The number of people who purchase from none of the three super markets is twice the number of people who purchase from Star Bazar only while the number of people who purchase from Star Bazar only is one third the number of people who make their purchases from all the three super markets. If the number of people who make their purchase from both More and Star Bazar is 2,100, find the number of people who purchase groceries from at least one of the two super markets Star Bazar and Fresh. (A) 3,640  (B) 2,520 (C) 4,580 (D) 3,260

If the total number of people in the locality is 90,000, then what is the number of people who purchase from More but not from all three super markets?

(A) 40,000 (B) 50,000 (C) 36,000 (D)Cannot be determined

The total number of people in the locality is 10,800 and the number of people who purchase from More is 1,600 more than the number of people who purchase from Fresh. Find the number of people who purchase from Star Bazar alone. (A) 400 (B) 1,600 (C) 800 (D) 2,000

The number of people who purchase from none of the three super markets is twice the number of people who purchase from Star Bazar only while the number of people who purchase from Star Bazar only is one third the number of people who make their purchases from all the three super markets. If the number of people who make their purchase from both More and Star Bazar is 2,100, find the number of people who purchase groceries from at least one of the two super markets Star Bazar and Fresh. (A) 3,640  (B) 2,520 (C) 4,580 (D) 3,260

Super-Markets :: More, Fresh and Star Bazar

M F

S

The number of people who do not purchase their groceries from any of the three super markets is equal to three-fourths of the number of people who purchase their groceries from More alone

4x

3x

Number of people who purchase their groceries from More alone is twice is double the number of people who purchase their groceries from Fresh and Star Bazar but not More.

2x

The number of people who purchase their groceries from Star Bazar alone is a quarter more than the number of people who make their purchases from More and Fresh but not Star Bazar.

5z

4z

The number of people who purchase from all three super markets is 50 percent more than the number of people who make their purchase from Fresh alone.

2y

3y

The number of people who purchase their groceries from both More and Star Bazar is three-and-a-half times the number of people who purchase their groceries from Fresh alone.

4y

Total number of people = 9x+9y+9z

M F

S

4x

3x

2x

5z

4z 2y

3y4y

10. If the total number of people in the locality is 90,000, then what is the number of people who purchase from More but not from all three super markets? (A) 40,000 (B) 50,000 (C) 36,000 (D)Cannot be determined

9x+9y+9z =900004x+4y+4z =40000

11. The total number of people in the locality is 10,800 and the number of people who purchase from More is 1,600 more than the number of people who purchase from Fresh. Find the number of people who purchase from Star Bazar alone. (A) 400 (B) 1,600 (C) 800 (D) 2,000

9x+9y+9z =10800

(4x+7y+4z) –(2x+5y+4z )=1600(2x+2y )=1600

(x+y )=800 and z =400

5z=2000

M F

S

4x

3x

2x

5z

4z 2y

3y4y

12. The number of people who purchase from none of the three super markets is twice the number of people who purchase from Star Bazar only while the number of people who purchase from Star Bazar only is one third the number of people who make their purchases from all the three super markets. If the number of people who make their purchase from both More and Star Bazar is 2,100, find the number of people who purchase groceries from at least one of the two super markets Star Bazar and Fresh. (A) 3,640  (B) 2,520 (C) 4,580 (D) 3,260

3x=10 z and 5z =y or 10z = 2y

3x=2y=10 z =30k

x=10k, y = 15k and z= 3k

7y = 2100 and y = 300 or k =20

(9x+9y+9z )- 7x

=2x+9y+9z

=20k+135k+27k

=182k

=3640

Each student is a member of at least one of the four clubs - Dramatics, Red Cross, Rotaract and Twisters.

The number of members of all the four clubs is 30 less than thrice the number of members of Red Cross alone.

The number of students who are members of all the clubs except Dramatics is 60.

The number of students who are members of all the clubs except Red Cross is 50.

The number of students who are members of all the clubs except Twisters is 40.

The number of students who are members of all the clubs except Rotaract is 45.

