Alex, Brook, Colin

Logic Level 3

Alex, Brook, Colin, Deco, and Eric recently found out that all of their birthdays were on the same day, though they are different ages.

On their mutual birthday, they were jabbering away, flapping their gums

about their recent discovery. And, lucky me, I was there. Some of the things

that I overheard were...

• Deco said to Brook: "I'm nine years older than Eric."

• Eric said to Brook: "I'm seven years older than Alex."

• Alex said to Brook: "Your age is exactly 70% greater than mine."

• Brook said to Colin: "Eric is younger than you."

• Colin said to Deco: "The difference between our ages is six years."

• Colin said to Alex: "I'm ten years older than you."

• Colin said to Alex: "Brook is younger than Deco."

• Brook said to Colin: "The difference between your age and Deco's is the
same as the difference between Deco's and Eric's."

Since I knew these people -- and how old they were, I knew that they were not telling the whole truth.

After thinking about it, I realized that when one of them spoke to someone older, everything they said was true, but when speaking to someone younger, everything they said was false.

How old are Alex, Brook, Colin, Deco and Eric respectively?

(27, 60, 55, 44 , 35) (30, 61, 54, 42 , 39) (30, 51, 55, 46 , 37) (33, 54, 43, 47 , 38) (21, 35, 55, 49, 50)

3 solutions

Mohammad Khaza
Feb 7, 2018

Alex said to Brook: "Your age is exactly 70% greater than mine."

$\text{looking at this statement and the answers-i get 21 is exactly 70 percent of 30.}$

$\text{as Brooks age is 70 percent greater than Alex and according to the condition the statement is right.And also the final questions serial Alex.Brook,....}$

it's no tougher to get the answer without reading the whole problem.

Saya Suka
Mar 19, 2021

Tlhe second element (Brook's age) must be a multiple of 17, and there's only one option that fits this requirement.

Nguyen Minh
Nov 17, 2020

1) If Colin is younger than Alex, and he said "I'm ten years older than you.", it would be a lie, so Colin must be older than Alex (but the difference between their age is not 10)

2) Since Colin is older than Alex, "Brook is younger than Deco." is wrong, and the only right statement is Brook is older than Deco

3) As Deco is younger than Brook, Deco said "I'm nine years older than Eric." is right, and so Eric is younger than Deco and Deco is younger than Brook

4) Since Eric is younger than Brook, Eric said "I'm seven years older than Alex." is right, and so Alex is younger than Eric

5) If Colin is younger than Brook, then Brook said "Eric is younger than you." is wrong, and Colin must be younger than Eric, and that means he is younger than Deco, but it means Colin said "The difference between our ages is six years." is right and it is not possible since Deco is 9 years older than Eric, and that would mean Colin have to be older than Eric instead. Hence, Colin is older than Brook

We have: Alex < Eric < Deco < Brook < Colin (*), and:

$Deco - Eric = 9$

$Eric - Alex = 7$

$1.7 * Alex = Brook$

$Colin - Deco = 9$

We would have $Colin - Alex = 25$ , and that also means $Brook - Alex < 25$ because Brook is younger than Colin. From the equation $1.7 * Alex = Brook$ , we can deduct that $Alex < 35$ , and because $1.7*Alex$ is an integer so Alex must be divisible by 10, so Alex is 10, 20 or 30

If $Alex = 10$ , we would have $Brock = 17$ and $Eric = 17$ , which is not possible since everyone has different age.

If $Alex = 20$ , we would have $Brock = 34$ , $Eric = 27$ and $Deco = 36$ . That would makes Deco older than Brook and not fits (*)

Hence,

Alex = 30

Brock = 51

Eric = 37

and

Deco = 46

and

Colin = 55

Alex, Brook, Colin

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