Logical Reasoning & DI (LRDI) Test

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Logical Reasoning & DI (LRDI) Test - 5

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Question 1
3 / -1

Directions For Questions

A Hockey tournament was played between 6 teams A, B, C, D, E and F. Each team played against all the other team once. The following table gives the number of goals conceded by one team (in the row) against the other (in the column). For example in row 2 column 3, the value is 1 which is the number of goals conceded by A against B.

It is also known that the number of matches won by A, B, C, D and E are 2, 1, 3, ,3 and 1 respectively. Also, E had only 1 drawn match and B had zero matches drawn. Also, the match between A and D was not a draw.

...view full instructions

How many matches did A lose ?

A
1

B
2

C
3

D
cannot be determined

Solution

The following table gives the number of goals scored when a match is played by two teams. The value in column A and row B is 2 - 1 in which 2 is the goal scored by A against B and 1 is the goal scored by B against A

From the information given chart C has won 3 matches. Thus, w > 1 => C won the match against A
Given, A has won 2 matches=> x<=2 Also, the match between A and D is given not to be a draw => x < 2.
Given, D has 3 wins, Since, w > 1, D won the match against E. Therefore, D won the match against A and the match against F was either lost or drawn. Thus, y <=3
E has 1 win and 1 draw, thus y = 3.

B has only 1 win and because y = 3, B won the match against E. Since B has zero draws, z is definitely greater than 1.Therefore, F won the match against B.

The completed table is as follows:

From the table, it is clear that A lost 3 matches.
Question 2
3 / -1

Directions For Questions

A Hockey tournament was played between 6 teams A, B, C, D, E and F. Each team played against all the other team once. The following table gives the number of goals conceded by one team (in the row) against the other (in the column). For example in row 2 column 3, the value is 1 which is the number of goals conceded by A against B.

It is also known that the number of matches won by A, B, C, D and E are 2, 1, 3, ,3 and 1 respectively. Also, E had only 1 drawn match and B had zero matches drawn. Also, the match between A and D was not a draw.

...view full instructions

What is the minimum value of w + x + y + z ?

A
7

B
74

C
77

D
79

Solution

The following table gives the number of goals scored when a match is played by two teams. The value in column A and row B is 2 - 1 in which 2 is the goal scored by A against B and 1 is the goal scored by B against A

From the information given chart C has won 3 matches. Thus, w > 1 => C won the match against A
Given, A has won 2 matches=> x<=2 Also, the match between A and D is given not to be a draw => x < 2.
Given, D has 3 wins, Since, w > 1, D won the match against E. Therefore, D won the match against A and the match against F was either lost or drawn. Thus, y <=3
E has 1 win and 1 draw, thus y = 3.

B has only 1 win and because y = 3, B won the match against E. Since B has zero draws, z is definitely greater than 1.Therefore, F won the match against B.
The completed table is as follows:

w + x + y + z = 2 + 0 + 3 + 2 = 7
Question 3
3 / -1

Directions For Questions

A Hockey tournament was played between 6 teams A, B, C, D, E and F. Each team played against all the other team once. The following table gives the number of goals conceded by one team (in the row) against the other (in the column). For example in row 2 column 3, the value is 1 which is the number of goals conceded by A against B.

It is also known that the number of matches won by A, B, C, D and E are 2, 1, 3, ,3 and 1 respectively. Also, E had only 1 drawn match and B had zero matches drawn. Also, the match between A and D was not a draw.

...view full instructions

The final outcomes (win/loss/draw) of how many matches cannot be uniquely determined ?

A
0

B
2

C
4

D
5

Solution

The following table gives the number of goals scored when a match is played by two teams. The value in column A and row B is 2 - 1 in which 2 is the goal scored by A against B and 1 is the goal scored by B against A

From the information given chart C has won 3 matches. Thus, w > 1 => C won the match against A
Given, A has won 2 matches=> x<=2 Also, the match between A and D is given not to be a draw => x < 2.
Given, D has 3 wins, Since, w > 1, D won the match against E. Therefore, D won the match against A and the match against F was either lost or drawn. Thus, y <=3
E has 1 win and 1 draw, thus y = 3.

B has only 1 win and because y = 3, B won the match against E. Since B has zero draws, z is definitely greater than 1.Therefore, F won the match against B.
The completed table is as follows:

From the table it is clear that the final outcomes of all matches can be uniquely determined.
Question 4
3 / -1

Directions For Questions

A Hockey tournament was played between 6 teams A, B, C, D, E and F. Each team played against all the other team once. The following table gives the number of goals conceded by one team (in the row) against the other (in the column). For example in row 2 column 3, the value is 1 which is the number of goals conceded by A against B.

