard questions and to do that you have to answer 15-20 questions right in a row. Since GMAT Math is in a form of CAT (Compute Adaptive Test), the questions get harder if you correctly answer questions, and get easier when you get easy questions wrong. Therefore, after answering the first 7 questions correctly, you can expect your score to be around 35-40. These first few questions will be fairly basic and straightforward. In fact, you will have to keep going for a while, as the questions that are representative of difficulty and score of 50-51 usually appear after a question number 20. Therefore, it is crucial to get the first 20 questions right as otherwise you will not be able to get to hard enough questions to even get a shot at Q50/51.

2. What Concepts/Topics Do I Focus when Targetting Q51 Score?

Overview: It is vital to note in preparation for GMAT Math that Integer Properties, Statistics, Probability, Inequality, and Absolute Value are the most important 5 chapters. Among them, Integer Properties and Statistics are especially important. If you get every question right in “Integer section”, your score can go up as high as 49, and if you get every question right only in “Integer and Statistics section”, you can expect 50 for Math section. Thus, it is vital that you get every key question right from those five areas to score a 51.

Integer Properties and Statistics. One question format in particular that keeps reoccurring is a question with a combination of 2 or 3 of “different positive integers, median, mean, range, absolute value, and inequality” (that’s what we have seen on the test and what we keep hearing from our students). Answering it correctly or incorrectly will be the deciding factor, whether you get the perfect score or not – no second chances. These can be both PS or DS and they are especially hard in DS and you will have to solve them as they are designed to look deceivingly obvious or simple, for example have 3 variables but only 2 equations/data points. (Note: Math Revolution has a methodology that allows answering up to 80% of easy/medium DS questions without solving them by matching the number of variables and the number of equations). It is not easy to solve these types of questions in just two minutes and they are designed this way on purpose.

Here are 2 examples of the Statistics and Integer Questions:

Statistics: There are 3 different positive integers. If their average (the arithmetic mean) is 8, what are their values? 1) The largest integer is twice the smallest integer. 2) One of them is 9.

Integer Properties: The smallest of 7 positive integers is 1. Is the range of them greater than 3? 1) The average (the arithmetic mean) of them is 4. 2) The median of them is 4.

Additional Practice: please try questions DS: #14 from OG15, or Question #121, #135 from OG 2016. (OG 2016 Quant directory).

Logic Questions – on the path to Q51, you will have to master Trick Questions or as we call them “Mistake Type” questions. If you get them wrong, the highest you can count on is Q49.

Side Note: What is a “Mistake Type” Trap Question? There are 5 types of questions that GMAT Math test makers design to trap students. Here are 2 of the most commonly used on the DS:

DS Trap 1: If answer choice C seems too attractive and obvious, go back and check choice A or B alone. Look at the example below. What is the value of a and b ? 1) 2a + 6b = 8 2) 3b + a = 4 More practice in this C-trap collection http://gmatclub.com/forum/c-trap-questions-177044.html

DS Trap 2: If an answer choice A or B seem too attractive and obvious, consider answer choice D. A good example is in this discussion

TIP! Important to note that GMAC likes to use DS questions as the deciding factor for their Q50/Q51 scores…. most likely because DS questions are unique to the GMAT and thus would be a good level “measuring stick” even for a person with a strong quantitative background. Therefore, if you are looking to score Q51, you will need to pay especially careful attention to the DS questions and learn how to spot Mistake Type/Trap Questions.

3. Analysis of Specific Question Types to Master for Q51

DS Tips:

As mentioned above, Integer and Statistics are the main chapters to focus for DS. Besides the “Mistake Type”, one specific type of DS questions to master is Hidden Integer Questions. These questions often present prices of products, number of fruit, coins, people, stamps, cars, etc as “hidden integers”. These are countable numbers that are not given to increase complexity. These are logic questions and you should solve them logically rather than calculation. It is possible to calculate and solve these question that way but it takes much longer and a lengthy calculation is exactly the trap the test wants to catch you with – to waste your time and slow you down.

