13_46_8_180_210_75 = 64 . Use + and – in the empty places to make the equation…
2023
13_46_8_180_210_75 = 64 . Use + and – in the empty places to make the equation holds good. Take m = number of + and n = number of – . Find m – n?
- A.
-1
- B.
0
- C.
2
- D.
1
Attempted by 12 students.
Show answer & explanation
Correct answer: A
Solution:
We must insert + or - into 13 _ 46 _ 8 _ 180 _ 210 _ 75 = 64. There are 5 operator slots, so m + n = 5.
Find a placement that yields 64: 13 - 46 - 8 - 180 + 210 + 75 = 64
Verify the arithmetic: 13 - 46 = -33; -33 - 8 = -41; -41 - 180 = -221; -221 + 210 = -11; -11 + 75 = 64.
Count the signs: plus signs = 2 (between 180 and 210, and between 210 and 75); minus signs = 3 (the other three).
Therefore m = 2, n = 3 and m - n = -1.
Note: Because m + n = 5 is odd, m - n must be odd, so answers like 0 or 2 are impossible; the valid result here is -1.