The number of members of Red Cross and Rotaract alone is 10 more than twice the number of members of Dramatics and Twisters alone.

The number of members of Rotaract and Twisters alone is 10 lesser than the number of members of Dramatics alone.

The number of members of Red Cross and Twisters alone is 20 more than twice the number of members of Dramatics and Rotaract alone.

The number of students who are members of Dramatics club alone is 85 which is 30 more than the number of students who are members of Rotaract club alone and 50 more than the number of students of Twisters alone.

The number of members of only Dramatics and Red Cross is equal to the number of members of Twisters alone.

20. If the number of members of the Dramatics, Red Cross and Rotaract clubs are 385, 430 and 445 respectively what is the number of members of the Twisters club? (A) 375 (B) 445 (C) 390 (D) 430

21. The number of students who are members of at least one of the four clubs is 785. The number of members of Dramatics or Rotaract club is 640. The number of members of Twisters club is 425. Find the number of members of exactly two clubs. (A) 385 (B) 330 (C) 365 (D) 350

22. The number of members of Red Cross is 31 less than the number of members of Twisters. The number of members of Rotaract is 35 more than the number of members of Red Cross. The number of members of Red Cross is 24 more than the number of members of Dramatics. Find the number of students in Imperial engineering college. (A) 704 (B) 705 (C) 706 (D) 707

SMART CAT 6 QUANTS

Each student is a member of at least one of the four clubs - Dramatics, Red Cross, Rotaract and Twisters.

The number of members of all the four clubs is 30 less than thrice the number of members of Red Cross alone.

The number of students who are members of all the clubs except Dramatics is 60.

The number of students who are members of all the clubs except Red Cross is 50.

The number of students who are members of all the clubs except Twisters is 40.

The number of students who are members of all the clubs except Rotaract is 45.

The number of members of Red Cross and Rotaract alone is 10 more than twice the number of members of Dramatics and Twisters alone.

x

2x+10

The number of members of Rotaract and Twisters alone is 10 lesser than the number of members of Dramatics alone.

7550

The number of members of Red Cross and Twisters alone is 20 more than twice the number of members of Dramatics and Rotaract alone.

0

2y+20

35

60

The number of students who are members of Dramatics club alone is 85 which is 30 more than the number of students who are members of Rotaract club alone and 50 more than the number of students of Twisters alone.

85

55

35

The number of members of only Dramatics and Red Cross is equal to the number of members of Twisters alone.

3z-30

z

40

45

y

20. If the number of members of the Dramatics, Red Cross and Rotaract clubs are 385, 430 and 445 respectively what is the number of members of the Twisters club? (A) 375 (B) 445 (C) 390 (D) 430

Dramatics= 225+x+y+3z = 385 implies x+y+3z = 160

Red Cross=180+2x+2y+4z = 430 implies 2x+2y+4z = 250

Rotract=260+2x+y+3z=445 implies 2x+y+3z =185

x

2x+10

50

2y+20

55

35

3z-30

40

45

60

y

3585 z

0

75

Twisters=255+x+2y+3z

x+y+3z = 1602x+2y+4z = 2502x+y+3z =1852x+2y+6z=3202x+2y+4z = 2502z = 70Z=35x+y = 552x+y = 80X = 25Y=30Twisters=255+25+60+105=445

Option (B)

21. The number of students who are members of at least one of the four clubs is 785. The number of members of Dramatics or Rotaract club is 640. The number of members of Twisters club is 425. Find the number of members of exactly two clubs. (A) 385 (B) 330 (C) 365 (D) 350

Dramatics= 225+x+y+3z

Red Cross=180+2x+2y+4z

Rotract=260+2x+y+3z

Twisters=255+x+2y+3z

To find 140+3x+3y

x

2x+10

50

2y+20

55

35

3z-30

40

45

60

y

3585 z

0

75

Twisters=255+x+2y+3z =425

x+2y+3z =170

Total= 480+ 4z+3x+3y Total= 480+ 4z+3x+3y = 785

3x+3y + 4z= 305

z+2y+ 55= 145

2y+z= 90

x+2y+3z =170

3x+3y + 4z= 305

x+2z= 80

3x+6y+9z =510

6x+6y + 8z= 610

3x-z =100

x+2z= 80

6x-2z=200

7x=280

x=40

z=20

y=35

140+120+105=365

Choice (c)

