A complete breakdown of GMAT Math question types and its history Updated on Aug 20th, 2020 What should you study more? Arithmetic? Geometry? Probability? All? When preparing for the GMAT, test-takers often ask about which math concepts are covered on the GMAT and about the most common question types that appear in the actual test. Therefore, in this article, I will not only delve into past trends but also the current trend of the GMAT Math test. Also, I will discuss the types of questions that appear on the test every month. You can also find our observations regarding the hardest question types that appear on the test here: The Ultimate Q51 Guide The scope of Math Tested on the GMAT 1. Topics that appear frequently on the GMAT - This is what you need to study and know: Integer: Questions in this section involve dividing an integer n by 5 or 10, solving the units digit for an integer n , finding the remainder of an integer n after dividing it by 3 or 9, and solving for factors and prime factors. Geometry: Questions in this section involve Pythagorean Theorem, special angles (1:1: \sqrt{2} , 1: \sqrt{3} :2), and solving for the area of different figures. Statistics: Questions in this section involve finding the average, standard deviation, median, and range. Speed Rate: Questions in this section involve solving average speed rate problems. Inequality: Questions in this section involve inequality questions that ignore squares and DS questions related to the inclusion relation. Equation: Questions in this section involve calculations using (a − b)(a + b) = a^2 − b^2. DS questions: Common Mistake Type questions that are determined and categorized by Math Revoluition NOTE: Please refer to the table below for additional types of questions that appear on the test. However, remember that the types mentioned above are the most common types of questions. Quant Topics and Types of Questions Tested on the GMAT Today Topics Questions that frequently appear Questions that appear occasionally Questions that infrequently appear Integer Remainders Factors multiples Evens and odds Prime factors GCD and LCM Remainder questions after dividing the number by 4 or 8 Consecutive integers Estimated integers Modula questions Gaussian integers Perfect numbers Numbers, Fractions, Decimals Decimal digits Rounding numbers Mixed and compound fractions Number lines Terminating decimals Reciprocals Undefined functions Non-real numbers Ratios, Rates, Proportions, and Percentages Properties of ratios Properties of work rates Percent changes Average speed Round trips Matching ratios Inverse proportions Equations Basics of factoring Polynomial equations Algebraic expressions Discount problems Profit problems Duplicated square roots Mixture problems Data interpretation problems Indeterminate and impossible equations Exponents Properties of exponents Comparison of exponents Operations of numbers with exponents Inequalities Five fundamental concepts 3 properties Relationship between a question and the conditions (DS) 1 is standard Maximum and minimum ranges The effect of negative numbers Positive numbers Non-zero numbers Non-negative numbers Absolute Value 4 properties 7 frequent cases Distance between x and y on a number line Relationship between the nth root and absolute value Two types of absolute value inequalities Counting Methods Factorials Combinations Permutations with the same letters Permutations Circular permutations At least (counting methods) Permutations with restrictions on the order Probability Events and probability Relationship between numbers and ratios At least (probability) The rule of addition in probability Binomial Theorem Independent and exclusive events Statistics Means Medians Ranges Standard deviations Harmonic means Modes Sets with the same elements Normal distributions Modes Relationships among mean, median, range, and standard deviation Geometry Pythagorean Theorem Circles Lines Properties of triangle sides Special angle problems Areas of geometric diagrams Cubes Rectangular solids Circular cylinders Spheres Regular n-polygons (DS) Quadrilaterals Number of diagonals in n-polygons Diagonal Theory Heron’s Theory Area of parallelograms and trapezoids Coordinate Geometry Quadrants Line equations x- and y-intercepts Parabolas Symmetric axis Discriminant Equation of a circle Distance between points and a line Functions Functions with repeated intervals Additional graphs Reflections Binary operations Domains Codomains Ranges Equation of an ellipse Sets Venn Diagrams Intersections Unions Complements Addition rule 3 sets Subsets Start with the intersection Disjoint or mutually exclusive sets Difference between two sets Sequences Arithmetic and geometric sequences Counting consecutive integers Simple and compound interest rates Sum of arithmetic and geometric sequences Other sequences Counting consecutive multiples Adding the reciprocals of consecutive integers Note: Max Lee, founder of Math Revolution has been analyzing these types of questions for decades. 