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

Question

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

GMATinsight · Answer

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

Answer: Option A

BrentGMATPrepNow · Answer

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

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

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