The given analogy is
343 : 989 :: x : 669
What is x?
- 223
- 332
- 333
- 233
The answer is:
Option #4 $-$ $233$
Reason:
To get from the number on the left to the number on the right, triple the first number, double the second, and triple the third.
$343 : 989$
$3\times 3 = 9,\ 4\times 2 = 8,\ 3\times 3 = 9$
$233 : 669$
$2\times 3 = 6,\ 3\times 2 = 6,\ 3\times 3 = 9$
The answer could also be
option 1. The left side is a cipher of the right side: 3 ↦ 9, 4 ↦ 8, and given the options, we must have 2 ↦ 6. So the "encoded" version of 669 is 223.
C : 333. From right to left, half even numbers and divide odd multiples of $3$ by $3$.
The answer is
the first choice, 223. Each digit of the first term in each pair is $1$ less than the length of the English name of the corresponding digit in the second term in that same pair.
I know this is answered and ticked, but:
1. 223
Add 4 to even digits and 6 to odd digits.
This type of puzzle is an exercise in mind reading. All 4 answers have roughly equally valid logic supporting them, so you have to "read the mind" of the person posing the question to get the "correct" answer.
Other answers have explained why 3 of the 4 choices are logical solutions. The remaining puzzle is therefore to find a similarly convincing explanation for the remaining choice. Here is mine:
#2: 332
because
If we rank the digits, the second number of each pair is the opposite of the first. For example, 343 has the pattern low-high-low, and the opposite of that is high-low-high, which 989 fits. In the second pair, we see 669, which is low-low-high, so we need to find a number with the opposite pattern, high-high-low. Only choice #2 fits this.
:
and::
denoting? Are they operators? Relations? $\endgroup$