2. Mathematical concepts that are partially covered In the case of sequences, only fundamental concepts such as arithmetic and geometric sequences are included within the scope of the test. This means more complex concepts like difference sequences will not be tested. There are also questions regarding probability and statistics, but these questions tend to be fairly simple. In other words, concepts like combinations with repetition, conditional probability, discriminating distributions, and average deviations will not be on the test. In the end, test-takers are not trying to go to a graduate program in mathematics! 3. Questions/Topics that Never Appear The level of GMAT Math is generally what people learn in high school. This means that the scope of GMAT Math does not include difficult concepts like trigonometrical functions, logarithms, differentiation, integration, or limits. Also, even though basic concepts such as calculating volume and areas of geometric figures and finding diagonal length appear in the test, more difficult concepts such as vectors or inner products do not appear. During decades of experience in teaching GMAT Math, I have encountered only 2 matrix questions. Due to its infrequency, we can say matrixes are not included within the scope of GMAT Math. Additionally, questions regarding imaginary numbers - a complex number ( \sqrt{-1} = i ) - also are not included in GMAT Math. NOTE: During my extensive experience teaching GMAT Math, I found some patterns on the GMAT test. It was that some questions, which were on the test in 2001, have reappeared recently. Even though I cannot give any assurance as to whether GMAC - the question bank of GMAT Math – reutilizes its questions, I believe that it occasionally uses some questions that appeared on previous exams along with new questions it creates every year. History and Evolution of GMAT Math In this part, I will analyze GMAT Math trends beginning from 2001, the year when I started teaching. Evolution of Topics Tested Since 2001 Topics 2001 - 2005 2006 - 2011 2011 - Today NOTE Arithmetic 40% 40% 30% Consistent Algebra 35% 30% 30% Consistent Geometry 10% 10% 15% The number of questions is increasing, and the questions are becoming more difficult. Word Problems 5% 5% 5% The number of work rate questions is increasing. Data Interpretation 5% 5% 10% The number of questions is increasing, and the questions have characteristics related to daily life. Common Mistake Types 3 and 4(A or B) 5% 5% 10% The number of questions is increasing, and the questions are becoming more difficult. Note: This table is based on my decades of experience. Conclusion I want to emphasize that it would be especially helpful for those preparing for the GMAT Math to focus on mastering the integer and statistics sections. In fact, I have seen students who get every integer and statistics question right in prep tests (mock tests distributed freely by GMAC) and achieve late 40’s. Additionally, I want to advise test-takers to focus on studying questions that appear every month. As explained earlier, integer questions are the most common type of questions (not only the number of questions but the number of different types of integer questions are numerous). Hence, spending more time learning these areas than on other concepts would be an effective and time-efficient way to tackle GMAT Math. Also, the recent trend of GMAT Math is that questions contain characteristics of daily life. Thus, it would be helpful for test-takers to have a general understanding of the culture of the United States. Additionally, questions involving geometric figures are increasing in number. I want to advise test-takers to spend some time learning this concept. As mentioned earlier, questions are becoming wordier. So, while studying the Official Guide, please spend some time observing the trend and styles of the questions. It is vital for test-takers to regularly exercise generating equations after reading difficult and wordy questions. As many test-takers are already aware, solving 31 questions in just 62 minutes is very challenging. Therefore, it is important to have strategies for time management. Many people can solve simple questions in approximately 1 minute with no problems. However, those who solve questions using the conventional method of approach take approximately 5 minutes to solve just one difficult question. Thus, it is very helpful to learn various techniques and tips that can guide test-takers to solve difficult questions in approximately 2 minutes. The average GMAT score is 38 (it is 33 for the United States alone). However, I firmly believe that if test-takers clearly understand about GMAT Math trends and the history of the test, they will not only be able to exceed the average score but will be able to score at least 45 or even get a score of 49 to 51. Thank you so much for reading this article, and I wish you the best of luck. *** 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, Founder of Math Revolution who has taught 30,000+ students and solved 100,000+ problems over the last few decades. He discovered and analyzed types of GMAT Math questions after continuous and numerous interviews with students who wrote the GMAT exam. Thus, please note that the information herein is based solely on the experience of Max Lee. Due to the nature of the test and lack of transparency regarding the algorithm used in preparing the questions, this guide is a best-effort attempt based on the best information available. If you have any questions or other information to share, please feel free to post it here for the benefit of the community.

