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4th sem Solution .pdf


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1. Which of the following has most number of divisors?
A. 99
B. 101
C. 176
D. 182
Solution:
Option(C) is correct
Divisors of 99=1,3,9,11,33,9999=1,3,9,11,33,99
Divisors of 101=1,101
Divisors of 176=1,2,4,8,11,22,44,88,176
Divisors of 182=1,2,7,13,14,26,91,182
Therefore 176 has most number of divisors
2. A girl wrote all the numbers from 100 to 200. Then she started counting the number of one's that has been used while
writing all these numbers. What is the number that she got?
A. 111
B. 119
C. 120
D. 121
Solution:
Option(C) is correct
From 100 to 200 there are 101 numbers.
There are 100, 1's in the hundred place.
10, 1's in tens place and10, 1's in unit place.
Thus, the answer is 100+10+10=100+10+10= 120.
3. If each of the three nonzero numbers a, b and c is divisible by 3, then abc must be divisible by which one of the following
the numbers?
A. 8
B. 27
C. 81
D. 121
Solution:
Option(B) is correct
Since each one of the three numbers a, b, and c is divisible by 3, the numbers can be represented as 3p, 3q and 3r, respectively,
where p, q and r are integers.
The product of the three numbers is 3p×3q×3r=27(pqr).
Since p, q and r are integers, pqr is an integer and therefore abc is divisible by 27.
4. The LCM of two numbers is 280 and their ratio is 7:87:8. The two numbers are
A. 70, 80
B. 35, 40
C. 42, 48
D. 28, 32
Solution:
Option (B) is correct
Let the number be 7x and 8x
HCF =x
Hence, HCF × LCM=7x ×8x
⇒ 280x=56x × x
⇒ x=5
Thus numbers are 35 and 40.
5. If we write down all the natural numbers from 259 to 492 side by side get a very large natural number 259260261....491492.
How many 8's will be used to write this large natural number?
A. 32
B. 43
C. 52
D. 53
Solution:
Option(D) is correct
From 259 to 458, there are 200 natural numbers so there will be 2×20=40 8's
From 459 to 492 we have 13 more 8's and so answer is 40+13=40+13= 53
6. What is the remainder when 7187 is divided by 800?
A. 143
B. 243
C. 343
D. 443
Solution:
Option(C) is correct
7187= (74)46 × 73= (2401)46 ×343
Now 2401=2400+1, where 2400 is perfectly divisible by 800
⇒(2401)46 is divided by 800, the remainder must be 11
So, the remainder when 7187 is divided by 800800 is 1×343=343
7. IBM-Daksh observes that it gets a call at an interval of very 10 minutes from Seattle, at every 12 minutes from Arizonia, at
the interval of 20 minutes from New York and after every 25 minutes it gets the call from Newark.
If in the early morning at 5:00 a.m. it has received the calls simultaneously from all the four destinations, then at which time it
will receive the calls at a time from all places on the same day?
A. 10:00 am
B. 3:00 am
C. 5:00 am
D. Both (A) and (B)

