Test of Divisibility

Test of Divisibility

Divisibility by 2: A number is divisible by 2, if its unit is any of 0, 2, 4, 6, 8.

Divisibility by 3: A number is divisible by 3, if the sum of its digits is divisible by 3.

Ex. Which of the following number is divisible by 3?
(i) 541326 (ii) 5967013

Sol: Sum of digits in 541326 is 21, which is divisible by 3. So, 541326 is divisible by 3.
Sum of digits in 5967013 is 31, which is not divisible by 3. So 5967013 is divisible by 3
Hence 5967013 is not divisible by 3.

Divisibility by 9: A number is divisible by 9. If the sum of its digit is divisible by 9.

Ex. Which of the following numbers is divisible by 9 ?
(i) 19725462 (ii) 36870521

Sol: Sum of digits in 19725462 is 36, which is divisible by 9. So, 19725462 is divisible by 9
Sum of digits in 36870521 is 32, which is not divisible by 9.
So, 36870521 is not divisible by 9.

Divisibility by 4: A number is divisible by 4, if the number formed by last two digits is divisible by 4.

Ex. Which of the following numbers is divisible by 4
(i) 67920594 (ii) 618703572
Sol: The number formed by the last two digits in 67920594 is 94, which is not divisible by 4.
:. 67920594 is not divisible by 4.
The number formed by the last 2 digits in 618703572 is 72, which is divisible by 4.
:. 618703572 is divisible by 4.

Divisibility by 8 : A number is divisible by 8, if the number formed by the last 3 digits of the given number is divisible by 8.

Ex. Which of the following numbers is divisible by 8 ?
(i) 98016542 (ii) 106598304
Sol. The number formed by the last 3 digits of 98016542 is 542. Which is not divisible by 8.
:. 98016542 is not divisible by 8.
The number formed by the last 3 digits of the given number 304, which is divisible by 8.
:. 106598304 is divisible by 8.

Divisibility by 11: A number is divisible by 11. If the difference of the sum of its digits at odd places and the sum of digits at even places, is either 0 or a number divisible by 11.

Ex. Show that 4832718 is divisible by 11.
Sol. (Sum of digits at odd places) + (Sum of digits at even places)
[(8 + 7 + 3 + 4) - ( 1 + 2 + 8)] = 11. which is divisible by 11
:. 4832718 is divisible by 11

Co-Prime: Two numbers are said to be co-prime, if their H.C.F is 1.
e.g. (2, 3), (4, 5), (7, 9), (8, 11) are co-primes.
Note: A number is divisible by ab only when that number is divisible by each one of a and b, where a and b are co-primes

Ex. Without actual division show that 52563744 is divisible by 24.
Sol. 24= 3x8, where 3 and 8 are co prime.
The sum of the digits in given number is 36, which is divisible by 3.
So, the number is divisible by 3.
The number formed by the last 3-digits of the given number is 744, which is divisible by 8.
So the given number is divisible by 8.
Thus, the given number is divisible by both 3 and 8, where 3 and 8 are co-prime
So, it is divisible by 3x8, i.e. 24

Coding and Decoding -1

1. 'LOAD' is coded as 'MPBE' and DRIVE as 'ESJWF', how will you code 'LADDER' ?
(a) NCFFGT (b) MBEEFS (c) MDEEFS (d) MBEESP

2. 'START=WALKA and BUDPI=BUDPI=XZFMQ, what would be 'STUPID'= ?
(a) WAZMQF (b) BAZMQF (c) WAZNOF (d) WAZMMF

Note : Here the coding scheme is A=Z, B=Y, C=X and so on answer the following
3. LIMIT
(a) KNRNG (b) JKOKG (c) ORNRG (d) MHLHS

4. SOUR
(a) HLFI (b) IFLT (c) IHIF (d) FLTI

5. POCKET
(a) KLXUPG (b) KLXVPG (c) KLXPUC (d) KLXPVG

6. GROUP
(a) TILEL (b) TILFK (c) TFGFK (d) TILGH

7. ZERO
(a) BUHN (b) AUTL (c) AVIL (d) AYTI

8. SHOOT
(a) TJPPR (b) VKRRW (c) UMSSX (d) VKSSW

9. VWDUW
(a) START (b) STAIN (c) STEPS (d) STAND

10. GRZQ
(a) OWNS (b) DONE (c) SHUT (d) DOWN

11. if 'DBMDVUUB' stands for CALCUTTA, how will you write 'BOMBAY' ?
(a) DPNCBX (b) CPMCBZ (c) CPNCBZ (d) DOODDX

