For All Positive Integers m, [m] = 3m When m is Odd and [m] = (1/2)*m GMAT Problem Solving

Question: For all positive integers m, [m] = 3m when m is odd and [m] = (1/2)*m when m is even. What is [9]*[6] equivalent to?

1. [81]
2. [54]
3. [37]
4. [27]
5. [18]

Correct Answer: D
Solution and Explanation:
Approach Solution 1:

It should be noted that [] is nothing more than a function with the property that "[m]=3m when m is odd and [m]=(1/2)*m when m is even."

If m is an odd number, then [m] equals 3m, and if m is an even number, then [m] equals (1/2)*m.

Since 9 is an odd number, [9] is 3 times 9 which equals 27;

Given that 6 is an even number, [6] is equivalent to 1/2 * 6 = 3;

So [9]*[6]=27*3=81. Noting that the numbers in the options for the solution are also in the boxes, we get the result: [m] = 81. m might be 27, and because 27 is an odd integer, [27]=3*27=81 would be the correct answer. OR 162 (given that 162 is an even number, [162]=162/2=81) --> the only answer option that contains the number 27 is this one.

Approach Solution 2:
It should be noted that [] is nothing more than a function with the property that "[m]=3m when m is odd and [m]=(1/2)*m when m is even."

If m is an odd number, then [m] equals 3m, and if m is an even number, then [m] equals (1/2)*m.

If 9 is an odd number, then [9] equals 3 * 9 = 27, and if 6 is an even number, then [6] equals 1/2 * 6 = 3.

So [9]*[6]=27*3=81. Noting that the numbers in the options for the solution are also in the boxes, we get the result: [m] = 81. m might be 27, and because 27 is an odd integer, [27]=3*27=81 would be the correct answer. OR 162 (given that 162 is an even number, [162]=162/2=81) --> the only answer option that contains the number 27 is this one.

Approach Solution 3:
[9] = 9*3 = 27
[6]= 6/2= 3
[9] * [6] = 27 * 3 = 81 ............. (1)

From all the given options, we require to calculate to get answer 81

1. [81] = 81 * 3 = 243 .... IGNORE
2. [54]= 54/2= 27.........IGNORE
3. [37] = 37*3 = 111 ..... IGNORE
4. [27] = 27*3 = 81 ........... Matches with (1)
5. E.[18]= 18/2= 9...........IGNORE

“For all positive integers m, [m] = 3m when m is odd and [m] = (1/2)*m when”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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