Discussion
For all numbers x, [x] denotes the value of x3 rounded to the nearest multiple of ten.
*This question is included in Nova Math - Problem Set B: Substitution 2, question #9
| Column A | Column B | |
| [x + 1] | [x] + 1 |
| (A) | Column A is larger |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 03/09/2012 14:49
I do not understand what the question is asking. I reviewed the example, but I don't see the relationship to the question.
Posted: 03/09/2012 16:58
Jessica, this is a medium difficult question, so don't feel bad. It is an operator problem, where we practice to transform a "thing" to another form using a mathematical operation. In this case, the operator is symbolized by [..], and can be expressed verbally as "raise to the power of 3 anything inside the square brackets".
So, in Column A, we have [x+1], which can now be mathematically expressed as (x+1) raised to the power of 3, or (x+1)^3. Similarly in Column B we have [x] +1, which can be mathematically expressed as x^3 +1.
The question is asking, how does (x+1)^3 compare to x^3 +1? Which one is larger? Or are they equal? Or is there not enough information to decide?
Now that you understand the question, I am sure you can follow the explanation in the Solution.
So, in Column A, we have [x+1], which can now be mathematically expressed as (x+1) raised to the power of 3, or (x+1)^3. Similarly in Column B we have [x] +1, which can be mathematically expressed as x^3 +1.
The question is asking, how does (x+1)^3 compare to x^3 +1? Which one is larger? Or are they equal? Or is there not enough information to decide?
Now that you understand the question, I am sure you can follow the explanation in the Solution.
Posted: 09/28/2014 19:22
I'm confused about when x=5 [x]=0 or [x]=10?
Posted: 09/28/2014 21:56
Reply: when x=5, [x]=5^3 rounded to to the nearest 10 = 75 rounded to the nearest 10, which is 80.
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Edit
Posted: 01/02/2013 15:06
In your solution, how is [1] = to 0, and how is [2] = 10.
Posted: 01/03/2013 01:35
Hi William,
[1] denotes the value of 1^3 = 1 rounded to the nearest multiple of ten. Now, the multiples of 10 that are closest to 1 are 0 and 10, and clearly 0 is closer to 1 than is 10. So, [1] = 0.
Note: Zero is a multiple of 10 because 0 = 0(10).
[2] denotes the value of 2^3 = 8 rounded to the nearest multiple of ten. Now, the multiples of 10 that are closest to 8 are 0 and 10, and clearly 10 is closer to 8 than is 0. So, [2] = 10.
Nova Press
[1] denotes the value of 1^3 = 1 rounded to the nearest multiple of ten. Now, the multiples of 10 that are closest to 1 are 0 and 10, and clearly 0 is closer to 1 than is 10. So, [1] = 0.
Note: Zero is a multiple of 10 because 0 = 0(10).
[2] denotes the value of 2^3 = 8 rounded to the nearest multiple of ten. Now, the multiples of 10 that are closest to 8 are 0 and 10, and clearly 10 is closer to 8 than is 0. So, [2] = 10.
Nova Press
Posted: 09/03/2013 10:28
Just i wanna understand that when i faced problem like this i should follow the rule 0 and 10. I'll compare the result wether close to 0 or 10!!!!! Is it correct??????
Posted: 10/30/2013 14:03
Hello, I can understand the answer being D, but my argument is if you say round up to the nearest multiple of 10 are you allowed to go backwards in maths? From 2 to 0 as opposed to from 2 to 10. I thought it was the same principle with approximating decimals. Eg 2.4 is approximately 3 not going backwards to 2.
Posted: 10/30/2013 19:41
Jane, the problem says "rounded to", not "rounded up to".
To answer the other question, 2.4 is rounded to 2, not 3. 2.5 would be rounded to 3.
To answer the other question, 2.4 is rounded to 2, not 3. 2.5 would be rounded to 3.
Posted: 09/22/2014 22:43
I don't really get the point of the question. Most of time, without a range for x, the comparison is always unknown. Then why bother setting up such a difficult operation...
Posted: 09/23/2014 08:49
T, there is a range for x, in this problem it is "all numbers"