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Overview of GMAT Math Question Types and Patterns on the GMAT

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MathRevolution

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[Math Revolution GMAT math practice question]

Is xy>0?

1) x+y>0
2) |x|+|y|<1

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
If x = 1/2 and y = 1/4, then xy > 0 and the answer is ‘yes’.
If x = 1/2 and y = -(1/4), then xy < 0 and the answer is ‘no’.

Since the answer is not unique, both conditions are not sufficient, when taken together.

Therefore, E is the answer.
Answer: E

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Please tell me the pattern most which is most recently applied in Gmat.

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[Math Revolution GMAT math practice question] 7

What is the units digit of (3^101)(7^103)?

A. 1
B. 3
C. 5
D. 7
E. 9

=>

The units digit is the remainder when (3^101)(7^103) is divided by 10.

The remainders when powers of 3 are divided by 10 are
3^1: 3,
3^2: 9,
3^3: 7,
3^4: 1,
3^5: 3,
…
So, the units digits of 3^n have period 4:
They form the cycle 3 -> 9 -> 7 -> 1.
Thus, 3^n has the units digit of 3 if n has a remainder of 1 when it is divided by 4.
The remainder when 101 is divided by 4 is 1, so the units digit of 3^101 is 3.

The remainders when powers of 7 are divided by 10 are
7^1: 7,
7^2: 9,
7^3: 3,
7^4: 1,
7^5: 7,
…
So, the units digits of 7^n have period 4:
They form the cycle 7 -> 9 -> 3 -> 1.
Thus, 7^n has the units digit of 3 if n has a remainder of 3 when it is divided by 4.
The remainder when 103 is divided by 4 is 3, so the units digit of 7^103 is 3.

Thus, the units digit of (3^101)(7^103) is 3*3 = 9.

Therefore, the answer is E.
Answer: E

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10 Sep 2018, 18:40

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[Math Revolution GMAT math practice question]

Is n an odd number?

1) n is the sum of 2 prime numbers
2) n is a multiple of 11

=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If n = 2 + 3, then n = 5 is odd and the answer is ‘yes’.
If n = 3 + 5, then n = 8 is even and the answer is ‘no’.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
If n = 11, then n is odd and the answer is ‘yes’.
If n = 22, then n is even and the answer is ‘no’.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
If n = 2 + 31, then n = 33 is odd and the answer is ‘yes’.
If n = 13 + 31, then n = 44 is even and the answer is ‘no’
Since we don’t have a unique solution, both conditions 1) and 2) are not sufficient, when taken together.

Therefore, E is the answer.

Answer: E
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

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13 Sep 2018, 18:13

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[Math Revolution GMAT math practice question]

If r is a positive integer, n=^r3 and 4,14, and 27 are factors of n, which of the following must be a factor of n?

A. 16
B. 32
C. 36
D. 48
E. 64

=>

Since 4 = 2^2,14 = 2*7, 27 = 3^3 are factors of n and n is a perfect cube, the smallest possible value of n is 2^3*3^3*7^3.

When n = 2^3*3^3*7^3, 16 = 2^4, 32 = 2^5, 48=2^4*3 and 64 = 2^6 can’t be factors of n. The only answer choice that is a factor of n is 36 = 2^2*3^2.

Therefore, the answer is C.
Answer: C

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17 Sep 2018, 18:25

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[Math Revolution GMAT math practice question]

x=?

1) x^3+x^2+x=0
2) x=-2x

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
x^3+x^2+x=0
=> x(x^2+x+1)=0
=> x = 0 since x^2+x+1 ≠ 0
Condition 1) is sufficient.

Condition 2)
x = -2x
=> 3x = 0
=> x = 0
Condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

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20 Sep 2018, 18:29

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[Math Revolution GMAT math practice question]

What is the value of 22C19?

A. 770
B. 1540
C. 3080
D. 4620
E. 6160

=>

Since nCn-r = nCr,
22C19 = 22C3 = (22*21*20)/(1*2*3) = 11*7*20 = 1540.

Therefore, the answer is B.
Answer: B

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24 Sep 2018, 06:26

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[Math Revolution GMAT math practice question]

If n is an integer, is n(n+2) divisible by 8?

1) n is an even number.
2) n is a multiple of 4.

=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If n is an even integer, then n and n + 2 are two consecutive even integers.
Products of two consecutive even integers are multiples of 8 since one of them must be a multiple of 4, and the other a multiple of 2.
Condition 1) is sufficient.

