Examine the following three figures in which the numbers follow a specific…
2023
Examine the following three figures in which the numbers follow a specific pattern:
What is the missing number (?) in the third figure?
Answer: C. 3 — CONCEPTEuclidean division writes an integer a as a = dq + r for a positive divisor d, where q is the quotient. The remainder must satisfy 0 ≤ r < d. Here,…
- A.
8
- B.
6
- C.
3
- D.
More than one of the above
- E.
None of the above
Attempted by 7 students.
Show answer & explanation
Correct answer: C
CONCEPT
Euclidean division writes an integer a as a = dq + r for a positive divisor d, where q is the quotient.
The remainder must satisfy 0 ≤ r < d. Here, each lower number is the remainder when the left top number is divided by the right top number.
APPLICATION
For 65 and 56, 65 = 56 × 1 + 9, so the remainder is 9.
For 83 and 38, 83 = 38 × 2 + 7, so the remainder is 7.
For 71 and 17, 71 = 17 × 4 + 3, so the missing number is 3.
CROSS-CHECK
The value 3 satisfies 0 ≤ 3 < 17.
Also, 71 − 3 = 68, and 68 is divisible by 17.
Therefore, the missing number is 3.