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Intern  Joined: 14 Mar 2014
Posts: 19
Schools: HBS '17
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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1
chetan2u wrote:
ruhibhatia wrote:
MathRevolution , can you please explain the solution of the below question.

When both positive integers a and b are divided by 7, both have a remainder of 4. What is the remainder when ab3 is divided by 7?
A. 6
B. 5
C. 4
D. 3
E. 2

Can we assume that a and b and single digit integers, since abc3 is a three-digit integer?

Hi ruhi,
there are two things which ab3 can mean..a three digit number or a*b*3..
1)if ab3 is three digit number, as you have said a and b should be a single digits..
so a and b have to be 4, as the next number to leave a remainder of 4 would be 11, which is not a single digit number..
so our number is 443.. and remainder when 443 is divided by 7 is 6..
2)if ab3 actually meant a*b*3...
remainder will be 4*4*3=48..
48 when divided by 7 leaves a remainder 6..

Hope it helps u

hi Chetan

one correction:>> 443/7 will give remainder 2. but i agree with what you say... it should be clear whether ab3 is 3 digit number or a product.

Thanks Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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One of common questions is the distance between two absolute values.
On the number line m, s, t are there. If t and m are positive, is m=t?
1) |t-s|=|m-s|
2) s<0
There are 3 variables (m,s and t) in the original condition. In order to match the number of equations and the number of variables, we need 3 equations. Hence, there is high chance that E is the correct answer. Using both the condition 1) and the condition 2), we get a diagram like below.
The answer is always yes, and the conditions are sufficient. Hence, the correct answer is C.
Attachments 1.png [ 6.69 KiB | Viewed 1974 times ]

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Math Revolution GMAT Instructor V
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Also, there are speed questions that include the concept that the same time passed for the subjects in the test.
Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many minutes it takes John to reach the station?
A. 5 min B. 6 min C. 7 and 1/2 min D. 8 min E. 10 min
Since the question states “after 15 minutes”, Tom traveled 15/4km in 15 minutes. John traveled 10/4km in 15 minutes. Hence, John needs to travel (15/4)-(10/4)km=5/4km more. The speed of John is 10km per an hour and 1 km per 6 minutes. Hence, in order to travel 5/4km, it takes him about 6(5/4) minutes more. Then, 6(5/4)=15/2 minutes. Hence, the correct answer is C.
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There are many “relationship” question involving statistics.
(ex 4) Last year what is the median rainfall per month?
1) Last year each of the first 6 months has 8,000 as its monthly rainfall
2) Last year the greatest rainfall is 9,000
Since mean, median and range do not have relationships to each other, you can generally think E as the correct answer.
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Below is a very common percentage question.
If \$1,500 is increased by 1,300 percent, the result is what?
A. \$18,000 B. \$19,500 C. \$21,000 D. \$22,500 E. \$24,000
You can solve this question by IVY Approach. Increased by: +, Percentage: 1/100… Then, 1,500+1,300(1/100)(1,500)=14(1,500)=2,100. Hence, the correct answer is C.
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Below is a geometry question.
If AB=5, BD=3, BC=7 and AD⊥BC, AC=?
A. 8√2 B. 6√2 C. 4√2 D. 8√3 E. 6√3

According to Pythagorean theory, A=4 and DC=4. Then, AC=4√2. The answer is C.
Attachments 11.png [ 7.95 KiB | Viewed 1879 times ]

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Math Revolution GMAT Instructor V
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Please remember that questionsnowadays contain characteristics of our daily lives. It is important that non-American students to somewhat get used to or have general understanding of the culture of the United States.
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As said above, we have categorized some questions as dead or live questions. This means that there are some questions used in previous tests are being reused in today's test unlike others. It will certainly help to practice old types of questions.
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Intern  Joined: 06 Mar 2015
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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[*]Example 2:
40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 30 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?
A. 1/4
B. 9/14
C. 2/3
D. 7/8
E. 8/7

[Side effect rate for ducks of a certain sex = (number of ducks of that sex which had side effects) / (total number of ducks of that sex)]
[/list]

Hi,

I don't seem to understand how you have derived side effect rate for ducks?