Condition 2)
Since n is a multiple of 4, n + 2 is an even integer.
Thus, n(n+2) is a multiple of 8.
Condition 2) is sufficient.

Therefore, D is the answer.

Answer: D

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

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[Math Revolution GMAT math practice question]

x^4+12x^3+49x^2+78x+40 can be factored as a product of four linear polynomials with integer coefficients. Which of following cannot be a factor of x^4+12x^3+49x^2+78x+40?

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

=>

Assume x^4+px^3+qx^2+rx+s = (x+a)(x+b)(x+c)(x+d).
Then, s = abcd.
The constant terms a, b, c and d of the linear factors are factors of the constant term s of the original polynomial.

Since 3 is not a factor of 40, x + 3 cannot be a factor of the original polynomial x^4+12x^3+49x^2+78x+40.

Therefore, C is the answer.
Answer: C

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Are you sure that statistics is up there with the most important concepts? I have seen various books and online courses which stress upon Number Properties, Algebra and geometry as the three main areas to concentrate from.

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30 Sep 2018, 23:01

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[Math Revolution GMAT math practice question]

Is x>x/y?

1) y>1
2) xy>0

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The question x>x/y is equivalent to xy(y-1) > 0 as shown below:
x>x/y
=> xy^2 > xy since y^2 > 0
=> xy^2 – xy > 0
=> xy(y – 1) > 0

Condition 1) tells us that y – 1 > 0, and condition 2) tells us that xy > 0. Thus, both conditions together are sufficient.

Therefore, C is the answer.

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03 Oct 2018, 18:23

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[Math Revolution GMAT math practice question]

Is |x+y|<|x|+|y|?

1) x<0
2) y>0

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The question |x+y|<|x|+|y| is equivalent to xy<0 as shown below

|x+y|<|x|+|y|
=> |x+y|^2<(|x|+|y|)^2
=> |x+y|^2-(|x|+|y|)^2< 0
=> (x+y)^2-(|x|+|y|)^2< 0
=> x^2+2xy+y^2-(|x|^2 +2|x||y|+|y|^2) < 0
=> x^2+2xy+y^2-(x^2 +2|xy|+y^2) < 0
=> 2xy-2|xy| < 0
=> xy-|xy| < 0
=> xy < |xy|
=> xy < 0

This occurs if x < 0 and y > 0. Thus, both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

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[Math Revolution GMAT math practice question]

The 2 lines x+2y=3, 2x+py=q have infinitely many points of intersection in the xy-plane. Which of the following could be the value of p?

A. 0
B. 1
C. 2
D. 3
E. 4

=>

If the 2 lines have infinitely many points of intersection, their equations must specify the same straight line.
The equation x+2y=3 is equivalent to 2x+4y=6.
So, p = 4 and q = 6.

Therefore, the answer is E.
Answer: E

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07 Oct 2018, 18:41

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[Math Revolution GMAT math practice question]

If the integers p, q, r, and s satisfy p<q<r<s, are they consecutive?

1) r-q=1
2) (p-q)(r-s)=1

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 4 variables (p, q, r and s) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since r – q = 1 or r = q + 1 from condition 1), q and r are consecutive integers.
Since we have (p-q)(r-s) = (q-p)(s-r) =1, where p < q, r < s and p-q and r-s are integers, we have q-p = 1 and s-r = 1, or q = p +1, and s = r +1.
Thus p, q, r and s are consecutive integers and both conditions are sufficient when applied together.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
p = 1, q = 2, r = 3 and s = 4 are consecutive integers satisfying r – q = 1, and the answer is ‘yes’.
P = 1, q = 2, r = 3 and s = 5 satisfy r – q = 1, but are not consecutive integers, and the answer is ‘no’.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
p = 1, q = 2, r = 3 and s = 4 are consecutive integers satisfying (p-q)(r-s)=1,
and the answer is ‘yes’.
p = 1, q = 2, r = 4 and s = 5 satisfy (p-q)(r-s)=1, but are not consecutive integers, and the answer is ‘no’.
Since we don’t have a unique solution, condition 2) is not sufficient.

Therefore, C is the answer.
Answer: C

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[Math Revolution GMAT math practice question]

If xy=y, |x|+|y|=?