22. The number of members of Red Cross is 31 less than the number of members of Twisters. The number of members of Rotaract is 35 more than the number of members of Red Cross. The number of members of Red Cross is 24 more than the number of members of Dramatics. Find the number of students in Imperial engineering college. (A) 704 (B) 705 (C) 706 (D) 707

Dramatics= 225+x+y+3z

Red Cross=180+2x+2y+4z

Rotraact=260+2x+y+3z

Twisters=255+x+2y+3z

x

2x+10

50

2y+20

55

35

3z-30

40

45

60

y

3585 z

0

75

Total= 480+ 4z+3x+3y

75-x-z=31 or x+z=44

80-y-z=35 or y+z=45

-45+x+y+z= 24

x+y+z= 69

x+y+2z= 89

z= 20

x= 24

Total= 480+ 80+147=707

y= 25

Choice (d)

The faces of a cube are painted using six different colours. The following information is also known:The red face is adjacent to the yellow and brown face but they do not meet at a corner.The green face is adjacent to the silver face.The silver and pink face are opposite each other.The pink face is adjacent to the green face.The bottom face is brown in color.

SM 5 & Qn. 52. The face opposite the face coloured red isA ) Pink B ) Brown C ) Silver D ) Green

SM 5 & Qn. 53. The faces adjacent to green areA ) Yellow, Pink, Red and SilverB ) Brown, Pink, Red and SilverC ) Red, Silver, Yellow and PinkD ) Pink, Silver, Yellow and Brown

SM 5 & Qn. 54. The upper face is _______ in colourA ) Red B ) Pink C ) Yellow D ) Silver

Choice (d)

Choice (d)

Choice (C)

A cuboid of dimensions 7*3*3, painted red, is cut into minimum no of cubes.

Qn.29 At most how many of the smaller cubes will have 5 faces painted red?

(a)1 (b) 0 (c) 2 (d) 10

The question requires cutting the cuboid into minimum number of cubes and not minimum number of identical cubes.The big cuboid can be cut into 2 cubes of dimensions 3*3*3 and 9 cubes of 1*1*1 as shown above. (cubes of Dimension 1*1*1 is obtained after cutting 3*3*3 from both sides. These 2 cubes of dimension 3*3*3 at the both edges will have 5 faces painted red

A cuboid of dimensions 7*3*3, painted red, is cut into minimum no of cubes. 30 At most how many of the smaller cubes will have 4 faces painted red? (a) 1 (b) 0 (c) 2 (d) 10

The question requires cutting the cuboid into minimum number of cubes and not minimum number of identical cubes.The big cuboid can be cut into 2 cubes of dimensions 3*3*3 one after the other and 9 cubes of 1*1*1 as shown above. First Cube of Dimension 3*3*3 will have 5 sides painted red and the next cube will have 4 faces painted red.

Some students in a college play Bridge, Snooker, Carrom and Chess. Each plays at least two games. Following information is also known.

1. Number of students who play only Snooker and Chess is 50% of those who play all the four games.

2. Number of students who play only Bridge, Carrom and Chess is 50% more than who play only Bridge and snooker.

3. Number of students who play only Snooker, Carrom and Chess is same as those who play only Carrom and chess.

4. Number of students who play only Snooker,Chess and Bridge is same as those who play all the four games.

5. Number of students who play only Snooker and Carrom is same as those who play only Bridge and Chess

6. Number of students who play only Snooker and Chess is same as those who play only Bridge and snooker.

7. Number of students playing only bridge and chess is same as those who play Carrom and chess and twice the number of students who play Bridge and snooker.

