12. Matrix Arrangement
12.1 Number Test
12.2 Time Sequence Test
12.1 number test
In this type of test a series of numbers is given. The candidate has to find out the. number of times
the given digit occurs under certain conditions.
Illustration 1
How many 3’s are there in the following number series which are preceded by 6 but not followed by 7?
2374356374638963518372428639
(A) One (B) Two (C) Three (D) Four (E) More than four
Solution
(C)– Reqd. 3’s are printed boldly in the series.
2374356374638963518372428639
Illustration 2
How many numbers are there from 3 to 100 which are divisible by 4 and either unit digit or tenth digit or both include 4?
(A) 10 (B) 12 (C) 19 (D) 25 (E) Less than 10
Solution
(E)– The numbers which are divisible by 4 from 3 to 100 and include 4 at any place are printed boldly in the following numbers.
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92,96, 100
Thus reqd. numbers are 7 in all.
Illustration 3
If 69 × 87 = 1515 then 76 × 68 = ?
(A) 1315 (B) 1214 (C) 1415 (D) 1317 (E) None of these
Solution
(E)– As,
69 x 87 ® 1515
6 + 9 = 15 8 + 7 = 15
Similarly,
But 1314 is not given in any alternative.
Hence the correct answer is (E).
Illustration 4
If 73 × 68 = 3687 then 24 × 15 = ?
(A) 2415 (B) 5142 (C) 4152 (D) 1425 (E) None of these
Solution
(C)– As,
Similarly,
Hence the correct answer is (C).
12.2 time sequence test
There are two types of questions under this.
(1) The value of time or digit is found from the statements of two people.
The common value in the two statements is taken as correct.
Illustration 5
Manjeet remembers that his father’s birth day falls after 9th May and before 12th May,
while his sister Anandita remembers that her father’s birth day falls after 10th May and before 13th May.
What is date of birth day of their father’s ?
(A) 9th May (B) 10th May (C) 11th May (D) 12th May (E) None of these
Solution
(C)– According to Manjeet, his father’s birth day = May (10 and 11)
But according to Anandita her father’s birth day = May (11 and 12)
But 11th May is common to both.
Hence their father’s birth day is 11th May.
(2) Under this head questions based on time are asked. The following shortent formula is used for this.
Time of information given
=
Illustration 6
The station master said to Samant, “A train for Surat leaves after every 1-15 hours
. A train had already left 35 minutes ago. The next train will leave at 5-40.”
At what time this information was given to Samant by the station master ?
(A) 4-25 (B) 5-00 (C) 4-45 (D) 5-15 (E) None of these
Solution
(B)– Time of information given = (5.40 – 1.15) + 0.35
= 4.25 + 0.35 = 5.00
Hence the correct answer is (B).
EXERCISE-I
1. How many 7’s are there in the following number series, which are preceded by an even number but not followed by any odd?
437523721367542742712276572
(A) On (B) Two (C) Three (D) Four (E) More than four
2. How many 5’s are there in the following number series, which are preceded by 3 but not followed by 2?
5243546785325735642354752358356
(A) One (B) Two (C) Three (D) Four (E) More than four
3. How many 3’s are there in the following number series, which are preceded by an odd number but not followed by an even number ?
3425315213673182785391345235435
(A) One (B) Two (C) Three (D) Four (E) More than four
4. If 25 is related with 52 in the same way 29 is relate d to which of the following numbers?
(A) 11 (B) 18 (C) 92 (D) 22 (E) None of these
5. If 25 x 35 = 78, then 45 x 52 = ?
(A) 97 (B) 2010 (C) 106 (D) 610 (E) None of these
6. If 31 is related to 13 in the same way 53 is related to which of the following numbers?
(A) 24 (B) 8 (C) 15 (D) 35 (E) None of these
7. If the numbers which are divisible by 4, from 4 to 84 are written in reverse order then which number will be at the 7th place ?
(A) 60 (B)28 (C) 20 (D) 32 (E) None of these
8. How many numbers are there from 5 to 100, which are divisible by 3 and either unit or tenth digit or both include 3?
(A) 10 (B) 8 (C) 6 (D) Less than 6 (E) None of these
9. Mohan says that the birthday of his sister Anita is before 24 October and after 21 October while his father remembers that A
nita’s birthday is after 22 October but before 25 October. On which date of October does the birthday of Anita fall ?
