Mr. Hon purchases a new car every 4 years. Ms. Jasper purchases a new car every 6 years. They both purchased new cars this year. When will they next both purchase new cars in the same year?
A.
in 2 years
B.
in 8 years
C.
in 12 years
D.
in 24 years
The next time Mr. Hon purchases a new car will be in 4 years. Likewise, the next time Ms. Jasper purchases a new car will be in 6 years. The question is asking when they will both purchase new cars in the same year.
One way to find the answer is to find the least common multiple of 4 and 6. The multiples of 4 are: 4, 8, 12, 16, 20, 24... The multiples of 6 are: 6, 12, 18, 24...
From the lists above, we see that the least common multiple of 4 and 6 is 12. Therefore, Mr. Hon and Ms. Jasper will next purchase new cars in the same year 12 years from now.
The answer is C. in 12 years.
To determine when Mr. Hon and Ms. Jasper will next purchase new cars in the same year, we need to find the common multiple of 4 years and 6 years.
The multiples of 4 years are: 4, 8, 12, 16, 20, 24, ...
The multiples of 6 years are: 6, 12, 18, 24, ...
We can see that the common multiple is 12 years.
Therefore, the answer is C. in 12 years.
To determine when Mr. Hon and Ms. Jasper will next purchase new cars in the same year, we need to find the least common multiple (LCM) of 4 and 6.
One way to find the LCM is by listing the multiples of each number:
For 4: 4, 8, 12, 16, 20, 24, 28, 32, ...
For 6: 6, 12, 18, 24, 30, 36, ...
From the lists, we can see that the first number they both have in common is 12.
Therefore, Mr. Hon and Ms. Jasper will next purchase new cars in the same year after 12 years.
So the answer is C. in 12 years.