Overview of GMAT Math Question Types and Patterns on the GMAT : Quantitative Questions

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

29 Nov 2021, 01:04

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MathRevolution wrote:

[GMAT math practice question]

(geometry) \(a, b,\) and \(c\) are the dimensions of a rectangular box. What is the value \(a + b + c\)?

1) the volume of the rectangular box is \(1000m^3\)

2) the surface area is \(720m^2\)

=>

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 \(3\) variables (\(a, b\), and \(c\)) and \(0\) equations, E is most likely 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)
We have \(abc = 100\) and \(2(ab + bc + ca) = 720\) or \(ab + bc + ca = 360.\)

If we have \(a = 10,\) then we have \(bc = 100\) and \(ab + bc + ca = 10(b+c) + 100 = 720\) or \(b + c = 62\), which yields \(a + b + c = 72.\)

If we have \(a = 5,\) then we have \(bc = 200\) and \(ab + bc + ca = 5(b+c) + 200 = 720\) or \(b + c = 104,\) which yields \(a + b + c = 5 + 104 = 109.\)

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

01 Dec 2021, 02:07

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MathRevolution wrote:

[GMAT math practice question]

(absolute value) What is the value of \(a\)?

1) \(|x - 1| = -(ax - 1)^2.\)
2) \(|ax - 1| = -√(x - 1).\)

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

Condition 1)
\(|x - 1| = -(ax - 1)^2\) is equivalent to \(x = 1\) and \(a = 1\) for the following reason.

\(|x - 1| = -(ax - 1)^2\)

=> \(|x - 1| + (ax - 1)^2 = 0\)

=> \(x - 1 = 0\) and \(ax - 1 = 0\)

=> \(x - 1 = 0\) and \(a - 1 = 0\)

=> \(x = 1\) and \(a = 1\)

Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
\(|ax - 1| = -√(x - 1)\) is equivalent to \(x = 1\) and \(a = 1\) for the following reason.

\(|ax - 1| = -√(x - 1)\)

=> \(|ax - 1| + √(x - 1) = 0\)

=> \(ax - 1 = 0\) and \(√(x-1) = 0\)

=> \(a - 1 = 0\) and \(x - 1 = 0\)

=> \(a = 1\) and \(x = 1\)

Since condition 2) yields a unique solution, it is sufficient.

Therefore, D is the answer.
Answer: D

Note: Tip 1) of the VA method states that D is most likely the answer if condition 1) gives the same information as condition 2).

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

04 Dec 2021, 02:04

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MathRevolution wrote:

[GMAT math practice question]

(geometry) What is the volume of a sphere?

1) The circumference of the sphere is \(6π\)

2) The surface area of the sphere is \(36π\)

=>

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.

Since we have \(1\) variable, the radius \(r\) for the sphere, and \(0\) equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
Since the circumference of the sphere is \(2πr = 6π\), we must have \(r = 3\).

The volume of the sphere is \((\frac{4}{3})πr^2 = (\frac{4}{3})π(3)^2 = 12π.\)

Condition 1) is sufficient since it yields a unique answer,

Condition 2)
Since the surface area of the sphere is \(4πr^2 = 36π\), we must have \(r = 3\).

The volume of the sphere is \((\frac{4}{3})πr^2 = (\frac{4}{3})π3^2 = 12π.\)

Condition 2) is sufficient since it yields a unique answer,

Therefore, D is the answer.
Answer: D

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).

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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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

07 Dec 2021, 02:30

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MathRevolution wrote:

[GMAT math practice question]

(algebra) What is the value of \(\frac{(3mr-nt)}{(4nt-7mr)}\)?

\(1) \frac{m}{n} = \frac{4}{3}\)

\(2) \frac{r}{t}= \frac{9}{14}\)

=>

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. We should simplify the conditions if necessary.

