Using the given figure, find the value of x.
2019
Using the given figure, find the value of x.
- A.
0
- B.
5
- C.
1
- D.
6
Attempted by 4 students.
Show answer & explanation
Correct answer: C
In a picture-based number pattern, rays directly opposite one another form pairs governed by one consistent relationship. If the relationship is cubing, a known base value n maps to the opposite value n3. The rule must first fit every complete pair before it is used for the incomplete pair.
Known ray value | Opposite ray value | Cube check |
|---|---|---|
4 | 64 | 43 = 64 |
2 | 8 | 23 = 8 |
3 | 27 | 33 = 27 |
1 | x | 13 = x |
The first three rows all satisfy the same cube relationship, so it is consistent across the complete opposite-ray pairs.
Apply that relationship to the incomplete pair: x = 13.
Since 13 = 1, the missing value is x = 1.
As a cross-check, squaring cannot explain all complete pairs because 42 = 16, not 64. Cubing reproduces 64, 8, and 27 from 4, 2, and 3 respectively, confirming x = 1.