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# If Φ is a digit in the number n and n = 3.Φ6, what is Φ?

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Joined: 02 Sep 2009
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If Φ is a digit in the number n and n = 3.Φ6, what is Φ?  [#permalink]

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01 Nov 2016, 04:49
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5% (low)

Question Stats:

83% (00:53) correct 17% (00:51) wrong based on 164 sessions

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If Φ is a digit in the number n and n = 3.Φ6, what is Φ?

(1) When rounded to the nearest tenth n is 3.9
(2) When rounded to the nearest integer n is 4

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Re: If Φ is a digit in the number n and n = 3.Φ6, what is Φ?  [#permalink]

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01 Nov 2016, 06:26
Bunuel wrote:
If Φ is a digit in the number n and n = 3.Φ6, what is Φ?

(1) When rounded to the nearest tenth n is 3.9
(2) When rounded to the nearest integer n is 4

Question : what is Φ?

Statement 1: When rounded to the nearest tenth n is 3.9
n = 3.Φ6 i.e. the tenths digit will increase by 1 to become 9 while rounding it off to tenths digit so initial tenths digit must be 8
SUFFICIENT

Statement 2: When rounded to the nearest integer n is 4
then n may be 3.56 or 3.86
hence Φ may have more than one possible values hence
NOT SUFFICIENT

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Re: If Φ is a digit in the number n and n = 3.Φ6, what is Φ?  [#permalink]

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10 Jan 2018, 09:13
Top Contributor
Bunuel wrote:
If Φ is a digit in the number n and n = 3.Φ6, what is Φ?

(1) When rounded to the nearest tenth n is 3.9
(2) When rounded to the nearest integer n is 4

Target question: What is Φ?

Given: Φ is a digit in the number n and n = 3.Φ6

Statement 1: When rounded to the nearest tenth n is 3.9
Since there's a 6 in the hundredths position, we must round the tenths digit UP to 9
So, the tenths digit of n must be 8
In other words, Φ = 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: When rounded to the nearest integer n is 4
There are several values of n that satisfy statement 2. Here are two:
Case a: n = 3.96. When we round 3.96 to the nearest integer, we get 4. In this case, Φ = 9
Case b: n = 3.86. When we round 3.86 to the nearest integer, we get 4. In this case, Φ = 8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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Re: If Φ is a digit in the number n and n = 3.Φ6, what is Φ?   [#permalink] 10 Jan 2018, 09:13
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