Solution:
Option(A) is correct
IBM – Daksh gets simultaneous calls from all the placers after an interval of time given by the LCM of 10, 12, 20 and 25
which is 300.
So, the next simultaneous calls are received after 300 minutes or after 5 hours or at 10:00 a.m.
Hence option(A) is the correct choice.
8. If n is a positive integer, which one of the following numbers must have a remainder of 3 when divided by any of the
numbers 4, 5 and 6?
A. 12n+312n+3
B. 24n+324n+3
C. 90n+290n+2
D. 120n+3
Solution:
Option (D) is correct
Let m be a number that has a remainder of 3 when divided by any of the numbers 4, 5 and 6.
Then m−3 must be exactly divisible by all three numbers.
Hence,m−3 must be a multiple of the Least Common Multiple of the numbers 4, 5 and 6.
The LCM is 3×4×5=60.
Hence, we can suppose m−3=60p, where p is a positive integer.
Replacing pp with n, we get m–3=60nm–3=60n.
So, m=60n+3.
Choice (D) is in the same format 120n + 3 =60(2n) +3
9. In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase
or decrease, and by how much
Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?
A. (1/3)
B. (1/8)
C. (2/8)
D. (1/16)
Answer: Option B
Explanation: This is a simple division series; each number is one-half of the previous number. In other terms to say, the
number is divided by 2 successively to get the next result.
4/2 = 2
2/2 = 1
1/2 = 1/2
(1/2)/2 = 1/4
(1/4)/2 = 1/8 and so on.
10. Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?
A. 7
B. 10
C. 12
D. 13
Answer: Option B
Explanation: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is
subtracted.
11. Look at this series: 36, 34, 30, 28, 24, ... What number should come next?
A. 20
B. 22
C. 23
D. 26
Answer: Option B
Explanation: This is an alternating number subtraction series. First, 2 is subtracted, then 4, then 2, and so on.
12. Look at this series: 22, 21, 23, 22, 24, 23, ... What number should come next?
A. 22
B. 24
C. 25
D. 26
Answer: Option C
Explanation: In this simple alternating subtraction and addition series; 1 is subtracted, then 2 is added, and so on.
13. Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?
A. 12
B. 14
C. 27
D. 53
Answer: Option B
Explanation: In this series, each number is repeated, then 13 is subtracted to arrive at the next number.
14. In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase
or decrease, and by how much
Look at this series: 21, 9, 21, 11, 21, 13, 21, ... What number should come next?
A. 14
B. 15
C. 21
D. 23
Answer: Option B
Explanation: In this alternating repetition series, the random number 21 is interpolated every other number into an otherwise
simple addition series that increases by 2, beginning with the number 9.

15. Look at this series: 58, 52, 46, 40, 34, ... What number should come next?
A. 26
B. 28
C. 30
D. 32
Answer: Option B
Explanation: This is a simple subtraction series. Each number is 6 less than the previous number.
16. Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next?
A. 7
B. 10
C. 14
D. 15
Answer: Option D
Explanation: This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7; then 1 is added,
and so on.
17. A can do piece of work in 30 days while B alone can do it in 40 days. In how many days can A and B working together do
it?
1
1
1
1
A. 167
B. 177
C. 187
D. 197

18. Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened
simultaneously, then the cistern will be filled in
A. 7.5 hr
B. 8 hr
C. 8.5 hr
D. 10 hr
Solution:
Option(A) is correct
Work done by all the tanks working together in 1 hour

19. Mr. Ram is on tour and he has Rs 360 for his expenses. If he exceeds his tour by 4 days he must cut down daily expenses
by Rs 3. The number of days of Mr. Ram's tour programme is
A. 28 Days
B. 24 Days
C. 22 Days
D. 20 Days
Solution:
Option(D) is correct
Let Ram under takes a tour of x days.

20. A and B together can complete a piece of work in 35 days while A alone can complete the same work in 60 days. B alone
will be able to complete the same working in:
A. 74 Days
B. 80 Days
C. 84 Days
D. 90 Days

21. How many times will minute hand and hour hand coincide in one day?
A. 21
B. 22
C. 23
D. 24
Solution:
Option(B) is correct
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).
AM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
PM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
The hands overlap about every 65 minutes, not every 60 minutes.
Thus the minute hand and the hour hand coincide 22 times in a day.

22. How many times will minute hand and hour hand perpendicular in one day?
A. 22
B. 23
C. 24
D. 44
Solution:
Option(D) is correct
In 12 hrs. the hands of the clock will be perpendicular to each other for 22 times as in 1 hr. time the hands of the clock wil be
at rt. angles for 2 times but between 1 1'o clock and 1'o clock they will be at rt. angles only twice.
Therefore, in 24 hrs. they will be at right angles 44 times.
23. How many times will minute hand and hour hand opposite in one day?
A. 22
B. 22
C. 23
D. 24
Solution:
Option(B) is correct
Eleven times in 12 hrs. The hands will be directly opposite each other at the following times:
12:32 and 8/11 of a minute
1:38 and 2/11 of a minute
2:43 and 7/11 of a minute
3:49 and 1/11 of a minute
4:54 and 6/11 of a minute
6:00
7:05 and 5/11 of a minute
8:10 and 10/11 of a minute
9:16 and 4/11 of a minute
10:21 and 9/11 of a minute
11:27 and 3/11 of a minute.
Therefore, the hands of the clock will be opposite to each other 22 times.
24. To complete a piece of work A and B take 8 days, B and C 12 days. A, B and C take 6 days. A and C will take:
A. 7 Days
B. 7.5 Days
C. 8 Days
D. 8.5 Days
Solution:
Option (C) is correct.