It is also known that the number of matches won by A, B, C, D and E are 2, 1, 3, ,3 and 1 respectively. Also, E had only 1 drawn match and B had zero matches drawn. Also, the match between A and D was not a draw.

...view full instructions

In how many matches the total number of goals scored in a match is definitely less than 4 ?

A
3

B
4

C
5

D
8

Solution

The following table gives the number of goals scored when a match is played by two teams. The value in column A and row B is 2 - 1 in which 2 is the goal scored by A against B and 1 is the goal scored by B against A

From the information given in the table C has won 3 matches. Thus, w > 1 => C won the match against A
Given, A has won 2 matches=> x<=2 Also, the match between A and D is given not to be a draw => x < 2.
Given, D has 3 wins, Since, w > 1, D won the match against E. Therefore, D won the match against A and the match against F was either lost or drawn. Thus, y <=3
E has 1 win and 1 draw, thus y = 3.

B has only 1 win and because y = 3, B won the match against E. Since B has zero draws, z is definitely greater than 1.Therefore, F won the match against B.
The completed table is as follows:

From the table it is clear that in four matches the total number of goals scored is less than 4.
Question 5
3 / -1

Directions For Questions

A Hockey tournament was played between 6 teams A, B, C, D, E and F. Each team played against all the other team once. The following table gives the number of goals conceded by one team (in the row) against the other (in the column). For example in row 2 column 3, the value is 1 which is the number of goals conceded by A against B.

It is also known that the number of matches won by A, B, C, D and E are 2, 1, 3, ,3 and 1 respectively. Also, E had only 1 drawn match and B had zero matches drawn. Also, the match between A and D was not a draw.

...view full instructions

How many matches resulted in a draw in the tournament?

A
2

B
3

C
4

D
Cannot be determined

Solution

The following table gives the number of goals scored when a match is played by two teams. The value in column A and row B is 2 - 1 in which 2 is the goal scored by A against B and 1 is the goal scored by B against A.

From the information given in the table C has won 3 matches. Thus, w > 1 => C won the match against A
Given, A has won 2 matches=> x<=2 Also, the match between A and D is given not to be a draw => x < 2.
Given, D has 3 wins, Since, w > 1, D won the match against E. Therefore, D won the match against A and the match against F was either lost or drawn. Thus, y <=3
E has 1 win and 1 draw, thus y = 3.

B has only 1 win and because y = 3, B won the match against E. Since B has zero draws, z is definitely greater than 1.Therefore, F won the match against B.
The completed table is as follows:

There are three draw matches, i.e. C-D, E-F and D-F.

The answer is option B.
Question 6
3 / -1

Directions For Questions

Ramesh uses a software so that he can encrypt all the passwords. All the passwords created by him consist only alphabets before encryption. Software always displays encrypted password to anyone who accesses it. Any password that is entered into the software is encrypted in the following manner:

1) Each alphabet from A to Z is assigned a number from 1 to 26 respectively.
2) Each letter in the password, from left to right, is assigned a number according to the above rule.
3) In any password, if any vowel is immediately followed by a consonant, then the number assigned to the vowel is decreased by 1. Otherwise, the number assigned to the vowel is increased by 1.
The software displays the passwords only as a string of the numbers assigned to each letter of the passwords based on the above rules.

...view full instructions

What will be the encrypted password that software displays for the 5-letter word ‘UDAAN’?

A
2040014

B
2040214

C
2042014

D
2142210

Solution

Initially, we can assign the number 1 to 26 for the letters from A to Z. The number assigned to the consonant remains unchanged. However, the numbers assigned to the vowel will depend on the letter that follows the vowel.

Further we can determine number assigned to vowels in different cases:

For 5 letter word 'UDAAN'

Since U is followed by a consonant so number assigned to U = 20

Number assigned to D = 4

Number assigned to first A(not followed by a consonant) = 2

Number assigned to second A(followed by a consonant) = 0

Number assigned to N = 14

Hence the software will display = 2042014 (Answer :C)
Question 7
3 / -1

Directions For Questions

Ramesh uses a software so that he can encrypt all the passwords. All the passwords created by him consist only alphabets before encryption. Software always displays encrypted password to anyone who accesses it. Any password that is entered into the software is encrypted in the following manner:

1) Each alphabet from A to Z is assigned a number from 1 to 26 respectively.
2) Each letter in the password, from left to right, is assigned a number according to the above rule.
3) In any password, if any vowel is immediately followed by a consonant, then the number assigned to the vowel is decreased by 1. Otherwise, the number assigned to the vowel is increased by 1.
The software displays the passwords only as a string of the numbers assigned to each letter of the passwords based on the above rules.