(A) 21 (B) 22 (C) 24 (D)25 (E) None of these
10. How many 4’s are there in the following number-series which are preceded by 5 but not followed by 7?
23423425473243192547547234529546
(A) One (B) Two (C) Three (D) Four (E) More than four
11. If the numbers between 4 to 90, which are divisible by 5, and which contain 5 in the unit, tenth or both place,
are removed, then how many numbers divisible by 5 will be left?
(A) 7 (B) 8 (C) 18 (D) 12 (E) None of these
12. Sumitra remembers that her elder son was bom after 15 July and before 18 July.
While her husband Arvind remembers that his son was born after 16 July but before 19 July
If the statement of both are correct then on what day of July their son was born ?
(A) 18 (B) 16 (C) 17 (D)19 (E) None of these
13. How many 9’s are there in the following number series, which are neither preceded by 5 nor followed by 7?
94523856234964879512394597692
(A) One (B) Two (C) Three (D) Four (E) None of these
14. Rajan remembers that his elder brother was born between 13th and 16th April while his mother remembers that he
was born after 14th April and before 17th April. If the statements of both are
considered correct then on which date of April he was born?
(A) 14 (B) 16 (C) 14 or 15 (D) 15 (E) 15 or 16
15. How many numbers are there from 1 to 60, which are divisible by 3 and either unit digit or tenth digit or both include 3 ?
(A) 5 (B) 9 (C) 15 (D) More than 15 (E) None of these
16. If the following numbers are written in descending order then what will be the middle digit of the middle term ?
723,.789, 595, 659, 713, 785, 689
(A) 1 (B) 7 (C) 8 (D) 3 (E) 2
17.A bus for Bombay leaves after every forty minutes from a bus stand. An enquiry clerk told a passenge
r that the bus had already left ten minutes ago and the next bus will leave at 10.45 a.m.
At what time did the enquiry clerk give this information to the passenger ?
(A) 10.05 a.m. (B) 9.55 a.m. (C) 10.35 a.m. (D) 1015 a.m. (E) 10.25 a.m.
18. How many 1, 3 and 7 are there in the following number series in which 7 comes in between 1 and 3,
which are on the left and right side of 7 respectively?
2973173771331738571377173906
(A) 2 (B) 3 (C) 4 (D) More than 5 (E) None of these
19. In the given number-series, how many 5’s are there, which are preceded by 4 but not followed by 3 ?
543765453624545543756455435
(A) 1 (B) 2 (C) 3 (D) None (E) None of these
20. If the numbers between 1 to 65 and divisible by 4 are written in reverse order
then which of the following numbers will be at 10th place?
(A) 44 (B) 24 (C) 40 (D) 28 (E) None of these
21 Rashmi remembers that her elder brother Jitendra was born after 13th May and before
16th May while her mother remembers that he was born after 15th May and before 18th May
. If the statements of both are supposed correct then on which date of May was he born ?
(A) 15 (B) 14 (C) 14or 15 (D)Can not be determined (E) None of these
22. Sanju remembers that his elder brother was born after 15th June and before 19th June.
While his mother remembers that he was born after 16th June and before 20th June.
If the statements of both are supposed to be correct then on which day of June he was born ?
(A) 17 (B) 17 or 18 (C) 18 (D) 18 or 19 (E) 17 or 19
23. Neelam remembers that her elder sister was married after 8th May and before 11th May.
While Puja remembers that she was married after 9th May and before 12th May.
If the statements of both are supposed to be correct then on which date of May she was married?
(A)10 (B) 11 (C) 10 or 11 (D) 9 (E) None of these
24.Kumar Akhilesh remembers that Mahendra got marks in Hatrics Exam, between 67% to 70%.
While Abhishek remembers that Mahendra got marks between 68% to 71%.
If the statements of both are correct then how many per cent marks did he got?
(A) 67 (B) 67 or 68 (C) 69 (D) 68 or 69 (E) None of these
25. How many 6’s are there in the following number-series which are preceded by 5 but not followed by 7?
56765649276743568649567
(A) One (B) Two (C) Three (D) Four (E) None of these
26. How many 4’s are there in the following number-series which are preceded and followed by only an even number ?
6432483154232464813242645
(A) One (B) Two (C) Three (D) Four (E) None of these
27. How many 2’s are there in the following number series which are preceded by 5 but not followed by an odd number ?
13523545245226245267823527524
(A) One (B) Two (C) Three (D) More than four (E) None of these
28 How many 3’s are there in the following series, which are not preceded by an odd number but followed by 4?
15323465347834923456343534
(A) None (B) Two (C) Four (D) One (E) None of these
29. How many B’s are there in the following letter-series, which are followed by G but G is not be followed by S ?
BGSQBRNOBGNSQLTBGQTDBGUWXBGF
(A) 4 (B) 3 (C) 2 (D) 5 (E) None of these
30. How many D’s are there in the following letter-series, which are preceded by K and followed by Q ?
KDRMBSKDQKRBLKDQMQDKEFQDK
(A) 4 (B) 2 (C) 1 (D) 3 (E) None of these
31. If the numbers from 4 to 55 which are divisible by 3 and also the numbers which contain 3 as one of the digits,
are removed, then how many numbers will be left ?