8. Number of students playing Chess is 5 more than those who play bridge.

9. Number of students playing Snooker is 1 less than those who play Carrom.

10. Number of players playing all the four games is 4.Qn.22. How many play only Bridge and Carrom ? (a) 2 (b) 1 (c) 3 (d) Cannot be determined

Qn.23. How many play only Bridge, Snooker and Carrom ? (a)2 (b) 1 (c) 3 (d) Cannot be determined

Qn.24. What is the difference between those who play Bridge and Carrom? (a)2 (b)1 (c)3 (d) CBD

Qn.25. How many students are involved in these games? 44 (b) 48 (c) 45(d) Cannot be determined

Some students in a college play Bridge, Snooker, Carrom and Chess. Each plays at least two games. Following information is also known.

1. Number of students who play only Snooker and Chess is 50% of those who play all the four games.

2. Number of students who play only Bridge, Carrom and Chess is 50% more than who play only Bridge and snooker.

3. Number of students who play only Snooker, Carrom and Chess is same as those who play only Carrom and chess.

4. Number of students who play only Snooker,Chess and Bridge is same as those who play all the four games.

5. Number of students who play only Snooker and Carrom is same as those who play only Bridge and Chess

6. Number of students who play only Snooker and Chess is same as those who play only Bridge and snooker.

7. Number of students playing only bridge and chess is same as those who play Carrom and chess and twice the number of students who play Bridge and snooker.

8. Number of students playing Chess is 5 more than those who play bridge.

9. Number of students playing Snooker is 1 less than those who play Carrom.

10. Number of players playing all the four games is 4.1. Given Z=4 (information in 10)

2. p=4 (information in 4)

3. b=4 (information in 5)

4. d=2 (information in 1)

5. a=2 (information in 6)

6. c=4 and e = 4 (information in 7)

7. q = 1.5a=3

8. n=c=4

Incorporating this in the table the table look like this

Playing Chess =25Playing Bridge =17+f+m=20 (information in 8)Playing Carrom =19+f+mPlaying Snooker =20 +m(19+f+m) – (20+m)= 1 gives f=1m =2The information translates in to this table

Qn.22. How many play only Bridge and Carrom? (a) 2 (b) 1 (c) 3 (d) CBD

From the table answer is (a)

Qn.23. How many play only Bridge, Snooker and Carrom ?(a) 2 (b) 1 (c) 3 (d) CBD

From the table answer is (b)

Qn.24. What is the difference between those who play Bridge and Carrom? (a)1 (b) 1 (c) 2 (d) CBD

From the table answer is (2)

Qn.25. How many students are involved in these games? (a) 34 (b) 48 (c) 45(d) CBD

From the table answer is (a)

Row No N 3 4 5 6 7 8 9

(1) Number of smaller Cubes Used to make a Larger Cube 27 64 125 216 343 512 729

(2) Number of smaller Cubes not visible 1 8 27 64 125 216 343

(3) n3/3 3 21 42 72 112 171 243

(4) (3)<(2) (3)<(2) (3)<(2) (3)<(2) (3)>(2) (3)>(2) (3)>(2)

A large cube is made up n3 smaller identical cubes such that number of cubes not visible from outside is more than one third of the cubes used. What is the minimum value of number of smaller identical cubes used?(1) 216 (2) 343 (3) 512 (4) 729

Minimum Number of cubes used to make a larger cube = 343

Answer Choice (2)Number of identical cubes required to make a large Cube =n3

Number of identical cubes not visible =(n-2)3

Professor Ajay Rathinam had made a shortlist of 80 Students in his Final year engineering students whom he considered as the best in the college who can clear a National level Olympiad covering 4 basic sections- Mathematics, Data Analysis, Logic and English. So that additional coaching can be planned. When he was analyzing the results, he found some interesting trend. The number of people who had scored above 80% in exactly one of the 4 sections was in the ratio 1:2:3:4. The number of people who had scored above 80% in exactly any two of the 4 sections is in the ratio 1:2:3:4:.5:6The number of people who had scored above 80% in exactly any three of the 4 sections was in the ratio 1:2:3:4. 12.5% of the people did not get 80% and above in none of the 4 sections.14. The percentage of number of students who scored more than 80% in all the four sections cannot be (1)10% (2) 11.25% (3) 36.25% (4) 32.375% 15. If the number of students who secured 80% and above in exactly one section is same as those who secured 80% and above in exactly three sections, How many could have secured more than 80% in exactly two sections if number of students who got more than 80% in all the four sections is a 2-digit number?(1) 21 (2) 42 (3) 63 (4) Cannot be determined.16. If four fifth of the people who did not secure 80% in any of the sections equals the number of students who secured more than 80% in all the four sections, how many secured 80% and above in exactly two sections?