The problem says there are 40% male ducks and 60% female ducks in the side effects study.
It further states some of the ducks had side effects - ......... (It does not mention how many have side effects or any % of the side effect rate)
Further states that 30% of the ducks who had side effects are male. Hence 70% of ducks that had side effects are female.

But we don't have the No of ducks who have side effects or the % of ducks who have side effects.
Hence how can we calculate "the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?"

For example if i presume that the % of ducks that were effected were 40%, the i can say that 30% of these were male and hence male ducks effected are 12%.
Then i can go ahead and calculate side effect rate as follows - 12/40*60 = 18
Calculate same ways for female and then that should give me the ratio.

Can you confirm where i am wrong, if i am?
Math Revolution GMAT Instructor V
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In a certain company, the manager gave 3 employees an off-day from Mon to Fri. If all 3 employees cannot have the off-day at the same time, how many possible cases are there?
A. 80 B. 100 C. 108 D. 112 E. 120

This is one of 50-51 level questions and also a key question. From 5*5*5-5=120, we can see the correct answer is E.
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In a certain company, 38% of female employees are managers and 25% of male employees are managers. What percent of all the employees in the company are females?
1) 30% of all the employees in the company are managers
2) The total number of all the employees in the company is 500
manager NOT manager
Females
Males

In case of 2-by-2 questions, if there are three %, that condition is sufficient (only if the question is in %).
Hence, the con 1) is % and it is sufficient. Thus, the correct answer is A and it is one of the most challenging 50-51 level questions.
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Below question is related to common mistake type 4(B)
(integer) If x, y are positive integers, is xy a multiple of 5?
1) x is a multiple of 5
2) y is a multiple of 5

Since 1)=2), xy=always a multiple of 5. The answer is yes and the conditions are sufficient. The correct answer is D.
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A geometry question is a difficual question as well
If n is positive integer, is n a square of integer?
1) √n is a square of an integer
2) n3 is a square of an integer
From the original condition, there is 1 variable. Hence, there is a high chance that D is the correct answer. Using common mistake type 4(B), we get D as the correct answer.
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As always, there are questions that is combined with the common mistake type 3 and 4. Let’s take a look at a question below. This is a 50-51 level question and is a question that involves the common mistake type 4(A). You need to be strong at these questions and have to know the relationship between the Variable Approach method and the Common Mistake Types.
If m and m are integers, is m+n an odd?
1) mn=even
2) m-n=odd
Both C and B can be an answer in this case. And it is a 50-51 level question. If con 2) is m-n=odd, from (m,n)=(even,odd) or (odd,even), the answer is always yes and the condition is sufficient. Thus, the correct answer is B.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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It is a 50-51 level question and is related to common mistake type 4(A)
If r and x are integers, is rx a multiple of 5?
1) r=0
2) r+x is a multiple of 5
From r=0, since 0 is a multiple of any numbers. The answer is yes and the condition is sufficient. Hence, the correct answer is A.
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There are 72 employees that work in department A, B, C, D. If each department has at least 17 employees, how many employees work in department B?
1) The department with the most employees has 20 employees.
2) Department C has 3 more employees than department B.
This is a common mistake type 4(B) question, in which both C and B can be answers.
The answer is B in this case.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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MathRevolution,
.
I had read in certain external forums that people from a certain demography memorize as many quant problems they can and their sole intent is to do this when writing the GMAT and they return with most of the questions memorized. Is that how you declare that these are the questions or type of questions you see on GMAT?
.
Your threads leads me to think as if you know what will and will not be tested on GMAT whereas the threads by test takers suggest otherwise. Can you clarify?
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
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1
A certain set contains 19. Is the range of them greater than 20?
1) The maximum of the set is 40
2) The set contains 25
Both C and A can be an answer here. However, if we apply the common mistake type 4(A), the correct answer is A.
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Good question. Are these from the recent GMAT administrations or practice sets created by you?
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
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This is a very touch 50-51 level question.
Is x^3(y)<0?
1) x^5(y)<0
2) x^2(y)<0
_________________ Re: Overview of GMAT Math Question Types and Patterns on the GMAT   [#permalink] 25 Jul 2016, 19:45

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