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hungvuong

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T is a set of 30 decimals, sum is S. These numbers are classified to two groups. In the first group (the tenth' digit is even), the decimal rounds up, for example, 4.4 rounds up to 5.0; in the second group, (the tenth' digit is odd), the decimal round down, for example, 4.1 to 4. The sum of 30 new numbers (rounded) is E. If 1/3 of30 decimals have an even tenth's digit, which of the following could be the value of E-S?

1.6

2. 10

3. -16

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I am not sure if we are to assume anything here. But let us consider the case where the numbers are positive

 

Let numbers be x1, x2, x3.....x30

For our purposes, let us also just treat x1...x10 as the even tenths digit ones, i.e. these are rounded up. The rest of x11....x30 are rounded down

S = x1+x2+x3+......+x30

S10 = sum of numbers rounded up = (x1+1) + (x2+1)......+(x10+1)

S20 = sum of numbers rounded down = (x11-1) + (x12-1).....+(x30-1)

E = S10 + S20 = (x1+x2+.......+x30) + 10 - 20

=> E = S - 10

=> E-S = -10

 

I don't find this in any of the answer choices though. But you provide only 3 choices.

The problem stem doesn't indicate how to treat negative numbers. So, how do we round -4.4 for example. Does round UP mean, increase in value or decrease in value? So, would -4.4 become -5 OR would -4.4 become 4? Leaving that case aside, I still don't find the answer in the list of choices.

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T is a set of 30 decimals, sum is S. These numbers are classified to two groups. In the first group (the tenth' digit is even), the decimal rounds up, for example, 4.4 rounds up to 5.0; in the second group, (the tenth' digit is odd), the decimal round down, for example, 4.1 to 4. The sum of 30 new numbers (rounded) is E. If 1/3 of30 decimals have an even tenth's digit, which of the following could be the value of E-S?

1.6

2. 10

3. -16

 

OK, so if I'm understanding this properly, any number with an even tenths digit is rounded up, and any number with an odd tenths digit is rounded down?

 

We have 10 numbers being rounded up and 20 being rounded down. The most that can be gained from the 10 that are rounded up is 8 (.8 * 10). The least that can be gained from the 10 that are rounded up is 1 (.100000....1 * 10).

 

The most that can be lost from the 20 being rounded down is 20 (.9999999....9 * 20). The least that can be lost is 2 (.1 * 20).

 

So, the most that can be gained from S to E is 8-2 = 6. The most that can be lost from S to E is 20-1 = 19.

 

Both II and III are possible.

 

** Note that I'm assuming that the decimal can go beyond the tenths digit.

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rounds up or down doesn't metter because...

for S 10*any integer should = #(any number)0 + 20*any integer should = "(any number) 0

For E same approach 30*any integer = #0

 

Do you know any 2 numbers that end on 0 and after deduction one can be ended on anything than 0?

 

so CAN't be 16, 8541, -995 or 19821,

should be the one that ends on 0 so 10

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