(A) 24 (B) 23 (C) 22 (D) 25 (E) None of these
32. If the numbers from 2 to 43, which are divisible by 3 and 3 comes at any place in the number,
are removed, then how many numbers will be left ?
(A) 37 (B) 34 (C) 33 (D) 36 (E) None of these
33. An enquiry clerk said to Suman, “A bus for Patna leaves after every 45 minutes.
The last bus has already left 15 minutes ago and the next bus will leave at 2-30 p. m.”
At what time did the enquiry clerk gave this information to Suman ?
(A) 1.45 P.M. (B) 2.15 P.M. (C) 1.30 P.M. (D) 2.00 P.M. (E) None of these
34. A Saint said to his disciple, “The bell of the temple rings after every 30 minutes.
The last bell has already rung 20 minutes ago and the next bell will ring at 8-15 a.m.”
At what time did the saint give this information to his disciple ?
(A) 8.20 (B) 7.45 (C) 8.05 (D) 7.25 (E) None of these
35. At a railway station a man said to Swapna, “A train leaves for Muzaffar Nagar after every 1.45 hours.
The last train has already left 50 minutes ago and the next train will leave at 5.15 p.m.
” At what time this information was given to Swapna ?
(A) 3.30 (B) 2.40 (C) 4.10 (D) 3.50 (E) None of these
36. A trader said to his servant Ramu, “I leave for my house after every 2.40 hours from his shop.
I have already gone to his house 55 minutes ago and next time. I shall go to my house from the shop at 8.15 p.m.”
At what time this information was given to the servant ?
(A) 6.30 (B) 6.00 (C) 6.15 (D) 4.40 (E) None of these
37. A doctor said to his compounder, “I go to see the patients at their residence after every 3.30 hours.
I have already gone to the patient 1.20 hours ago and next time I shall go at 1.40 p.m.”
At what time this information was , given to the compounder by the doctor ?
(A) 10.10 (B) 11.30 (C) 8:50 (D) 11.20 (E) None of these
EXERCISE-II
Directions (1-5): Read the following information carefully and answer the questions given
below:
(i) P,Q,R,S,T and U are six students procuring their masters degree in six
different subjects-English, History, Philosophy, Physics, Statistics and Mathematics.
(ii) Two of them stay in Hostel, two stay is paying guest (PG)
(iii) R does not stay as PG and studies Philosophy
(iv) The student studying statistics and history does not stay as paying guest.
(v) T studies Mathematics and S studies Physics.
(vi) U and S stay in hostel. T stays in PG and Q stays at home.
1. Which of the following pairs of students stays one each at hostel and home?
(A US (B) SR (C) QR (D) Data inadequate (E) None of these
2. Who studies English?
(A) S (B) T (C) U (D) R (E) None of these
3. Which of the following pairs of students stay at home?
(A) PQ (B) QR (C) RS (D) ST (E) None of these
4. Which of the following combinations of subject and place of stay is not correct?
(A) Physics–Hostel (B) English–Hostel
(C) Philosophy–Home (D) Mathematics–Paying Guest
(E) All are correct
5. Which subject (s) does Q study?
(A) History (B) Statistics (C) History or Statistics (D) Data inadequate (E) None of these
Directions (6–10): Read the following information and answer the given questions
(i) Six friends Ramesh, Dinesh, Lokesh, Nilesh, Shailesh and Hitesh work in different companies namely
P,Q,R,S,T and U and each one wears company sponsored different coloured tie i.e. blue, green, pink, yellow,
purple and red through not necessarily in the same order
(ii) The one wearing blue tie works in company S and the one waring green tie work in company P.
(iii) Hitesh does not work in company R or T.
(iv) Ramesh wears pink tie and works in company Q.
(v) Nilesh does not work in company T and purple colour tie is not sponsored by company R.
(vi) Shailesh works in company U and neither Nilesh nor Dinesh work in company S.
(vii) Company T does not sponsor purple or yellow coloured tie and Lokesh works in
company P.
