L3 - Set 3

One of 5 children, A, B, C, D, and E secretly took a cookie from a cookie jar.

A says: “I did not take the cookie”

B says: “I took the cookie”

C says: “E did not take the cookie”

D says: “I did not take the cookie”

E says: “A took the cookie”

Only 1 child lied. Who took the cookie?

• A

• B

• C

• D

• E

How many license plates consist of 2 letters followed by 3 digits?

(a)  

Given that 17^22 is 1 mod 23, what is the remainder when 17^112 is divided by 23?

(a)  

4 books, Language, Mathematics, Science, and Social Science, not necessarily in that order, are placed on a desk in 1 pile. Suppose:

·         The first book is not Mathematics and the 2^nd book is not Science

·         The 2^nd or 4^th book is Social Science

·         The 3^rd book is either Language or Social Science

·         The 4^th book is either Science or Social Science

Based on these conditions, what is the first book?

• Social Science

• Science

• Language

• Mathematics

Elvis took some tests. He scored 76 in one test, and the average score for the tests is 65. If he obtains 96 instead of 76, his average would be 89. How many tests did he take?

(a)  

3 years ago, father’s age was 15 times son’s age. 2 years from today, father’s age will be 5 time son’s age. How old is son today?

(a)  

The fraction 1/9 tripled by adding the same number to both the numerator and denominator. What is that number?

(a)  

A tells truths on Monday, Tuesday, Wednesday, and Thursday. B tells truths on Monday, Friday, Saturday, and Sunday. They lie on all other days. One day, they both said, “I lied yesterday”. What day was that?

(a)  

In a group of athletes, 24 play badminton, 20 play soccer, 11 play both, and 13 play neither. How many students are in that group?

(a)  

Consider the sentence: THIS IS ONE AWESOME MATHEMATICS COMPETITION. Every minute, the 1^st letter of each word moved to the other end of the word. After how many minutes will the original sentence reappear?

(a)