What is the sum of restaurant number of vacant restaurants?
Direction: Read the information given below and answer the question that follows.
10 restaurants are situated in a single horizontal row. Each of the restaurants faces north. Seven persons P, Q, R, S, T, U and V own seven restaurants. Each of the restaurants is marked by different restaurant numbers. Restaurants, whose owners are not known, are considered as vacant. No two vacant restaurants are adjacent to each other. There are three restaurants with restaurant number 5, 56 and 72.
S’s restaurant number is 45 and S’s restaurant is to the left of R’s restaurant. P’s restaurant is to the right of Q’s restaurant. Restaurant number of U is 35. The restaurant number of Q is a prime number between 10 and 20. Restaurant number of T and V are even numbers. V’s restaurant is third restaurant to the left of T’s restaurant. Restaurant number 59 is immediate right of Q’s restaurant. At most three restaurants are to the right of T’s restaurant. There are two restaurants between V’s and U’s restaurants. R’s restaurant number is twice of Q’s restaurant number but not greater than 35. The restaurant immediate right of T is marked as restaurant number 14. Q’s restaurant is adjacent to neither V’s nor T’s restaurant. P’s restaurant number is 26 and P’s restaurant is immediate left of a vacant restaurant. Neither P’s nor Q’s restaurant is at extreme end. Neither U’s nor R’s restaurant is adjacent to a vacant restaurant. Restaurant number of one of the extreme end restaurants is 22. Restaurant number of T is less than that of V.Question 1: What is the sum of restaurant number of vacant restaurants?
A. 78
B. 80
C. 71
D. 67
E. 87
Right Answer is: A
SOLUTION
Seven restaurant owners: P, Q, R, S, T, U and V.
1. V’s restaurant is third restaurant to the left of T’s restaurant.
2. At most three restaurants are to the right of T’s restaurant.
3. There are two restaurants between V’s and U’s restaurants.
4. The restaurant immediate right of T is marked as restaurant number 14.
5. Restaurant number of U is 35.
6. Restaurant number of T and V are an even number.
7. Restaurant number 59 is immediate right of Q’s restaurant. Restaurant number of one of the extreme end restaurants is 22.
8. Q’s restaurant is adjacent to neither V’s nor T’s restaurant.
9. The restaurant number of Q is a prime number between 10 and 20. So, restaurant number of Q can be among 11, 13, 17 and 19.
10. R’s restaurant number is twice of Q’s restaurant number but not greater than 35. So, R’s restaurant number could be 22, 26, 34. Also, Q’s restaurant number could be 11, 13, 17.
11. P’s restaurant number is 26 and P’s restaurant is immediate left of a vacant restaurant. So, Q’s restaurant number would be either 11 or 17.
12. P’s restaurant is to the right of Q’s restaurant.
13. Neither P’s nor Q’s restaurant is at extreme end.
14. S’s restaurant number is 45 and S’s restaurant is to the left of R’s restaurant. (This eliminates case 1 as R’s restaurant number is either 22 or 34 no such position possible in case 1)
15. Neither U’s nor R’s restaurant is adjacent to a vacant restaurant. (This eliminates case 2)
16. There are three restaurants with restaurant number 5, 56 and 72. So, restaurant number of V and T must be 56 and 72. (There is no place for restaurant 5 in case 3(b) so this eliminates case 3 (b)).
17. Restaurant number of T is less than that of V.
Sum of restaurant number of vacant restaurants = 59 + 5 + 14 = 78
Hence, 78 is the sum of restaurant number of vacant restaurants.
