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# What is the hundredths digit in the decimal representation of a certai

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Senior SC Moderator
Joined: 14 Nov 2016
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What is the hundredths digit in the decimal representation of a certai  [#permalink]

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07 Mar 2017, 19:14
2
2
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Difficulty:

55% (hard)

Question Stats:

59% (01:33) correct 41% (01:31) wrong based on 102 sessions

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What is the hundredths digit in the decimal representation of a certain number?

(1) When rounded to the nearest tenth, the result is 0.4
(2) When rounded to the nearest hundredth, the result is 0.40

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Re: What is the hundredths digit in the decimal representation of a certai  [#permalink]

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08 Mar 2017, 12:11
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ziyuen wrote:
What is the hundredths digit in the decimal representation of a certain number?

(1) When rounded to the nearest tenth, the result is 0.4
(2) When rounded to the nearest hundredth, the result is 0.40

Dear [url]ziyuen[/url],

I'm happy to respond.

Statement #1 is useless. Technically, statement #1 is a tautological statement. The hundredths digit could be anything and it wouldn't matter. This is insufficient.

Statement #2: When rounded to the nearest hundredth, the result is 0.40
Possibilities include
N = 0.400
N = 0.401
N = 0.402
N = 0.399
N = 0.398
N = 0.397

Thus, it could be true that the hundredths digit is zero or 9.

Statement #1 is so useless that combining it with Statement #2 adds nothing. All of the numbers above would round to 0.4 is rounded to the tenths place. Thus, nothing is sufficient.

OA = (E)

Does all this make sense?
Mike
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Posts: 55150
Re: What is the hundredths digit in the decimal representation of a certai  [#permalink]

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01 Jan 2018, 11:33
hazelnut wrote:
What is the hundredths digit in the decimal representation of a certain number?

(1) When rounded to the nearest tenth, the result is 0.4
(2) When rounded to the nearest hundredth, the result is 0.40

VERITAS PREP OFFICIAL SOLUTION:

Statement 1: To round to the nearest tenth, examine the digit in the hundredths position. Statement 1 is insufficient because a range of numbers with varying hundredths digits can round to 0.4 (see examples below). For example:

0.35 -> 0.4 hundredths digit = 5
0.36 -> 0.4 hundredths digit = 6
0.41 -> 0.4 hundredths digit = 1
The hundredths digit could be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. INSUFFICIENT

Statement 2: Statement 2 is also insufficient – see examples of various possibilities below:

0.398 -> 0.40 hundredths digit = 9
0.399 -> 0.40 hundredths digit = 9
0.401 -> 0.40 hundredths digit = 0
0.402 -> 0.40 hundredths digit = 0
The hundredths digit could be 0 or 9. INSUFFICIENT

Together: Combining the two statements, we see that the hundredths digit could be either 0 or 9, thus the correct answer is E.
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Re: What is the hundredths digit in the decimal representation of a certai  [#permalink]

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12 May 2019, 08:57
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Re: What is the hundredths digit in the decimal representation of a certai   [#permalink] 12 May 2019, 08:57
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