Answer Key of THE LAST LAP ANALYTICAL SKILLS-3

THE LAST LAP ANALYTICAL SKILLS-3

1 At 12:00 hours Jake starts to walk from his house at 6 Km an hour. At 13:30 hours,
Paul follows him from Jake’s house on his bicycle at 8 Km per hour. When will Jake
be 3 Km behind Paul?
(a) 19:30hrs (b) 18:30hrs (c) 20:30hrs (d) 19:00hrs

2 Two cars start from A and B and travel towards each other at speeds of 50 kmph and
60 kmph respectively. At the time of their meeting the second car has travelled 120
km more than the first, the distance between A and B is:
(a) 600 Km (b) 1320 Km (c) 720 Km (d) 3120Km

3 A tree of height 36 m at the edge of a road broke at a certain height and it fell in such
a way that its top touched the other edge of the road. If the breadth of the road is
12m, then the height at which the tree broke was
(a) 24 (b) 16 (c) 18 (d) 12

4 .A, B and C can do some work in 36 days. A and B together do twice as much work as
C alone, and A and C together can do thrice as much work as B alone. Find the time
taken by C to do the whole work.
(a) 72 (b) 120 (c) 108 (d) 96

5 Oranges can be packed in sets of 10 oranges in a box type A or 25 oranges in box
type B. A carton comprising of 1000 oranges of type A and type B boxes in packed.
How many different combinations are possible in the number of type A and type B
boxes while organizing the oranges?
(a) 19 (b) 21 (c)18 (d) 20

6 George, Paul and Hari start a business by contributing Rs. 30000, Rs. 40000 and Rs.
50000 respectively. After ½ a year George withdraws half his contribution. At the
end of the year the business showed a profit of Rs. 90000 which was divided
amongst the 3 men proportionate to amount and duration of their investment in the
enterprise. Paul got:
(a) Rs. 18000 (b) 25000 (c) 32000 (d) 24000

7 Arun makes a popular brand of ice-cream in a rectangular shaped bar 6 cm long, 5
cm wide and 4 cm thick. To cut costs, the company had decided to reduce the volume
of the bar by 19%. The thickness will remain the same, but the length and width will
be decreased by the same percentage. The new width will be
(a) 6.5 m (b) 4.5 m (c) 5.5 m (d) 7.5 m

8 Certain positive integers have these properties:
(I).the sum of the squares of their digits is 50
(II) each digit is larger than one to its left.
The product of the digits of the largest integer with both properties is
(a) 7 (b)25 (c) 36 (d) 48

9 A circular swimming pool is surrounded by a concrete walk 4 feet wide. If the area of
the walk is 11/25 of the area of the pool, the radius of the pool in feet is
(a) 8 feet (b) 20 feet (c) 16 feet (d) 30 feet

10 Ten people form a circle. Each one thinks of a number and whispers it to the two
neighbours adjacent to her in the circle. Then each person computes and announces
the average of the numbers she heard from her two neighbours. The numbers
announced by the persons are 47, 11, 21, 28, 35, 45, 50, 60, 69, 36. What was the
number picked by the person who announced the average 69?
(a) 80 (b) 38 (c) 68 (d) 28

11 Consider all permutations (i.e. arrangements) of the digits 1, 2 and 3. We will say
that a hit has been scored if at least one digit occurs in the proper position in the
permutations, i.e. if 1 occurs in the first position, or 2 occurs in the second position,
or 3 in the third position. In how many of these permutations is a hit score?
(a) 2 (b) 1 (c) 3 (d) 4

12 A team won 80% of the games it played. It played 5 more games of which it won 3
and lost 2. Its loss percentage changed to 25%. How many games did it play overall?
(a) 25 (b) 14 (c) 16 (d) 20

13 George works 5 times as fast as his son and hence completes a job 40 days earlier
than his son. Find the time they, working together, would take to finish the job.
(a) 7.5 (b) 6 (c) 8.33 (d) 12.5

14 If 15 women or 10 men can complete a project in 55 days, in how many days will 5
women and 4 men working together complete the same project?
(a) 75 (b) 95 (c) 55 (d) 65

15 A number when successively divided by 5,3,2 gives remainders 0,2 and 1
respectively in that order. What will be the remainders when the same number is
divided successively by 2, 3 and 5 in that order?
(a) 2,1,3 (b) 4,1,2 (c) 4,3,2 (d) 1,0,4