(1) 21 (2) 42 (3) 63 (4) Cannot be determined.

The following Venn diagram can be drawn from the data given in the question

14. The percentage of number of students who scored more than 80% in all the four sections cannot be (1) 10% (2) 11.25% (3) 36.25% (4) 32.375%

Answer Choice (4)Number of Students = 80Number of students who did not score 80% in any area = 10 (being 12.5% of 80) Number of students who scored 80% in one or more areas= 70 10k+21p+10m+x=70

K P M X1 1 1 291 1 2 192 1 1 191 1 2 193 1 1 91 1 3 91 2 1 8

Percentage of X can be 100*29/80 =36.25%Percentage of X can be 100*19/80 =23.75%Percentage of X can be 100*9/80 =11.25%Percentage of X can be 100*8/80 =10%

15. If the number of students who secured 80% and above in exactly one section is same as those who secured 80% and above in exactly three sections, How many could have secured more than 80% in exactly two sections if number of students who got more than 80% in all the four sections is a 2-digit number?(1) 21 (2) 42 (3) 63 (4) Cannot be determined.Answer Choice (1)

Number of Students = 80

Number of students who did not score 80% in any area = 10 (being 12.5% of 80)

Number of students who scored 80% in one or more areas= 70

10k+21p+10m+x=70 K=m20k+21p+x=70

K P X1 1 29

2 1 9

16. If four fifth of the people who did not secure 80% in any of the sections equals the number of students who secured more than 80% in all the four sections, how many secured 80% and above in exactly two sections?(1) 21 (2) 42 (3) 63 (4) Cannot be determined.Answer Choice (2)

Number of Students = 80

Number of students who did not score 80% in any area = 10 (being 12.5% of 80)

Number of students who scored 80% in one or more areas= 70

10k+21p+10m+x=70x=10*4/5=810k+21p+10m =62P can only be 2.Hence 42 is the answer

1 23

4

5 67

8

910

1112

131415

16

125 small cubes are arranged as a cube and kept in a corner of a room. Then three faces are painted with 3 different colours:

CUBES

Ex.21 How many cubes will have 3 faces with 3 different colours? (a) 8 (b) 4 (c) 2 (d) 1

Ex.22 How many cubes will have 2 faces painted? (a) 36 (b) 12 (c) 18 (d) 20

1

12

Ex.23 How many cubes will have 1 face painted? (a) 54 (b) 48(c) 36 (d) 24 48Ex.24 How many cubes will have no face painted? (a) 58 (b) 64 (c) 51 (d) 54

Ex.15: In how many ways a cube can be painted using colours Red & White?

CUBES

All faces White - 1 way

5 faces White and 1 face red – 1way

4 faces White & 2 faces red – 2 ways

3 faces White and 3 faces red – 2 ways

Similarly 2 faces white and 4 faces red – 2 waysSimilarly 1face white and 5 faces red – 1 waySimilarly All faces red – 1 wayTotally - 10 ways

78 identical cubes each with 2 cm edge are joined together to form a cuboid. If the perimeter of the base of the cuboid is 64 cm, then the number of cubes along the height of the cuboid is? (a) 2 (b) 4 (c) 6 (d) Not possible

78 = 2*3*13

Answer : 2 cubes

66 identical cubes each with 3 cm edge are joined together to form a cuboid. If the perimeter of the base of the cuboid is 78 cm, then the height of the cuboid is? (a) 3 (b) 9 (c) 6 (d) Not possible

66 = 2*3*11

Answer : 9 cms