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Is x=1?

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Is x=1?  [#permalink]

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New post 18 Jun 2013, 09:16
4
13
00:00
A
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C
D
E

Difficulty:

  85% (hard)

Question Stats:

44% (01:45) correct 56% (01:31) wrong based on 158 sessions

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Is x=1?

(1) If x were rounded to the nearest thousandth, the result would be 1
(2) If x were rounded to the nearest tenth, the result would be equal to the exact value of x

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Re: Is x=1?  [#permalink]

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New post 22 Jun 2013, 12:42
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5
Good question. +1.

1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS

Is x=1?

(1) If x were rounded to the nearest thousandth, the result would be 1. This implies that x is of the form 1.000b..., where b can be 0, 1, 2, 3, or 4. So, x can be:

1.0000...
1.0001...
1.0002...
1.0003...
1.0004...

Not sufficient.

(2) If x were rounded to the nearest tenth, the result would be equal to the exact value of x. This statement basically implies that all the digits after the tenth are zeros. Still insufficient. For example, x can be 1.1, or 2.7 or 0.1 or 1.

(1)+(2) From (1) we know that x is 1.000b and from (2) we know that the digits after the tenth in x are zero, thus x=1. Sufficient.

Answer: C.
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Re: Is x=1?  [#permalink]

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New post 20 Jun 2013, 02:03
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Re: Is x=1?  [#permalink]

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New post 26 Aug 2014, 11:04
But if x, after rounding to nearest tenth is exactly equal to x, shouldn't it mean that x before and after rounding is the same, or, that everything after the decimal is zero?

I arrived at this reasoning by this: if x before rounding is 2.1, and after rounding it is 2.0 the condition of exact equality (before and after) is not met. so it has to be 2.0 both before and after.

Please correct if I am missing something.
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Re: Is x=1?  [#permalink]

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New post 22 Aug 2015, 15:22
1
Question:
If x = 0.995 then statement A would be satisfied too. i.e if we round 0.995 to the nearest thousandths then it would be 1. Isn't this correct ?
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Re: Is x=1?  [#permalink]

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New post 17 Sep 2015, 11:52
bunuel, thank's for explanation. It is more or less clear with 1.0001, 1.0002 etc. But can the number be 1.0098 for example? will rounding to the nearest thousandth require to put 1 in hundreths place?
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New post 13 Apr 2019, 07:45
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Re: Is x=1?   [#permalink] 13 Apr 2019, 07:45
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