Last year, Vincent's history and math classes had regular tests. Each history test had 22 questions and each math test had 14 questions. If Vincent had to answer the same number of history questions and math questions last year, what is the smallest number of each type of question he must have answered?
Question
Last year, Vincent's history and math classes had regular tests. Each history test had 22 questions and each math test had 14 questions. If Vincent had to answer the same number of history questions and math questions last year, what is the smallest number of each type of question he must have answered?
Solution
To solve this problem, we need to find the least common multiple (LCM) of the number of questions on the history tests (22) and the math tests (14). The LCM is the smallest number that is a multiple of both numbers.
Step 1: Prime factorize the numbers.
- Prime factors of 22 are 2 and 11.
- Prime factors of 14 are 2 and 7.
Step 2: Find the LCM.
- The LCM is the product of the highest powers of all primes that appear in either number.
- Here, the primes are 2, 7, and 11. The highest power of 2 that appears is 2^1 (from both 22 and 14), the highest power of 7 that appears is 7^1 (from 14), and the highest power of 11 that appears is 11^1 (from 22).
- So, the LCM is 2^1 * 7^1 * 11^1 = 2 * 7 * 11 = 154.
So, the smallest number of each type of question Vincent must have answered is 154.
Similar Questions
In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections: A,B and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is_________.
Balpreet's quiz scores in English are 80, 82, 79, and 84. Her quiz scores in History are 90 and 71. What is the sum of the scores she would need to get on her next English quiz and her next History quiz to raise each class' quiz score average to 85?
A student scored 75% on a test with 80 questions. How many questions did the student answer correctly?
In a test consisting of 143 questions, any question can be classified as Difficult/Easy or Precise/Long or Quants/Reasoning based. It was found that 20 of the questions are Easy, Precise and Reasoning based and 20 of the questions are Difficult, Precise and Reasoning based, 50 of the difficult questions are either Long or Quant based. 20 questions are Easy, Long and Quants based. In total, 64 questions are Quants based of which one fourth are Precise and Difficult. 10 of the questions are Difficult, Long and Quants based. At the quarterly birthday party of Sherry, a baby boy, 40 persons chose to kiss him and 25 chose to shake hands with him. 10 persons chose to both kiss him and shake hands with him. How many persons turned out at the party?Choices:- 35 75 55 2
In a test, a candidate attempted only 8 questions and secured 50% marks in each of the questions. If he obtained a total of 40% in the test and all questions in the test carried equal marks, how many questions were there in the test?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.