Rationale: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
The answer: (A)
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
(A) 27
(B) 29
(C) 31
(D) 34
(E) 35
Reasoning: Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Ans: (C)
Question: For some integer m, m^2 - 5 is divisible by all of the following EXCEPT
Options:
(A) 38
(B) 41
(C) 30
(D) 31
(E) 29
Rationale: 11 cartons total
7 large boxes (7 * 8 = 56 boxes)
4 small boxes (4 *10 = 40 boxes
11 total cartons and 96 boxes
The answer: (E)
Question: A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?
Options:
(A) 13
(B) 25
(C) 17
(D) 12
(E) 11
Reasoning: Total expenditure = 40 + 25 + 15 + 15 = 95%
Saving = (100 - 95) = 5%
5/100 Salary = 1200, Salary = 24000 Rs.
Ans: (B)
Question: A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 15% on conveyance. If his savings at the end of the month is Rs. 1200, then his salary per month in rupees is:
Options:
(A) 4000
(B) 24000
(C) 8000
(D) 10000
(E) None of these
Rationale: Let Rahul's age = x years
So, Madhan's age = ( x + 16 )years
Also, 3(x - 6) = x + 16 - 6 or, x = 14
Rahul's age = 14 years
And, Madhan's age 14 + 16 = 30 years
The answer: (A)
Question: The ages of Rahul and Madhan differ by 16 years. Six years ago, Madhan's age was thrice as that of Rahul's,find their present ages
Options:
(A) 14 years, 30 years
(B) 12 years, 28 years
(C) 16 years, 34 years
(D) 18 years, 38 years
(E) none of these
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
The answer: (A)
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
(A) 40 sec
(B) 22 sec
(C) 27 sec
(D) 17 sec
(E) 37 sec