# Thread: Odd one out in sequence

1. ## Odd one out in sequence

Hello!

What number doesn't belong in the following sequence and why?
7, 9, 13, 17, 24, 35

Choose odd one out
706 507 489 250
It's 250 but don't know reason

Choose odd one out
232 431 612 813
It's 813 but don't know reason

2. ## Re: Odd one out in sequence

Since you have finite sequences, you can choose any one, and it works. For example, in the first sequence, I can say 24 doesn't belong since every other number listed is the product of at most two primes (but 24 is the product of four primes $24 = 2^3\cdot 3$).

Alternately, if I consider differences between adjacent terms, I find they are 9-7=2, 13-9=4, 17-13=4, 24-17=7, 35-24=11. Since 35 is the only one that is more than 10 greater than the previous term, I can say that is the one that doesn't belong.

I can create an argument for any term in the sequence. There is no "correct" answer. There are only answer and reason pairs. For each number, I can find a reason why it doesn't belong.

Here are some reasons for the numbers you picked for the next two finite sequences:
1. Neither 250 nor 813 has an element proceeding it.
2. $706 = 2\cdot 353, 507 = 3\cdot 13^2, 489 = 3\cdot 163, 250 = 2\cdot 5^3$, so 250 is the only number among the four that is the product of more than three primes (not distinct)
$232 = 2^3\cdot 29, 431 = 431, 612 = 2^2\cdot 3^2\cdot 17, 813 = 3\cdot 271$, so 813 is the only number among the four with two prime factors.
3. $706-507 = 199, 507-489 = 16, 489-250 = 239$, so 250 is the only one that is more than 200 less than the preceding number.
$431-232 = 199, 612-431 = 181, 813-612=201$, so 813 is the only one that is more than 200 greater than the preceding number.

The list of reasons why you might choose 250 and 813 respectively is endless.

3. ## Re: Odd one out in sequence

I do not understand why students are even given these problems. As SlipEternal says, there are an infinite number of correct answers.

Here is an alternative for sequence 1:

9 -7 = 2, 24 - 17 = 7, 35 - 24 = 11. If 13 is really supposed to be 12, then 12 - 9 = 3 and 17 - 12 = 5, and the numbers in the sequence differ by the sequence of primes.

4. ## Re: Odd one out in sequence

Originally Posted by JeffM
I do not understand why students are even given these problems. As SlipEternal says, there are an infinite number of correct answers.
There are busy work from a non-creative instructor.

5. ## Re: Odd one out in sequence

Originally Posted by SlipEternal
Since you have finite sequences, you can choose any one, and it works. For example, in the first sequence, I can say 24 doesn't belong since every other number listed is the product of at most two primes (but 24 is the product of four primes $24 = 2^3\cdot 3$).

Alternately, if I consider differences between adjacent terms, I find they are 9-7=2, 13-9=4, 17-13=4, 24-17=7, 35-24=11. Since 35 is the only one that is more than 10 greater than the previous term, I can say that is the one that doesn't belong.

I can create an argument for any term in the sequence. There is no "correct" answer. There are only answer and reason pairs. For each number, I can find a reason why it doesn't belong.

Here are some reasons for the numbers you picked for the next two finite sequences:
1. Neither 250 nor 813 has an element proceeding it.
2. $706 = 2\cdot 353, 507 = 3\cdot 13^2, 489 = 3\cdot 163, 250 = 2\cdot 5^3$, so 250 is the only number among the four that is the product of more than three primes (not distinct)
$232 = 2^3\cdot 29, 431 = 431, 612 = 2^2\cdot 3^2\cdot 17, 813 = 3\cdot 271$, so 813 is the only number among the four with two prime factors.
3. $706-507 = 199, 507-489 = 16, 489-250 = 239$, so 250 is the only one that is more than 200 less than the preceding number.
$431-232 = 199, 612-431 = 181, 813-612=201$, so 813 is the only one that is more than 200 greater than the preceding number.

The list of reasons why you might choose 250 and 813 respectively is endless.
You are absolutely correct by saying that the reasons to choose a number is endless in a finite series. Thank you for getting that into my head!

Though I just now said that there is no CORRECT answer, JeffM's answer for the 1st probably seems more appropriate.

Anyway thank you guys

6. ## Re: Odd one out in sequence

Hello, lingping7!

These are more like riddles or trick questions.

What number doesn't belong in the following sequence and why?
. . 7, 9, 13, 17, 24, 35

24 is the only even number.

Choose odd one out.
. . 706 507 489 250
(It's 250, but don't know reason.)

250 is the only number whose sum-of-digits is a one-digit number.

Choose odd one out .
. . 232 431 612 813
(It's 813, but don't know reason.)

813 is the only number whose sum-of-digits is a two-digit number.