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03 Aug 2009, 12:58
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C
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Difficulty:
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54% (01:32) correct
46%
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What is the result when x is rounded to the nearest hundredth?
(1) When x is rounded to the nearest thousandth the result is 0.455.
(2) The thousandth digit of x is 5.
(1) When x is rounded to the nearest thousandth the result is 0.455.
(2) The thousandth digit of x is 5.
27 Oct 2011, 20:58
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Responding to a pm:
When you round off to the hundredth digit, you look at only the thousandth digit i.e. you focus only on the next digit.
Say x = .4546
When you round it to the nearest hundredth digit, you get x = .45 (not .46). The reason is that the thousandth digit is 4 which is less than 5. 0.4546 is closer to 0.45 than it is to 0.46
You do not follow a sequence of roundings to arrive at x = .455 and then x = .46
Say x = .4553
Now when you round to the nearest hundredth, you get x = .46 because the thousandth digit is 5. .4553 is closer to .46 than to .45
Therefore statement 1 is not sufficient alone. If you round off x to thousandth and get .455, you do not know whether x was .4546 or .4553 initially (or similar). Hence you do not know what you will get when you round it to nearest hundredth. Statement 2 tells you that the thousandth digit was 5 so now you know that x was .4553 (or similar) and it will be rounded to .46
When you round off to the hundredth digit, you look at only the thousandth digit i.e. you focus only on the next digit.
Say x = .4546
When you round it to the nearest hundredth digit, you get x = .45 (not .46). The reason is that the thousandth digit is 4 which is less than 5. 0.4546 is closer to 0.45 than it is to 0.46
You do not follow a sequence of roundings to arrive at x = .455 and then x = .46
Say x = .4553
Now when you round to the nearest hundredth, you get x = .46 because the thousandth digit is 5. .4553 is closer to .46 than to .45
Therefore statement 1 is not sufficient alone. If you round off x to thousandth and get .455, you do not know whether x was .4546 or .4553 initially (or similar). Hence you do not know what you will get when you round it to nearest hundredth. Statement 2 tells you that the thousandth digit was 5 so now you know that x was .4553 (or similar) and it will be rounded to .46
26 Oct 2009, 16:47
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I believe the answer is C.
Statement 1: When x is rounded to the nearest thousandth the result is 0.455.
Two cases.
Case 1: Thousandths digit is 5 (0.4550 <= x < 0.4555). Then x rounded to the nearest hundredth would be 0.46.
Case 2: Thousandths digit is 4 (0.4545 < x < 0.4550). Then x rounded to the nearest hundredth would be 0.45.
Therefore, insufficient.
Statement 2: The thousandths digit of x is 5.
Doesn't give any information about any of the other digits of x. Insufficient.
Evaluting Both Statements.
Since we know that the thousandths digit of x is 5, this falls under Case 1. X rounded to the nearest hundredths digit if 0.46. Therefore, sufficient.
Statement 1: When x is rounded to the nearest thousandth the result is 0.455.
Two cases.
Case 1: Thousandths digit is 5 (0.4550 <= x < 0.4555). Then x rounded to the nearest hundredth would be 0.46.
Case 2: Thousandths digit is 4 (0.4545 < x < 0.4550). Then x rounded to the nearest hundredth would be 0.45.
Therefore, insufficient.
Statement 2: The thousandths digit of x is 5.
Doesn't give any information about any of the other digits of x. Insufficient.
Evaluting Both Statements.
Since we know that the thousandths digit of x is 5, this falls under Case 1. X rounded to the nearest hundredths digit if 0.46. Therefore, sufficient.
