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Five friends (Adele, Brenda, Carol, Dana and Emily) were born peculiarly in consecutive years.

It is known from their diaries that:

Carol was born 2 years before Dana and is not the oldest of them all.

Brenda is not younger than Emily.

Brenda is not the oldest of them all.

If Emily is 25 years old and everyone has already had their birthday this year, how old is Brenda?

The alternatives given in my book are as follows:

  1. 28 years
  2. 27 years
  3. 26 years
  4. 29 years

How exactly should I get Brenda's age? At this point I'm stuck because it doesn't seem to be possible to determine who's the oldest of the group.

So far I have:

Carol > someone > Dana

Then

Emily > Brenda

Then "Brenda is not the oldest of all" seems to overlap with Carol because both state that those two girls are not the oldest of all. So who's the youngest? It only mentions Emily but it doesn't indicate anything else. Can Brenda's age be determined with these few clues?

For reference this problem was obtained from my Logic and reason book from 2000s, and it seems to be an adaptation from a reprinted copy of Martin Gardner's 1970s Puzzle carnival.

Can a logic grid be used here? Please try to include a solution with step by step explanation so I can understand because I'm lost here. Justification is also important.

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Answer

Brenda is 27

Reasoning

"Carol was born 2 years before Dana and is not the oldest of them all."
This means that Carol is 2nd and Dana is 4th (Scenario 1)
or Carol is 3rd and Dana is 5th (Scenario 2).

"Brenda is not younger than Emily"
This means Brenda must be older than Emily.

"Brenda is not the oldest..."
This means that Adele must be the oldest since we have been told explicitly it's not Brenda or Carol and Dana is younger than Carol and Emily is younger than Brenda.
In the Scenario 1 above, Brenda is 3rd oldest and Emily is 5th.
In Scenario 2, Brenda is 2nd oldest and Emily is 4th.
In either scenario, Brenda is two years older than Emily.

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  • $\begingroup$ Can you please explain the first and the second scenario?. The two of them result in the same answer?. I mean with Brenda having 27 years old?. This is the part where I'm stuck. Which clue made you conclude that Adele is the oldest?. Can you please explain this part?. $\endgroup$ Jan 6 at 16:55
  • $\begingroup$ @ChrisSteinbeckBell I've tried to flesh my answer out a bit to make it more clear. Hope this helps. $\endgroup$
    – hexomino
    Jan 6 at 17:10
  • $\begingroup$ Thanks for doing that. But I voice my opinion that it should be noted that since the gap between the two people in both scenarios is $2$ because of this reason Brenda's age is $27$ which it can be concluded. While not the same for the other girls as you indicated there are two options possible. $\endgroup$ Jan 6 at 17:26
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@hexomino has already answered this question, but here's my answer, which is more visual, and should be easy to follow.

From the puzzle, we can determine that:

- Brenda is not the eldest (Brenda is not the oldest of them all.)

- Carol is not the eldest (Carol...is not the oldest of them all.)

- Dana is not the eldest, because Carol was born before (Carol was born 2 years before Dana...)

- Emily is not the eldest, because Brenda is older (Brenda is not younger than Emily.)

This means that

Adele must be the eldest.

We also know that

- Carol's age is Dana's age, plus 2 (Carol was born 2 years before Dana...)

- Brenda is older than Emily (Brenda is not younger than Emily.)

- Emily is 25 years old (the puzzle says to assume this)

- All of their ages are consecutive ([They] ...were born peculiarly in consecutive years.)

We can arrange the sisters from right-to-left, with the eldest, on the right:

one

Since

Carol and Dana are separated by two years, they have to be two boxes apart, with Dana coming before Carol, since she is younger. There are only two possible positions for this:

Dana is the youngest: two

Dana is the second-youngest: three

Also,

since Brenda is older than Emily, we can fill out these possibilities, with Emily coming before Brenda:

Dana is the youngest: four

Dana is the second-youngest: five

And since

Emily is 25, and the sisters' ages are consecutive, we can determine all their ages easily:

Dana is the youngest: six

Dana is the second-youngest: seven

In both cases,

Brenda is the same age, so we know that Brenda must be

27 years old

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