12. In a certain code 'DELHI' is written as 'CDKGH', 'MADRAS' aS 'LZCOZR', how will 'PATNA' be coded ?

13. If A=E, B=F, C=G and H=L, how will you code 'GO AHEAD' ?
(a) HPBIFBE (b) HPBIFDE (c) KSFLIFH (d) KSELIEH

If 'TENDER' is coded as 'SDMCDQ', select the appropriate code for the following words
14. SOUPS
(a) PNTQS (b) RMTOR (c) RNTOR (d) TPUQT

15. LIMITED
(a) DETIMIL (b) KHLHSDC (c) DETIMIL (d) KHLHSDE

16. PEONS
(a) ODNMS (b) ODNMT (c) ODMNR (d) ODNMR

17. If 'FRIIHH' stands for 'COFFEE' how will you write 'NOODLES' ?
(a) QRRGOHV (b) RSSHPIW (c) RSSHPIW (d) SELDOON

ANSWERS

1. b 2. a 3. c 4. a 5.d 6. b 7. c
Note : From 8 to 10 the code used is based on the skipping pattern. each letter is coded with the fourth one in alphabetic order, i.e A=(BC)D, B=(CD)E, C=(DE)F, D=(EF)G AND so on

8. b 9. a 10. d 11.c 12. a 13. d 14. c 15. a 16. d 17. a

Critical Reasoning - 1

Critical Reasoning - 1



Answer the questions on the basis of the following directions
Asha and Dara are the children of Mr Dass. Asha marries Suresh Chopra and Sunil, Sanjay and Sonu are born to them. Sunil is married to the eldest daughter of Mr and Mrs. Roy. Bindu is younger to Rita and older than Sita and all are daughters of Mr and Mrs Roy. Gita is Sunils's daughter.

1. What is Surname of sunjay

1. Das 2. Roy 3. Chopra 4. None of these

2. Who is married to Sunil

1. Bindu 2. Sita 3. Rita 4. None of these

3. How is Dara related to Gita

1. Brother-in-law 2. Uncle 3. Maternal Uncle 4. Brother

4. What is Surname of Gita

1. Chopra 2. Dass 3. Roy 4. Suresh

Direction 5 to 7 : If the first six letters of the word THOUGHT FULESSNESS are reversed, next six letters are written as they are and then the remaining letters are reversed.

5. Which letter will be exactly in the middle ?

1. F 2. U 3. L 4. T 5. None

6. Which two letters will be sandwiched between double T and double L ?

1. NS 2. FE 3. FU 4. HT 5. None

7. If all vowels are removed which letter will be exactly in the middle?

1. T 2. L 3. F 4. H 5. None

Directions 8 to 12 : if the word "DISINTERESTEDNESS" is rewritten by reversing the order of first seven and last six letters, then
8. If the vowels are removed, which letter will have one preceding and one following letter in the same order as in the english alphabet?
1. T 2. D 3. N 4. R 5. S
9. Which letter will be the tenth letter towards right ?
1. R 2. E 3. T 4. N 5. R
10. Which will be the sixth letter from and towards left ?
1. R 2. E 3. S 4. N 5. T
11. Which consonant will be exactly in the middle ?
1. T 2. E 3. S 4. R 5. None
12. How many vowels are there to the left of the letter exactly in the middle ?
1. 1 2. 2 3. 3 4. 4 5. None

Directions 13 to 16 :
(a) A and B Play Football and Hokey
(b) C and D play Badminton and Cricket
(c) B and C play Crocket and Football
(d) A and D play Hockey and Badminton
13. One who plays Badminton, Football and Hockey
1. A 2. B 3. C 4. D 5. None
14. One who plays Badminton, Football and Cricket
1. A 2. B 3. C 4. D 5. None
15. One who plays Cricket, Football and Hockey
1. A 2. B 3. C 4. D 5. None
16. One who does not play cricket ?
1. A 2. B 3. C 4. D 5. None