...view full instructions

If the software displays encrypted passwords as ‘21462416’ for an account, then which of the following can be the password of that account?

A
BAEFADO

B
AOFBDP

C
BOFBDO

D
More than one of the above.

Solution

Initially, we can assign the number 1 to 26 for the letters from A to Z. The number assigned to the consonant remains unchanged. However, the numbers assigned to the vowel will depend on the letter that follows the vowel.

Further we can determine number assigned to vowels in different cases:

An encrypted number can have multiple password hence it is east to trace back i.e. finding out encrypted number will the help of passwords given in options.

Option A: BAEFADO = (2)(2)(4)(6)(0)(4)(16) = 22460416 (Here each () represents the number corresponding to each letter.)

Option B: AOFBDP = (2)(14)(6)(2)(4)(16) = 21462416

Option C: BOFBDO = (2)(14)(6)(2)(4)(16) = 21462416

Hence we can see that both option B and C give us the same result.(Answer :D)
Question 8
3 / -1

Directions For Questions

Ramesh uses a software so that he can encrypt all the passwords. All the passwords created by him consist only alphabets before encryption. Software always displays encrypted password to anyone who accesses it. Any password that is entered into the software is encrypted in the following manner:

1) Each alphabet from A to Z is assigned a number from 1 to 26 respectively.
2) Each letter in the password, from left to right, is assigned a number according to the above rule.
3) In any password, if any vowel is immediately followed by a consonant, then the number assigned to the vowel is decreased by 1. Otherwise, the number assigned to the vowel is increased by 1.
The software displays the passwords only as a string of the numbers assigned to each letter of the passwords based on the above rules.

...view full instructions

Ramesh’s sister, Sarita, who was not aware of any of Ramesh’s passwords, used the software to retrieve an encrypted password for one of Ramesh’s accounts. If Sarita was able to find out the correct password from the encrypted password with the help of rules mentioned above, which of the following could have been the encrypted password for that account?

A
318432

B
717263

C
67217237

D
None of the above.

Solution

Initially, we can assign the number 1 to 26 for the letters from A to Z. The number assigned to the consonant remains unchanged. However, the numbers assigned to the vowel will depend on the letter that follows the vowel.

Further we can determine number assigned to vowels in different cases:

Option A : '318432' - Considering first 4 letters 3186

1st digit '3' will definitely represent 'C'.

2nd digit '1' alone won't corresponds to any letter since A can take either 0 or 2.

Hence we have to combine 2nd and 3rd digit now number '18' will corresponds to letter = R

4th digit can represent either D or E because 5th digit's number corresponds to C, which is a consonant. Last digits can represent both A or B hence we have total four passwords which will give us same result post encryption

All four passwords = (CRDCA, CRDCB, CRECA, CRECB) Hence Sarita won't able to find out the exact password.

Similarly finding all possible passwords for remaining options

Option B: 717263 = (GQBFC, GQZC)

Option C: 67217237 = (FGBQWG, FGBQBCG)

Since every encrypted password corresponds to multiple passwords hence Sarita won't able to retrieve correct password with any of given option (A,B,C). (Answer :D)
Question 9
3 / -1

Directions For Questions

Ramesh uses a software so that he can encrypt all the passwords. All the passwords created by him consist only alphabets before encryption. Software always displays encrypted password to anyone who accesses it. Any password that is entered into the software is encrypted in the following manner:

1) Each alphabet from A to Z is assigned a number from 1 to 26 respectively.
2) Each letter in the password, from left to right, is assigned a number according to the above rule.
3) In any password, if any vowel is immediately followed by a consonant, then the number assigned to the vowel is decreased by 1. Otherwise, the number assigned to the vowel is increased by 1.
The software displays the passwords only as a string of the numbers assigned to each letter of the passwords based on the above rules.

...view full instructions

Which of the following sequence of the number will corresponds to maximum number of passwords?

A
318432

B
717263

C
67217237

D
7826622

Solution

Initially, we can assign the number 1 to 26 for the letters from A to Z. The number assigned to the consonant remains unchanged. However, the numbers assigned to the vowel will depend on the letter that follows the vowel.

Further we can determine number assigned to vowels in different cases:

Option A : '318432' - Considering first 4 letters 3186

1st digit '3' will definitely represent 'C'.

2nd digit '1' alone won't corresponds to any letter since A can take either 0 or 2.