Integer Properties: M bought several pencils. If each pencil cost either 23-cent or 21-cent, how many 23-cent pencils did M buy? 1) M bought a total of 6 pencils 2) The total price of all pencils M bought was 130 cents

→ The answer choice C is very attractive, but the correct answer is B. Pencil is a hidden integer, but if you don’t recognize this fact, you would say C is the answer. In addition, Statement 1 is actually not giving you any helpful information

Additional Practice: refer to OG15 DS: Question #132, OG16 DS: Question #47, #148, #150 and #153.

That is to say, among Mistake Types, there are many cases in which A or B easily seem like a right answer – but, in fact, D is a correct answer. In this case, one or two questions of this type play a decisive role in leading to a perfect 51.

Integer Properties: Numbers a and b are positive integers. If a^4-b^4 is divided by 3, what is the remainder? 1) When a+b is divided by 3, the remainder is 0 2) When a^2+b^2 is divided by 3, the remainder is 2

Additional Practice: please also refer to OG16 DS: Question #34 and Question #36.

In addition, You should be comfortable taclking inequality problems such as “greater than” and “less than” questions if you want to get a perfect 51. You should practice these so that your mind clicks when asked to figure out the minimum value (if asked “greater than”) and the maximum value (if asked “less than”).

Statistics: There are five homes. If the median price of a home is $200,000, is the range of all prices greater than $80,000? 1) The average price of the five homes is $240,000. 2) Three of five homes have the same price.

→ C looks like a right answer choice at first. However, the correct answer is A.

Of course we would be incomplete if we did not include the famous DS Probability questions that you are likely to see on your quest to Q51. Here is an example:

Probability: There are only apples and oranges in a box. What is the probability that the fruit selected at random from the box is an apple? 1) There are 2 apples in the box 2) The ratio of the number of apples to the number of oranges is 1 to 4.

→ C is an attractive answer choice but A is a correct answer.

Problem Solving Tips

Be prepared to see questions about finding Hidden Integers and problems on the so-called “Pigeonhole Principle”. You have a good chance of seeing one of them. We have provided the definition of the Hidden Integer questions above in the DS section. Tip: if you see integer questions just like the number of fruits, people, animals, stamps, and candies, it is a good chance you are facing this question type. The name of Pigeonhole principle comes from the old problem of having to calculate the number of cases of pigeons entering pigeon lofts. (it will more clear once you read the example below).

Integer Properties: There are 10 red balls, 10 blue balls and 10 white balls in a box. What is the maximum number of balls you can draw from the box and have fewer than 5 balls of the same color drawn?

→ This question asks for the maximum number of balls you can have, so the correct answer should be the unluckiest case. If you draw 4 red balls, 4 blue balls and 4 white balls all together, there can be no more than 4 balls of the same color. Hence, the correct answer choice is E.

Questions related to Murphy’s Law and Sally’s Law are the questions for a perfect 51 in PS. * (Integer) There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts needed to confirm that each of the 5 keys matches each of the 5 locks? A. 5,15 B. 4,15 C. 5,10 D. 4,10 E. 5,20

→ D is the correct answer choice. Can you figure out how to solve it quickly? Good – remember ths approach so you can refer to it on your test.

5. Conclusion

In this way, a perfect 51 is not an outcome of luck; you have to concentrate to excel in Integer and Statistics parts to that end. Especially, DS questions often will be the determining factor of a perfect Q51, and, therefore, you should not be misled by Mistake types. Please pay special attention to the Mistake type questions. Please remember solving 37 questions in 75 minutes in actual GMAT exam is a big challenge. You will need to manage time effectively to solve hard questions in 2 minutes or less per question. How can you reduce the time spent per question significantly? Since GMAT is a logical test, you should not question whether you can solve a problem or not, but you should practice to reach answers logically without having to solve problems.

*** We are math experts and if you find any grammatical issues – that is because we spend all of our time focusing on math; sorry grammar. Note that the information herein is based on the knowledge and experience of Max Lee, who taught 30,000+ students and solved 100,000+ problems in the past 15 years. He discovered and analyzed types of GMAT Math questions after continuous and numerous interviews with students who have achieved a score of 49 to 51 in the actual GMAT exam. Thus, please note that the information is herein is based solely on experience of Max Lee. Due to the nature of the test and lack of transparency about the algorithm this guide is a best efforts attempt based on the best information available. If you have any questions or different information, please post it here for the benefit of the community.

