| 1. Abhinav is a professional staying in Gurgaon, Haryana. His house has a specific number as per the following instructions: i. If his house number is a multiple of 3, then it is a number from 50 through 59. ii. If his house number is not a multiple of 4, then it is a number from 60 through 69. iii. If his house number is not a multiple pf 6, then it is a number from 70 through 79. What is Abhinav’s house number? |
Medium |
| A. 76 B. 78 C. 75 D. Can’t be determined |
View Answer
Answer: Option A
Explanation:
Let Abhinav’s house number be N.
From i, permissible values of N from 50 through 59 are: 51, 54, 57 —– ❶
From ii, permissible values of N from 60 through 69 are: 61, 62, 63, 65, 66, 67, 69 —– ❷
From iii, permissible values of N from 70 through 79 are: 70, 71, 73, 74, 75, 76, 77, 79 —– ❸
Now, all three values in ❶ are non-multiplies of 4 and from ii, these are eliminated as possible values of N.
Also, 63, 66 and 69, are multiples of 3, and from i, these values in ❷ are eliminated as possible values of N.
Further, from iii, the remaining values of ❷ [i.e., 61, 62, 65, 67] are eliminated as they are non-multiples of 6.
So, we are left with only values in ❸ as possible values of N. Out of these, 75 is a multiple of 3, and hence from i it is eliminated. Further, 70, 71, 73, 74, 77 and 79 are non-multiples of 4 and from ii they are also eliminated
-> The only value left after eliminating values in ❶, ❷ and ❸ is 76. Hence, Abhinav’s house number is 76.
| 2. P, Q, R and S are playing a game of table tennis (mixed doubles), such that: i. There are two pairs of siblings: P & Q and R & S. ii. Q is directly across the net from R. iii. S is diagonally across the net from the worst player’s sibling. iv. The best player and the worst player are on the same side of the net. Who is the best player? |
Medium |
| A. P B. Q C. R D. Can’t be determined |
View Answer
Answer: Option B
Explanation:
From ii, Q is directly across R —– ❶
From iii, S is diagonally across P/if Q is the worst player —– ❷
or S is diagonally across Q/if P is the worst player —– ❸
or S is diagonally across R/if S is the worst player —– ❹
Combining ❶, ❷, ❸ & ❹, we get only the following two possibilities:
In both the cases, ‘Q’ is the best player
| 3. A, B and C started going to the Shadows Salon last month. The way in which they visit the salon is as follows: i. One of them goes to the salon every 2 days, another one visits every 3 days, and the third one goes every 7 days. ii. A went to the salon for the first time in this month on a Monday, B went for the first time in this month on a Wednesday, and C went for the first time in this month on a Friday. iii. All three of them went at the salon on the same day this month, which was where they met. On which date of the month did they all meet? |
Difficult |
| A. 25th B. 26th C. 27th D. Can’t be determined |
View Answer
Answer: Option C
Explanation:
The person who visits every 2 days visits the salon for the first time this month on the 1st or the 2nd, depending whether this person visits the salon for the last time in the previous month on the penultimate or the last day respectively.
Similarly, the person goes every 3rd day visits the salon for the first time this month on the 1st, 2nd or 3rd, depending upon whether this person visits the salon for the last time in the previous month on the third last, penultimate or last day respectively.
From ii the first and the third day of this month need to be a Monday and a Wednesday respectively OR a Wednesday and a Friday respectively. Thus, the person visiting every second day will visit on the 1st, and the person visiting every 3rd day will visit on the 3rd, because they need to be separated by a day.
Case I: 1st day of this month is a Monday
In this case A goes to the salon on the 1st and then every 2 days; B goes to the salon on the 3rd day and then every 3 days; C goes on the 5th and thus every 7 days. So, the visiting pattern in this case is as follows:
A: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31
B: 3, 6, 9, 12, 15, 18, 21, 24, 29, 30
C: 5, 12, 19, 26
Note: The dates which are underlined will depend on the type of month. For example: 29, 30 and 31 are not possible for a leap month; 31 is not possible for months ending in 30 days.
Case II: 1st day of this month is a Wednesday
In this case B goes on the 1st and then every 2 days; C goes on the 3rd and then every 3 days; A goes on the 6th and then every 7 days. The visiting pattern is as follows:
B: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31
C: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
A: 6, 13, 20, 27
Out of the two cases, case I is ruled out because it does not satisfy condition iii which states that they all meet on a particular day this month. Thus, only case II is possible, and they meet on the 27th of this month.