Hence we have to combine 2nd and 3rd digit now number '18' will corresponds to letter = R

4th digit can represent either D or E because 5th digit's number corresponds to C, which is a consonant. Last digits can represent both A or B hence we have total four passwords which will give us same result post encryption

All four passwords = (CRDCA, CRDCB, CRECA, CRECB)

Similarly finding all possible passwords for remaining options

Option B: 717263 = (GQBFC, GQZC)

Option C: 67217237 = (FGBQWG, FGBQBCG)

Option D: 7826622 = (GHZFBB, GHZFAA, GHZFU, GHZFV,GHBFFBB, GHBFFAA, .... )

Clearly we can see that '7826622' will corresponds to maximum number of passwords among given options. (Answer :D)
Question 10
3 / -1

Directions For Questions

Ramesh uses a software so that he can encrypt all the passwords. All the passwords created by him consist only alphabets before encryption. Software always displays encrypted password to anyone who accesses it. Any password that is entered into the software is encrypted in the following manner:

1) Each alphabet from A to Z is assigned a number from 1 to 26 respectively.
2) Each letter in the password, from left to right, is assigned a number according to the above rule.
3) In any password, if any vowel is immediately followed by a consonant, then the number assigned to the vowel is decreased by 1. Otherwise, the number assigned to the vowel is increased by 1.
The software displays the passwords only as a string of the numbers assigned to each letter of the passwords based on the above rules.

...view full instructions

Which of the following number sequence will uniquely determine the encrypted password?

A
2101608

B
302614

C
3021120

D
4102432

Solution

Initially, we can assign the number 1 to 26 for the letters from A to Z. The number assigned to the consonant remains unchanged. However, the numbers assigned to the vowel will depend on the letter that follows the vowel.

Further we can determine number assigned to vowels in different cases:

Option A: 2101608

2 can represent either A or B.

If 2 represents A, it should not be followed by a consonant, i.e. it should be followed by vowel, i.e. I.

If 2 represent B, it can be followed by either I or J.

Therefore, possible passwords are BJPOH, BIOAH, AIOAH,....

Option B: 302614

More than 1 password is possible, i.e. CABFN, CAZN

Option C: 3021120

3 represents C and 0 should represent A.

If 0 represents A, it should be followed by consonant.

No alphabet represent number 21. This implies A is followed by a consonant B which is further followed by K(11).

The only possible password is CABKT.

Option D: 4102432

4 can either represent D or E.

Therefore, more than 1 password is possible, i.e. DIAECB, EJAECB

Password is uniquely determined in option C only.

The answer is option C.
Question 11
3 / -1

Directions For Questions

A bus of private roadways runs between Delhi, starting point, and Jalandhar, terminating point. There are exactly 5 stops in between as shown in the table. The following table gives the partial information about the number of passengers who boarded and got down at various bus stops.

Some additional information is known :
A)At least one-fourth of the passengers who boarded the bus at Delhi got down at Rohtak.
B)Fare charged by the bus between any two consecutive stops is Rs. 5.

...view full instructions

What can be the maximum number of passengers in the bus at any time?

A
57

B
65

C
53

D
69

Solution

The number of passengers who got down at Rohtak is at least 11. The solution table is as given below.
Question 12
3 / -1

Directions For Questions

A bus of private roadways runs between Delhi, starting point, and Jalandhar, terminating point. There are exactly 5 stops in between as shown in the table. The following table gives the partial information about the number of passengers who boarded and got down at various bus stops.

Some additional information is known :
A)At least one-fourth of the passengers who boarded the bus at Delhi got down at Rohtak.
B)Fare charged by the bus between any two consecutive stops is Rs. 5.

...view full instructions

What is the maximum number of passengers who boarded from Delhi and got down at Ludhiana?

A
25

B
254

C
257

D
259

Solution

In order to maximize the no. of people getting down at Ludhiana from Delhi, we have to minimize the no. of passengers who got down at Rohtak from Delhi. The number of passengers who got down at Rohtak is at least 11. The solution table is as given below. From the table the maximum number of passengers who got down at Ludhiana is 25.
Question 13
3 / -1

Directions For Questions

A bus of private roadways runs between Delhi, starting point, and Jalandhar, terminating point. There are exactly 5 stops in between as shown in the table. The following table gives the partial information about the number of passengers who boarded and got down at various bus stops.

Some additional information is known :
A)At least one-fourth of the passengers who boarded the bus at Delhi got down at Rohtak.
B)Fare charged by the bus between any two consecutive stops is Rs. 5.

...view full instructions

What is the minimum number of passengers who got down at Ludhiana?