16 Which of the following represents the largest 4 digit number which can be added to
7249 in order to make the derived number divisible by each of the following
numbers: 12, 14, 21, 33 and 54?
(a) 8316 (b) 8727 (c) 9123 (d) 9383

17 2 workers, one young and one old, live together and work at the same office. It takes
20 minutes for the young man to walk to office. the old man takes 30 minutes for the
same distance, When will the young man catch up with the old man, if the old man
starts at 10:00 am and the young man starts at 10:05 am?
(a) 11.00 am (b) 10.10 am (c) 10.15 am (d) 10.20 am

18 What is the largest integer that divides all three numbers 23400, 272304, 205248
without leaving a remainder?
(a) 48 (b) 24 (c) 96 (d) 72

19 We have an equal arms two pan balance and need to weigh objects with integral
weights in the range 1 to 40 kilograms. We have a set of weights and can place the
weights in any pan.(i.e.) some weights can be in a pan with objects and some weights
can be in the other pan. The minimum number of weights required is
(a) 4 (b) 10 (c) 5 (d) 6

20 A and B completed a work together in 5 days, had A worked at twice the speed and B
at half the speed, it would have taken them four days to complete the job. How much
time would it take for A alone to do the work.
(a) 10 days (b) 15 days (c) 20 days (d) 25 days

21 The rupee/coin changing machine at a bank had a flaw. It gives 10 ten rupees note if
you put a 100 rupee note and 10 one rupee coins if you insert a 10 rupee note but
gives 10 hundred rupee notes when you put a one rupee coin.
Sivaji, after being ruined by his rivals is left with a one rupee coin and discovers the
flaw in the machine by accident. By using the machine repeatedly, which of the
following amounts is valid amount that Sivaji can have when he gets tired and stops
at some stage (assume that the machine has an infinite supply of notes and coins)
(a) 9989 (b) 35965 (c) 24975 (d) 17984

22 A 3 x 3 grid is colored using red and blue colors such that if we rotate the grid about
its center in the plane by 180 degrees, the grid looks the same. The number of ways
to color this grid is:
(a) 256 (b) 64 (c) 16 (d) 32

23 A tourist wants to visit 3 or more of the 5 major cities in India: Chennai, Bengaluru,
Mumbai, Delhi, and Kolkata. In how many ways can he plan his tour such that
Chennai is always included? (Two plans of the tour are different if the cities in the
tour or the order of the cities in different.)
(a) 5! +2!
(b) 5! +4! +3!
(c) 5! + (4x4!) + (6x3!)
(d) 5(4! +3! +2!)

24 How many 6 digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so
that the digits should not repeat and the second last digit is even?
(a) 6480 (b) 2160 (c) 720 (d) 320

25 A owes B Rs. 50. He agrees to pay B over a number of consecutive days starting on a
Monday, paying single note of Rs 10 or Rs. 20 on each day. In how many different
ways can A repay B. (Two ways are said to be different if on at least one day, a note
of different denomination is given.)
(a) 6 (b) 8 (c) 7 (d) 5

26 A student selects 3 digits from numbers 1 to 9 such that they are in strictly
increasing order. How many selections have the property that the three digits form
an arithmetic progression?
(a) 7 (b) 12 (c) 16 (d) 14

27 Professor Absentminded has a very peculiar problem that he cannot remember
number larger than 15. However, he tells his wife, I can remember any number up to
100 by remembering the three numbers obtained as remainders when the number is
divided by 3, 7 and 11 respectively. For example (2, 3, 6) is 17. Professor remembers
that he had (2, 4, 8) rupees in the purse, and he paid (2, 5, 4) rupees to the servant.
How much money is left in the purse?
(a) 51 (b) 55 (c) 48 (d) 37

28 Ahmed, Babu, Chitra, David and Eesha each choose a large different number. Ahmed
says, “ My number is not the largest and not the smallest.” Babu says, “My number is
not the largest and not the smallest.” Chitra says,” My number is the largest”. David
says, “ My number is the smallest”. Eesha says, “My number is not the smallest”.
Exactly one of the five children is lying. The others are telling the truth. Who has the
largest number?
(a) David (b) Eesha (c) Chitra (d) Babu

29 Raj tossed three dice and their results are noted down. What is the probability that
Raj gets the sum as 10?
(a) 1/72 (b) 1/9 (c) 25/216 (d) 1/8

30 The letters in the word ADOPTS are permuted in all possible ways and arranged in
the alphabetical order. Find the word at position 42 in the permuted alphabetical
order.
(a) AOTDPS (b) AOTPDS (c) AOTDPS (d) AOSTPD