We rearrange \(\frac{(3mr-nt)}{(4nt-7mr)}\) to see if we can write in terms of the ratios m/n and r/t given in the conditions:
\(\frac{(3mr-nt)}{(4nt-7mr)}\)
\(= ( \frac{(3mr)}{(nt)} – \frac{(nt}{nt)} ) / ( 4\frac{(nt}{nt)} – 7\frac{mr}{nt} )\)
\(= ( 3(\frac{m}{n})*(\frac{r}{t}) – 1 ) / ( 4 – 7(\frac{m}{n})(\frac{r}{t}) )\)

Now, both conditions 1) & 2) together are sufficient since the simplified question requires only the values of \((\frac{m}{n})\) and \((\frac{r}{t})\).

Therefore, C is the answer.
Answer: C

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

09 Dec 2021, 03:12

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MathRevolution wrote:

[Math Revolution GMAT math practice question]

(number property) If \(n\) is an integer greater than \(1\), what is the value of \(n\)?

1) \(n\) is a prime number
2) \(\frac{(n+2)}{n}\) is an integer

=>

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)
Since there are many prime numbers, condition 1) is not sufficient.

Condition 2)
If \(n = 1\), then \(\frac{(n+2)}{n} = 3\) is an integer.
If \(n = 2,\) then \(\frac{(n+2)}{n} = 2\) is an integer.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
If \(n = 2\), then \(\frac{(n+2)}{n} = 2\) is an integer.
If \(n = 3\), then \(\frac{(n+2)}{n} = \frac{5}{2}\) is not integer.
If \(n\) is a prime number bigger than \(2\), \(\frac{(n+2)}{n}\) is not an integer.
Thus \(n = 2\) is the unique solution and both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

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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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

12 Dec 2021, 07:38

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MathRevolution wrote:

[GMAT math practice question]

(number properties) \(p\) and \(q\) are positive integers and relative primes. Is \(p\) divisible by \(1979\)?

1) \(p\) is a multiple of \(1979.\)

2) \(\frac{p}{q} = 1 - (\frac{1}{2}) + (\frac{1}{3}) - (\frac{1}{4}) +…- (\frac{1}{1318}) + (\frac{1}{1319}).\)

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

The question “is \(p\) divisible by \(1979\)” is equivalent to condition 1) “\(p\) is a multiple of \(1979\)”.

Condition 2)
Remember that \(\frac{-1}{2k} = \frac{1}{2k} – \frac{1}{k}\) for \(k = 1, 2, 3, …, 659.\)

\(\frac{-1}{2} = \frac{1}{2} – \frac{1}{1}\)

\(\frac{-1}{4} = \frac{1}{4} – \frac{1}{2}\)

\(\frac{-1}{6} = \frac{1}{6} – \frac{1}{3}\)
…
\(\frac{-1}{1318} = \frac{1}{1318} – \frac{1}{659}\)

\(\frac{p}{q} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + … + \frac{1}{1317} + \frac{1}{1318} + \frac{1}{1319} – 2(\frac{1}{2} + \frac{1}{4} + … + \frac{1}{1318})\)

\(= 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + … + \frac{1}{1317} + \frac{1}{1318} + \frac{1}{1319} – (\frac{1}{1} + \frac{1}{2} + … + \frac{1}{659})\)

\(= \frac{1}{660} + \frac{1}{661} + … + \frac{1}{1318} + \frac{1}{1319}\)

\(= (\frac{1}{660} + \frac{1}{1319}) + (\frac{1}{661} + \frac{1}{1318}) + … + (\frac{1}{989} + \frac{1}{990})\)

\(= \frac{1979}{(660*1319)} + \frac{1979}{(661*1318)} + … + \frac{1979}{(989*990)}\)

\(= \frac{(1979*k)}{(660*661*…*1318*1319)}\)

Then, we have \(p(660*661*…*1318*1319) = q(1979*k).\)

Since \(1979\) is a prime number, \(p\) is a multiple of \(1979\).

Therefore, D is the answer.
Answer: D

This question is a CMT4 (B) question: condition 1) is easy to work with, and condition 2) is difficult to work with. For CMT4 (B) questions, D is most likely to be the answer.

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

15 Dec 2021, 01:33

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MathRevolution wrote:

[Math Revolution GMAT math practice question]

(inequality) Is \(x^3-4x>0？\)

\(1) x>2\)
\(2) x>-2\)

=>

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.