1) x=-1
2) y=0

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Modifying the original condition:
The equality xy=y is equivalent to y = 0 or x = 1 as shown below:

xy=y
=> xy-y=0
=> y(x-1)=0
=> y = 0 or x = 1

Since we have 2 variables (x and y) and 1 equation (xy=y), D is most likely to be the answer.

Condition 1)
Since x = -1 from condition 1) and y = 0 or x = 1 from the original condition, y = 0.
Thus, |x| + |y| = |-1| + |0| = 1.
Condition 1) is sufficient.

Condition 2)
If x = 1 and y = 0, then |x|+|y| = 1.
If x = 2 and y = 0, then |x|+|y| = 2.
Since we don’t have a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

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11 Oct 2018, 18:15

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[Math Revolution GMAT math practice question]

Tom’s Mom is five times as old as him. In 6 years, Tom’s Mom will be three times as old as him. How old is Tom now?

A. 3
B. 4
C. 5
D. 6
E. 7

=>

We can set up this question using the IVY approach. “Is”
can be converted to “=” and “times” can be converted to the multiplication sign “x”.

Let m and t be Tom’s Mom’s age and Tom’s age now, respectively.
Then m = 5t since Tom’s mom is five times as old as Tom.
We also have
m + 6 = 3(t + 6) since Tom’s mom will be three times as old as Tom in 6 years.

Plugging m = 5t into the second equation yields
5t + 6 = 3t + 18 or 2t = 12.
So, t = 6.

Therefore, the answer is D.
Answer: D

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I will impart the post to my companions. I'm extremely awed with your article, such incredible and useful learning you specified here

MathRevolution

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14 Oct 2018, 18:59

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[Math Revolution GMAT math practice question]

The terminal zeros of a number are the zeros to the right of its last nonzero digit. For example, 30,500 has two terminal zeros because there are two zeros to the right of its last nonzero digit, 5. How many terminal zeros does n! have?

1) n^2 – 15n + 50 < 0
2) n > 5

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Consider 1)
n^2 – 15n + 60 < 0
=> (n-5)(n-10) < 0
=> 5 < n < 10

The number of terminal zeros of a number is determined by the number of 5s in its prime factorization.

The integers satisfying 5 < n < 10 are 6, 7, 8 and 9. We count the 5s in the prime factorizations of 6!, 7!, 8! and 9!:
6! has one 5 in its prime factorization.
7! has one 5 in its prime factorization.
8! has one 5 in its prime factorization.
9! has one 5 in its prime factorization.

Thus, for 5 < n < 10, n! has one terminal zero.
As it gives us a unique answer, condition 1) is sufficient.

Condition 2)

If n = 6, then 6 > 5 and 6! = 720 has one terminal 0.
If n = 10, then 10 > 5 and 10! = 3,628,800 has two terminal 0s.

Condition 2) is not sufficient since it does not give a unique solution.

Therefore, A is the answer.
Answer: A

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

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17 Oct 2018, 18:49

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[Math Revolution GMAT math practice question]

The points (1,6) and (7,-2) are two vertices of one diagonal of a square in the xy-plane. What is the area of the square?

A. 16
B. 25
C. 32
D. 36
E. 50

=>

The length of the diagonal of the square is √{ (7-1)^2 + (6-(-2))^2 } = √100 = 10.
The side-length of the square is 10/ √2 = 5 √2 since the side-length of a square is equal to the length of its diagonal divided by √2. Thus, the area of the square is (5 √2)^2 = 50.

Therefore, E is the answer.
Answer: E

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21 Oct 2018, 18:59

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[Math Revolution GMAT math practice question]

If |X| is the number of elements in set X, and “∪” is the union and “∩” is the intersection of 2 sets, what is the value of |A∩B|?

1) |A∪B|＝50
2) |B|=40

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Note that
|A∪B| = |A| + |B| - |A∩B| and |A∩B| = |A| + |B| - |A∪B|.

Since we have 4 variables (|A∩B|, |A|, |B|, |A∪B|) and 1 equation (|A∩B| = |A| + |B| - |A∪B|), E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Suppose A and B are disjoint sets, |A∪B| = 50, |A| = 10, and |B| = 40. Then |A∩B| = |A| + |B| - |A∪B| = 0.
Suppose A contains B, |A∪B| = 50, |A| = 50, and |B| = 40. Then |A∩B| = |A| + |B| - |A∪B| = 40.
Since we don’t have a unique solution, both conditions together are not sufficient.

Therefore, E is the answer.
Answer: E