(A+C) will take 8 days to complete the work together.

25. Walking at the rate of 4 kmph a man cover certain distance in 2 hr 45 min. Running at a speed of 16.5 kmph the man will
cover the same distance in.
A. 12 min
B. 25 min
C. 40 min
D. 60 min

26. Two trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a
distance of 110 km from one of the stations. What is the ratio of their speeds?
A. 11:9
B. 7:3
C. 18:4
D. None of these
Solution:
Option(A) is correct
In same time, they cover 110 km and 90 km respectively.
For the same time speed and distance is inversely proportional.
So ratio of their speed = 110:90 = 11: 9
27. A train covers a distance in 50 min, if it runs at a speed of 48 kmph on an average. The speed at which the train must run
to reduce the time of journey to 40 min will be.
A. 45 kmph
B. 60 kmph
C. 75 kmph
D. None of these

28. Sachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total
distance is?
A. 5 km
B. 6 km
C. 7 km
D. 8 km

29. Walking at the rate of 4kmph a man cover certain distance in 2hr 45 min. Running at a speed of 16.5 kmph the man will
cover the same distance in.
A. 12 min
B. 25 min
C. 40 min
D. 60 min
Option C

30. A passenger train takes two hours less for a journey of 300 km if its speed is increased by 5 km/hr from its normal speed.
The normal speed is:
A. 35 km/hr
B. 50 km/hr
C. 25 km/hr
D. 30 km/hr

31. A train covers a distance in 100 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run
to reduce the time of journey to 40 min will be:
A. 30 kmph
B. 50 kmph
C. 80 kmph
D. 120 kmph

32. A good train and a passenger train are running on parallel tracks in the same direction. The driver of the goods train
observes that the passenger train coming from behind overtakes and crosses his train completely in 60 sec. Whereas a
passenger on the passenger train marks that he crosses the goods train in 40 sec. If the speeds of the trains be in the ratio 1:2.
Find the ratio of their lengths.
A. 3:1
B. 2:1
C. 3:2
D. 4:3

Seating Arrangement
Set 1
Directions: (Q1-5): study the following information carefully and answer the questions given below
Eight Cet king students, A,B,C,D,E,F,G and H are sitting around a circular table for playing a game. Four of them A,B,E and
F are not facing the centre. D is third to the left of H, who is fourth to the right of E. A is third of the right of B, who is third
to the left of D. F is second to the left of C.
33. How many person sit between A and B (if the counting start from B in CW direction)?
A. None
B. One
C. Two
D. Three
E. Other than given option
Option C
34. Who among the following sits third to the left of E?
A. G
B. A
C. H
D. D
Option B
35. What is the position of G with respect to F?
A. Third to the right
B. Third to the left
C. Second to the right
D. Cannot be determined
Option A
36. Who among the following is the neighbour of F and C?
A. E
B. H
C. A
D. B
Option D

E. B

E. Other than given option

E. Other than given options

37. Four of the following five are alike in a certain way and hence form a group. Find the one that does not belong to that
group.
A. EC
B. AG
C. DE
D. HA
E. FB
Option E
Set 2
Direction (1-5): Read the information given below and then answer the questions that follow:
Eight Cet King A,B,C,D,E,F,G and H are sitting around a circle in such a way that three of them are facing outside and rest of
them are facing the centre.
E is 2nd to the left of H, Who is facing outside. D is second to the left of F and third to the right of E, who is facing the
centre. B is third to the left of G and faces outside. G is third to the left of A, who is not an immediate neighbour of E and F.
The friends outside are not adjacent.
38. Which of the following group is facing outside?
A. BHE
B. CBH
C. CDH
D. Cannot be determined
B
39. What is D’s position with respect to A?
A. Immediate right
B. 3rd to the left
A

C. Opposite

40. Who is 2nd to the right of B?
A. H
B. G
C. C
D

D. A

E. None

D. 2nd to the right

E. immediate left

E. D

41. If all the friends change the respective position to immediate right place then who are still facing inside the centre?
A. A and E
B. F and D
C. C and G
D. A and D
E. G and A
D
42. Which of the following is true about the given information?
A. C and F are facing each other
B. E is third to the left of F
C. C is the third to the left of B
D. G and A are two places away from each other.
E. None of these
D
43. The letter A is the ______ letter of the English alphabet.
A. last
B. first C. second
D. third
B


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