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M denotes the maximum of x and m the minimum of x.

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M denotes the maximum of x and m the minimum of x.

by Max@Math Revolution » Thu Apr 09, 2020 6:02 pm

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[GMAT math practice question]

M denotes the maximum of x and m the minimum of x. What is the integer part of \(\sqrt{M-m}\) ?

1) The integer part of \(\sqrt{3x-2}\) is 9.
2) x is a positive integer.
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Source: — Data Sufficiency |
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Re: M denotes the maximum of x and m the minimum of x.

by Max@Math Revolution » Sun Apr 12, 2020 3:48 am

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=>

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 1 variable (x) and 0 equations, D is most likely the answer. So, we should consider each condition on its own first.

Condition 1)

9 ≤ \(\sqrt{3x-2}\) < 10
=> 81 ≤ 3x - 2 < 100 (squaring)
=> 83 ≤ 3x < 102 (adding 2)
=> 83/3 ≤ x < 102/3 (dividing by 3)

Since x doesn’t have a maximum value, condition 1) is not sufficient.

Condition 2)

Since x doesn’t have a maximum value, condition 2) is not sufficient.

Conditions 1) & 2)
When we consider both conditions together, the possible values of x are 28, 29, …, 33.
Then we have M = 33 and m = 29.
Thus, we have \(\sqrt{M-m}=\sqrt{4}\) = 2.

Since both conditions together yield a unique solution, they 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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