How many probability questions can one expect in GMAT? Can probability and integer properties be combined?

1) The smallest prime factor of x is 2. 2) The greatest prime factor of x is 13.

==> In the original condition, there is 1 variable (x) and in order to match the number of variables to the number of equations, there must be 1 equations. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), since x always has 2 as the factor, you get x=even, hence yes, it is sufficient. For con 2), you get x=2*13 yes but x=13 no, hence it is not sufficient.

An alarm of a certain clock rings every 15 minutes. If the clock’s alarm rings first at 12:00, when will the 15th alarm ring?

A. 14:30 B. 14:00 C. 14:30 D. 15:00 E. 15:30

==> Since the alarm rings every 15 minutes, it rings 4 times in an hour. Thus, the 15th alarm rings after 3 hours plus 3 times. Since 13th alarm is at 15:00, 15th alarm rings at 15:30.

Therefore, the answer is E. Answer: E
_________________

A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through the center of the larger circle, what is the ratio of the area of the region shaded to the area of the larger circle?

A. 1/2 B. 2/3 C. 3/4 D. 4/5 E. 5/6

==> Square of the ratio of the length=ratio of the area. The diameter of the smaller circle is equal to the radius of the larger circle, so the ratio of the length becomes 1:2. Then, the ratio of the area becomes 1^2:2^2=1:4. Thus, if the area of the smaller circle=k, the area of the larger circle=4k. Therefore, the area of the region shaded:the area of the larger circle=(4k-k):4k=3:4=¾.

If x, y, and z are positive integers, is x+y divisible by 3?

1) x+z is divisible by 3 2) y+z is divisible by 3

==> In the original condition, there are 3 variables (x,y,z) and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), you need 1 more equation, so E is most likely to be the answer. By solving con 1) and con 2), if x=y=z=3 yes, but if z=2, x=y=1 no, hence it is not sufficient.

Therefore, the answer is E. Answer: E
_________________

If the sum of all the even numbers from 1 to n(n: odd number) is 69*70, what is the value of n?

A. 135 B. 137 C. 139 D. 141 E. 143

==> If n=2m+1, the even numbers until 2m+1 becomes until 2m, and the sum of the even numbers is 2+4+…+2m=2(1+2+…m)=2m(m+1)/2=m(m+1). From m(m+1)=69*70, you get m=69, which becomes 2m+1=2(69)+1=139.

➔ For this type of questions, the answer is A. ==> In the original condition, there is 2 variable (x,y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), you get x^y=1^1=1, hence it is unique and sufficient. The answer is C. However, according to tip4, a trivial condition cannot be the answer, so if you solve con 1) and con 2) separately, for con 1), you substitute x=1, and get x^y=1^y=1, which is unique and sufficient.

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

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25 Jul 2017, 09:02

Hi, is there a short cut to find the answer to the 1st stats problem ?

I reduced statement 1 to 3a+b=24, where a<b<c and then substituted values, and concluded only 5,9,10 were possible. But this was only after I checked out the answer !

==> 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.

Hi, is there a short cut to find the answer to the 1st stats problem ?

I reduced statement 1 to 3a+b=24, where a<b<c and then substituted values, and concluded only 5,9,10 were possible. But this was only after I checked out the answer !

There is a total of 1,800 pages that needs to be typed. If it takes 90 minutes when a types alone, 45 minutes when b types alone, and 30 minutes when c types alone. How many minutes does it take if 3 of them work together?

A. 10min B. 12min C. 15min D. 18min E. 20min

==> For work rate questions, if there is a “together and alone”, you need to solve the question reciprocally. In other words, A: 1,800pg/90mins, B:1,800pg/45mins, C: 1,800pg/30mins, and if you assume A&B&C:1,800pg/t mins, you get (1/90)+(1/45)+(1/30)=(1/t), and from (1+2+3)/90=1/t, you get t=15.

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