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Overview of GMAT Math Question Types and Patterns on the GMAT
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Author:  MathRevolution [ 22 Apr 2022, 03:44 ]
Post subject:  Re: Overview of GMAT Math Question Types and Patterns on the GMAT
[you-tube]
MathRevolution wrote:
[GMAT math practice question]

(number properties) If \(m\) and \(n\) are positive integers, is \(m+n\) divisible by \(15\)?

1) \(m\) is divisible by \(9\) and \(n\) is divisible by \(15\).
2) \(mn\) is divisible by \(225\).


=>

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 (\(m\) and \(n\)) 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 \(m = 45\) and \(n = 45\), then \(m + n = 90\) is divisible by \(15\) and the answer is ‘yes’.
If \(m = 9\) and \(n = 225\), then \(m + n = 234\) is not divisible by \(15\) and the answer is ‘no’.
Thus, both conditions together are not sufficient, since they do not yield a unique solution.

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.[/you-tube][you-tube][/you-tube]
Author:  MathRevolution [ 26 Apr 2022, 04:23 ]
Post subject:  Re: Overview of GMAT Math Question Types and Patterns on the GMAT
MathRevolution wrote:
[GMAT math practice question]

(algebra) Is \(y^x = x^y\)?

1) \(x = y\)
2) \(x = (1 + (\frac{1}{n}))^n, y = (1 + (\frac{1}{n}))^{n+1}\) for a positive integer \(n\).


=>

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) is sufficient, obviously.

Condition 2)
Since \(y^x = ((1 + (\frac{1}{n}))^{n+1})\)^\((1 + (\frac{1}{n}))^n\) \(= ((1 + (\frac{1}{n})))^{(n + 1)}*(1 + (\frac{1}{n}))^n\), the exponent of \(y^x\) with the base \((1 + (\frac{1}{n}))\) is \((n+1)*(1+(\frac{1}{n}))^n = n(1+\frac{1}{n})* (1+(\frac{1}{n}))^n = n(1+(\frac{1}{n}))^{n+1}\)

Since \(x^y = ((1 + (1/n))^n)\)^\((1 + (\frac{1}{n}))^{n+1} = ((1 + (\frac{1}{n})))^n(1 + (\frac{1}{n}))^n\), the exponent of \(x^y\) with the base \((1 + (\frac{1}{n}))\) is \(n(1 + (\frac{1}{n}))^n\) is equal to the exponent of \(y^x\).

So, we have \(y^x = x^y.\)

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.
Author:  MathRevolution [ 04 May 2022, 03:41 ]
Post subject:  Re: Overview of GMAT Math Question Types and Patterns on the GMAT
MathRevolution wrote:
[GMAT math practice question]

(inequality) \(a, b,\) and \(c\) are the lengths of the sides of an obtuse triangle. What is the maximum value of \(a\)?

1) \(a < b < c = 20.\)

2) \(a, b,\) and \(c\) are integers.


=>

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 (\(a, b,\) 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)

Since the triangle is obtuse, we have \(c^2 > a^2 + b^2\) or \(400 > a^2 + b^2\) from condition 1). Since \(a < b\) or \(a^2 < b^2\) and \(a\) is an integer, we have \(a^2 < 200\) or \(a ≤ 13\) from condition 2).

The maximum value of \(a\) is \(13\).

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.
Answer: C

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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