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1. A two-digit number has 3 in its unit digit. The sum of its digit is one-seventh of the number itself. What is the number?
- A. 73
- B. 73
- C. 73
- D. 73
Answer: Option B
Explanation:
Since it is in the form of a two digit number, then we can write it as a decimal expansion with a three in the units place.
Let y = 10x + 3
We also know that x + 3 = y⋅17x + 3 = y⋅17
This means if we multiply both sides by 7 we get:
y = 7(x + 3)y = 7(x + 3)
y = 7x + 21y = 7x + 21
Since these are both equal to y, we can set them equal one another to find x, the tens digit value:
7x + 21 = 10x + 37x + 21 = 10x + 3
−3x + 21 = 3−3x + 21 = 3
−3x = −18−3x = −18
x = 6x = 6
y = 10x + 3 = 10(6) + 3 = 63
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