6. Which colour is sponsored by company R?
(A) It can not be ascertained (B) Blue (C) Purple (D) Red (E)None of these
7. Which of the following colour of tie company-person combinations is correct?
(A) Green-R-Lokesh (B) Blue-S-Lokesh (C) Red-T-Dinesh (D)Yellow-R-Shailesh (E) None of these
8. Which of the following is true?
(A) Company U sponsors green lie (B) Shailesh wears red tie
(C) Nilesh works in company T (D) Red colour is sponsored by company T
(E) None of these
9. Which of the following sequences of companies represents Ramesh, Dinesh, Lokesh, Nilesh, Shailesh and Hitesh in the same order?
(A) Q, P, T, R, U, S (B) Q, T, P, R, U, S
(C) Q, P, T, S, U, R (D) Q, T, P, S, U, R (E) None of these
10. On a shelf are placed six volumes side by side labelled ABCDEF,
BCEF have green covers while others have yellow covers.
ADB are new volumes while the rest are old volumes. ACB are law reports while the rest are medical extracts.
Which two volumes are old medical extracts and have green covers?
(A) BC (B) CD (C) CE (D) EF
Directions(11-14): Study the following informations and answer the questions given below
(i) Jayant, Kunal, Namrata, Anjali and Tanmay are five members of a family.
(ii) They have their birth dates from January to May each member in one of these months.
(iii) Each one likes one particular item for his/her birthday out of Bengali Sweets, Chocolate, Pastries, Ice Cream, Dry Fruits.
(iv) The one who likes Pastries is born in the month which is exactly middle in the months given.
(v) Anjali does not like Ice Cream but brings Chocolates for Jayant in February
(vi) Tanmay who is fond of Bengali Sweets is born in the next month immediately after Namrata.
(vii) Namrata does not like Dry fruits or Ice Cream
11. What is the choice of Kunal?
(A) Bengal Sweets (B Dry Fruits (C)Ice Cream (D) Cannot be determined (E) None of these
12. In which month was Kunal born?
(A) January (B) May (C) January or May (D) Data inadequate (E) None
13 Which combination of month and item is TRUE for Jayant?
(A) February-Ice Cream (B) February-Pastry
(C) March-Pastry (D) Cannot be determined
(E) None of these
14. What is the choice of Anjali?
(A) Dry Fruits (B) Pastries (C)Bengal Sweets (D) Cannot be determined (E) None of these
Directions (15-19): Read the following informations carefully and answer the questions given below
(i) P,Q,R,S,T and U are six members of a family each of item are engaged in a
different profession-Doctor, Lawyer, Teacher, Engineer, Nurse, Manager.
(ii) Each of them remains at home on a different day of the week from Monday to Saturday
(iii) The Lawyer in the family remains at home on Thursday
(iv) R remains at home on Tuesday
(v) P, the Doctor does not remain at home either on Saturday or on Wednesday.
(vi) S is neither the Doctor nor the Teacher and remains at home on Friday.
(vii) Q is the Engineer and T is the Manager.
15. Who among them remains at home on the following day of the nurse?
(A) Q (B) Q or T (C) R (D) S (E) None of these
16. Which of the following combinations is not correct?
() R-Teacher (B) Q-Engineer (C) T-Manager (D) S-Nurse (E) All are correct
17. Which of the following combinations is correct?
(A) Lawyer-Tuesday ( B) Teacher-Wednesday
(C) Manager-Friday (D) Engineer-Thursday
(E) Nurse-Friday
18. Who remains at home on Saturday?
(A) S (B) T (C) R (D) Q or T (E) None of these
19. Who is the Nurse?
(A) S (B) R (C) U (D) Data inadequate (E) None of these
Answers
Exercise-I
1. (B) 2. (E) 3. (C) 4. (C) 5. (A)
6. (D) 7. (A) 8. (C) 9. (E) 10. (A)
11. (B) 12. (C) 13. (D) 14. (D) 15. (A)
16. (A) 17. ( D) 18. (B) 19. (C) 20. (D)
21. (D) 22. (B) 23. (A) 24. (C) 25. (B)
26. (D) 27. (E) 28. (C) 29. (A) 30. (B)
31. (D) 32. (A) 33. (D) 34. (C) 35. (E)
36. (A) 37. (B)
Exercise-II
1. (B) 2. (E) 3. (B) 4. (B) 5. (C)
6. (E) 7. (C) 8. (D) 9. (B) 10. (D)
11. (C) 12. (C) 13. (E) 14. (A) 15. (B)
16. (E) 17. (E) 18. (D) 19. (A)