\(x^3-4x>0\)
\(=> x(x^2-4)>0\)
\(=> x(x+2)(x-2)>0\)
\(=> -2<x<0\) or \(x > 2\)

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

Condition 1)
In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient
Since the solution set of the question, \(-2<x<0\) or \(x > 2\), includes the solution set of condition 1), \(x > 2\), condition 1) is sufficient.

Condition 2)
The solution set of the question, \(-2<x<0\) or \(x > 2\), does not include the solution set of condition 2), \(x > -2\), so condition 2) is not sufficient.

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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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

18 Dec 2021, 11:24

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MathRevolution wrote:

[GMAT math practice question]

(number properties) \(x\) and \(y\) are positive integers. What is the value of \(x*y\)?

\(1) x^{x+y} = y^4\)

\(2) y^{x+y} = x^4\)

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have \(2\) variables (\(x\) and \(y\)) and \(0\) equations, C is most likely 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)
\(x = 1\) and \(y = 1\) satisfies both conditions 1) & 2) together and we have \(x*y = 1\).

\(x = 2\) and \(y = 2\) satisfies both conditions 1) & 2) together and we have \(x*y = 4.\)

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

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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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

18 Dec 2021, 11:27

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MathRevolution wrote:

[GMAT math practice question]

(number properties) \(x\) and \(y\) are positive integers. What is the value of \(x*y\)?

\(1) x^{x+y} = y^4\)

\(2) y^{x+y} = x^4\)

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have \(2\) variables (\(x\) and \(y\)) and \(0\) equations, C is most likely 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)
\(x = 1\) and \(y = 1\) satisfies both conditions 1) & 2) together and we have \(x*y = 1\).

\(x = 2\) and \(y = 2\) satisfies both conditions 1) & 2) together and we have \(x*y = 4.\)

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

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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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

21 Dec 2021, 03:03

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MathRevolution wrote:

[GMAT math practice question]

(number properties) \(x, y\), and \(z\) are positive integers. What is the value of \(xyz\)?

\(1) xy + yz = 24\)

\(2) xz + yz = 13\)

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

Since we have \(3\) variables (\(x, y,\) and \(z\)) and \(0\) equations, E is most likely 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 we have \((x+y)z = 13\) from condition 2), we have \(x+y=13\) and \(z = 1.\)

We have \((x+z)y = (x+1)y = 24\) from condition 1) since \(z = 1.\)

If \(x = 1, y = 12, z = 1\), then \(xyz = 12.\)

If \(x = 11, y = 2, z = 1\), then \(xyz = 22.\)

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

23 Dec 2021, 02:16

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MathRevolution wrote:

[GMAT math practice question]

(statistics) \(k, m\) and \(n\) are positive integers. Is their average equal to their median?

1) The median of \(k, m\) and \(n\) is \(11\).

2) The range of \(k, m\) and \(n\) is \(13\)

=>

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. We should simplify the conditions, if necessary.

Without loss of generality, we may assume \(k ≤ m ≤ n.\)

If their average and their median are equal, then \(\frac{( k + m + n )}{3} = m\) or \(k + m + n = 3m\), so \(n + k = 2m\) and \(n-k=2m-2k\). So, the range of the numbers must be even.
Thus, condition 2) yields the unique answer ‘no’, and is sufficient by CMT 1).

Condition 1)
If \(k = 10, m = 11\) and \(n = 12\), then their average and median are equal, and the answer is ‘yes’.
If \(k = 10, m = 11\) and \(n = 13,\) then their average and their median are not equal, and the answer is ‘no’.
Condition 1) is not sufficient since it doesn’t yield a unique solution.

Therefore, B is the answer.
Answer: B

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

26 Dec 2021, 02:44

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MathRevolution wrote:

[GMAT math practice question]

\(m\) and \(n\) are positive integers. Are \(m\) and \(n\) consecutive integers?

\(1) m^2+n^2 = 5\)
\(2) m-n = 1\)

=>

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.

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

Condition 1)
The only positive integers satisfying \(m^2+n^2 = 5\) are \(m = 1\) and \(n = 2\), or \(m=2\) and \(n = 1.\)
These are consecutive integers, so condition 1) is sufficient.