Directions 17 to 22: Some friends are sitting on a bench; Sunil is sitting next to Sunita and Sanjay is next to Bindu. Bindu is not sitting with Sumit. Sumit is on the left end of the bench and Sanjay is on second position from right handside. Sunil is on the right side of Sunita and to the right side of Sumit. Sunil and sanjay are sitting together.
Based on the above seating arrangements, answer the following questions:
17. Sunil is sitting between
1. Sunita and Bindu 2. Sumit and Bindu 3. Sunita and sanjay 4. Sanjay and Sumit
5. Bindu and sanjay
18. Who is sitting in the centre ?
1. Sumit 2. Sunil 3. Bindu 4. Sanjay 5. Sanjay
19. Sanjay is sitting between
1. Bindu & Sunita 2. Sunil & Sumit 3. sunita & Bindu 4. Sumit & Bindu 5. Sunil & Bindu
20. Sumit is sitting on the
1. Secong place from right 2. Secong place from left 3. Extreme left 4. Extreme right
5. in the middle of all
21. Bindu is sitting on the
1.Extreme left side 2. Extreme right side 3. Secong from left side 4. third from left side
5. in the centre
22. Sunita is sitting away from Bindu places
1. 1 2. 2 3. 4 4. 5 5. 3

23. Ankit started walking towards north. after walking 30 metres, he turned left and walked 40 metres. He then turned left and walked 500 metre. He again turned left and walked 50 metres. How far was he from his original position ?
1. 50 metres 2. 40 metres 3. 30 metres 4. 20metres 5. 10 metres

24. A walks 10 metres in front and 10 metres to the right. Then every time turning to his left, he walks 5, 15, and 15 metres respectively. How far is he now from his starting point ?
1. 10 metres 2. 20 metres 3. 5 metres 4. 15 metres 5. 23 metres

25. Dilip walks 20 metres north. Then he turns right and walks 30 metres. Now, he turns right and walks 35 metres. Now, turning left, he walks 15 metres. Again, he turns left and moves 15 metres. In which direction and how far is he from his original position ?
1. 15 metres East 2. 45 metres East 3. 46 metres west 4. 45 metres west 5. None

26. From his house , Lokesh went 15 kms to the North. Then he turned west and covered 10 kms. Then, he turned south and covered 5 kms. Finally, turning to east he covered 10 kms. In which direction is he from his house ?
1. East 2. West 3. North 4. south

27. Six persons A, B, C, D, E and F are standing in a circle B is between F and C; A is between E and D. Who is between A and F ?
1. B 2. C 3. D 4. E

Directions 28 to 30 : Read the following information and answer the questions given below it :
i) Six friend A, B, C, D, E and F are sitting in a closed circle facing the centre.
ii) E is to the left of D
iii) C is between A and B
iv) F is between E and A.
28. Who is to the left of B ?
1. A 2. C 3. D 4. E 5. None
29. Who is to the right of C ?
1. A 2. B 3. D 4. E 5. F
30. Which of the above given statements is superflupus ?
1. I 2. II 3. III 4. IV 5. None

Answers
1. 3 2. 3 3. 3 4. 1 5. 5 6. 3
7. [3] HGHTTFL SSSNS 8. 5 9. 4 10. 3 11. 5 12. 3
Hints for 13 to 16
(i) Football = A, B, C
(ii) Hockey = A, B, D
(iii) Badminton = C, D, A
(iv) Cricket = C, D, B

13. 1 14. 3 15. 2 16. 1

hint: 17 to 22: Make a sketch of the sitting positions based on the description

left_____Sumit______Sunita________Sunil_____Sanjay_____Bindu____Right

17. 3 18. 2 19.5 20. 3 21. 2 22. 2

23. 5 24. 3 25. 2 26. 3 27.3

28. 3 Clearly D is to the left of B

29. 1 Clearly A is to the right of C

30. 5 Since all the statements are necessary to determine the arrangement. Noe of these is superflous