I am a three-digit number
i am less than 200
i am divisible by 12,and by 9
my units digit is less than my tens digit
Here are the numbers between 100 and 200 that are divisible by 12.
108, 120, 132, 144, 156, 168, 180, 192
Which of those numbers meets your other criteria?
To find the three-digit number that meets the given criteria, let's break it down step by step:
Step 1: The number is less than 200.
Since the number is three-digit and less than 200, we know that the hundreds digit is 1.
Step 2: The number is divisible by 12 and 9.
For a number to be divisible by both 12 and 9, it must also be divisible by their least common multiple (LCM), which is 36. So, the number we are looking for is a multiple of 36.
Step 3: The units digit is less than the tens digit.
Since the units digit is less than the tens digit, the number can be written as 1xy, where x is the tens digit and y is the units digit.
Now, let's find the possible values for x and y, using the given criteria:
Since the number is divisible by 36, the sum of its digits must also be divisible by 9.
Case 1: x = 6, y = 3
If x = 6 and y = 3, we have 163. But this number is not divisible by 9.
Case 2: x = 7, y = 2
If x = 7 and y = 2, we have 172. This number is divisible by 9 (1 + 7 + 2 = 10) and also divisible by 12 (3 * 12 = 36). Therefore, the number that meets all the given criteria is 172.
The final answer is 172.
To find the three-digit number that meets these conditions, we need to break down the given information step by step.
1. The number is less than 200.
Start by listing three-digit numbers that are less than 200: 100, 101, 102,..., 198, 199.
2. The number is divisible by 12 and 9.
Test each of the numbers from the previous step and see which ones are divisible by both 12 and 9.
Divisibility by 12: A number is divisible by 12 if it is divisible by both 3 and 4.
Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
Let's go through the numbers one by one:
100: Not divisible by 12 since 100 is not divisible by 3 or 4.
101: Not divisible by 12 since 101 is not divisible by 3 or 4.
102: Not divisible by 12 since 102 is not divisible by 3 or 4.
103: Not divisible by 12 since 103 is not divisible by 3 or 4.
.
.
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118: Not divisible by 12 since 118 is not divisible by 3 or 4.
119: Not divisible by 12 since 119 is not divisible by 3 or 4.
120: Divisible by 12! Now, let's check if it's divisible by 9.
We check if 120 is divisible by 9 by adding up its digits: 1 + 2 + 0 = 3.
Since 3 is not divisible by 9, we move on to the next number.
121: Not divisible by 12 since 121 is not divisible by 3 or 4.
.
.
.
190: Not divisible by 12 since 190 is not divisible by 3 or 4.
191: Not divisible by 12 since 191 is not divisible by 3 or 4.
192: Not divisible by 12 since 192 is not divisible by 3 or 4.
193: Not divisible by 12 since 193 is not divisible by 3 or 4.
194: Not divisible by 12 since 194 is not divisible by 3 or 4.
195: Not divisible by 12 since 195 is not divisible by 3 or 4.
196: Not divisible by 12 since 196 is not divisible by 3 or 4.
197: Not divisible by 12 since 197 is not divisible by 3 or 4.
198: Divisible by both 12 and 9! Now, let's check the final condition.
The unit digit is less than the tens digit, so we confirm that "198" is the three-digit number that satisfies all the given conditions.