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

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Oct 30, 2017 3:00 pm
AAPL 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

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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