Condition 2)
Since the difference between \(m\) and \(n\) is \(1\), they are consecutive integers. Condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

30 Dec 2021, 01:15

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MathRevolution wrote:

If n is an integer, is (n+1)(n+2)(n+3) divisible by 12?

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

Answer: B

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.

Since n+1, n+2 and n+3 are three consecutive integers, (n+1)(n+2)(n+3) is a multiple of 3.

Condition 2) tells us that n+1 and n+3 are odd integers, and n+2 is an even number which is not a multiple of 4. Thus, (n+1)(n+2)(n+3) is not a multiple of 4.
CMT(Common Mistake Type 1) states “no” is also an answer and a condition giving rise to the unique answer “no” is sufficient. Thus, condition 2) is sufficient.

Condition 1)
If n = 2, then (n+1)(n+2)(n+3) = 3*4*5 = 60 is a multiple of 12 and the answer is “yes”.
If n = 4, then (n+1)(n+2)(n+3) = 5*6*7 = 210 is not a multiple of 12 and the answer is “no”.
Thus, condition 1) is not sufficient, since it does not yield a unique solution.

Therefore, B is the answer.

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

02 Jan 2022, 02:43

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MathRevolution wrote:

[Math Revolution GMAT math practice question]

(inequality) Is \(\frac{x}{y}>1\)?

\(1) x>y\)
\(2) x-y>1\)

=>

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.

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

\(\frac{x}{y}>1\)
\(=> xy>y^2\)
\(=> xy-y^2>0\)
\(=> y(x-y)>0\)
By condition 2), \(x-y > 1 > 0\), but we can’t determine whether \(y\) is positive from condition 1).

Therefore, E is the answer.
Answer: E

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

02 Jan 2022, 02:44

Expert Reply

MathRevolution wrote:

[Math Revolution GMAT math practice question]

(inequality) Is \(\frac{x}{y}>1\)?

\(1) x>y\)
\(2) x-y>1\)

=>

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.

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

\(\frac{x}{y}>1\)
\(=> xy>y^2\)
\(=> xy-y^2>0\)
\(=> y(x-y)>0\)
By condition 2), \(x-y > 1 > 0\), but we can’t determine whether \(y\) is positive from condition 1).

Therefore, E is the answer.
Answer: E

L

MathRevolution

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 10156

Own Kudos [?]: 16671 [0]

Given Kudos: 4

GMAT 1: 760 Q51 V42

GPA: 3.82

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

05 Jan 2022, 02:57

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MathRevolution wrote:

[GMAT math practice question]

(Number) What is the units digit of \(3^n\)?

1) \(n\) is a multiple of \(4\)

2) \(n\) is a multiple of \(6\)

=>

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. We should simplify the conditions if necessary.

The units digits of \(3^n\) for \(n = 1, 2, 3, 4, …\) are \(3, 9, 7, 1, 3, 9, 7, 1, …\)

So, the units digits of \(3^n\) have period \(4\):

They form the cycle \(3 -> 9 -> 7 -> 1.\)

Thus, \(3^n\) has a units digit of \(1\) if \(n\) is a multiple of \(4.\)

Note that \(6\) is not a multiple of \(4.\)

Therefore, A is the answer.
Answer: A

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MathRevolution

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Joined: 16 Aug 2015

Posts: 10156

Own Kudos [?]: 16671 [0]

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

09 Jan 2022, 03:24

Expert Reply

MathRevolution wrote:

[GMAT math practice question]

(Number Properties) If \(\sqrt{980xy}\) is a positive integer, what is the value of \(xy\)?

1) \(x\) and \(y\) are positive integers

2) \(x ≥ y\)

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have \(2\) variables (\(x\) and \(y\)) and \(0\) equations, C is most likely 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)
We have \(980 = 2^25^17^2.\)

\(X = 5, y = 2 \)and \(x = 20, y = 2 \)are possible solutions.
Then we have \(xy = 10\) and \(40.\)
Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

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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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

09 Jan 2022, 03:24