A
1

B
0

C
3

D
None of these

Solution

The total number of passengers who boarded = 43+17+12+24+8+28 = 132
The number of passengers who got down at stops other than Rohtak and Ludhiana = 36+21+7+18+50 = 96
The number of passengers who got down at Rohtak and Ludhiana combined = 132 - 96 = 36.
To minimize the number of passengers who got down at Ludhiana the number of passengers who got down at Rohtak has to be maximized which is at most 36.
The solution table is as shown below.
Question 14
3 / -1

Directions For Questions

A bus of private roadways runs between Delhi, starting point, and Jalandhar, terminating point. There are exactly 5 stops in between as shown in the table. The following table gives the partial information about the number of passengers who boarded and got down at various bus stops.

Some additional information is known :
A)At least one-fourth of the passengers who boarded the bus at Delhi got down at Rohtak.
B)Fare charged by the bus between any two consecutive stops is Rs. 5.

...view full instructions

What is the minimum amount collected by the bus during the whole journey?

A
930

B
850

C
855

D
920

Solution

The total number of passengers who have boarded = 43+17+12+24+8+28 = 132.
Let the number of passengers who got down at Rohtak and Ludhiana be 'x' and 'y' respectively.
So the total number of passengers who got down = x+21+7+18+y+50 = 96+x+y
The number of passengers who got down must be equal to the number of passengers who boarded. So,
96+x+y = 132
=> x+y = 36.
The minimum amount would be collected when the maximum number of people get down at Rohtak which is the immediate next stop to Delhi.
As x+y = 36, the maximum value of x can be 36.
Therefore the maximum number who can get down at Rohtak is 36.

The minimum amount collected would be (36*5)+(7*10)+(14*5)+(3*10)+(4*5)+(8*10)+(10*5)+(28*5)+(14*15)+(8*10) = 180+70+70+30+20+80+50+140+210+80 = 930
Question 15
3 / -1

Directions For Questions

A bus of private roadways runs between Delhi, starting point, and Jalandhar, terminating point. There are exactly 5 stops in between as shown in the table. The following table gives the partial information about the number of passengers who boarded and got down at various bus stops.

Some additional information is known :
A)At least one-fourth of the passengers who boarded the bus at Delhi got down at Rohtak.
B)Fare charged by the bus between any two consecutive stops is Rs. 5.

...view full instructions

If it is known that 15 passengers who boarded from Delhi got down at Rohtak, find the amount collected by the bus before it reached Sangrur?

A
885

B
8854

C
8857

D
8859

Solution

The number of passengers who got down at Rohtak is 15. The solution table is as given below.

Total amount collected = 43(5) + 45(5) + 36(5) + 53(5) = 177(5) = 885

The answer is 885.
Question 16
3 / -1

Directions For Questions

A city consisting of 80000 people were surveyed for 3 magazines- India Today(IT), The Week(TW), Frontline(FL). These people were also surveyed for 3 FMCG brands- P&G, HUL and RB.
A) The number of natives in the city who like exactly two magazines is five times the number of natives who like all the magazines.
B) The sum of the number of natives who like IT and 42% of those who like TW but not IT is equal to the number of natives who like P&G.
C) The number of natives who like HUL is equal to the sum of 37.5% of the number of natives who like TW and 50% of those who like FL.
D) 30,000 natives like all the FMCG brands and 7,000 like all the magazines.
E) 37,000 natives like IT.
F) 28,000 natives do not like IT but like FL.
G) 22,000 natives like IT and exactly one more magazine.
H) 12,000 natives like only TW and the same number of natives like IT and FL but not TW.
I) The number of natives who like RB is same as the number of natives who like HUL.

...view full instructions

How many natives do not like any of the three magazines? (-1 if cannot be determined)

A
3000

B
30004

C
30007

D
30009

Solution

In the question, it is given that 37000 natives like IT, 12000 natives like only TW, 12000 natives like IT and FL but not TW, and 7000 natives like all three magazines.

In the question, it is given that the number of natives in the city who like exactly two magazines is five times the number of natives who like all the magazines. Therefore, the number of natives who like exactly two magazines = 5*7000 = 35000
It is given, 22,000 natives like IT and exactly one more magazine.

(only IT and TW) + (only IT and FL) = 22000

only IT and TW = 22000 - 12000 = 10000

The number of natives who like exactly two magazines is 35000

Therefore, only TW and FL = 35000 - 12000 - 10000 = 13000

It is given that 28,000 natives do not like IT but like FL.

(only FL) + (only FL and TW) = 28000

only FL = 28000 - 13000 = 15000

Final arrangement:

The number of natives who do not like any magazine = 80000 - 77000 = 3000

The answer is 3000.
Question 17
3 / -1

Directions For Questions

A city consisting of 80000 people were surveyed for 3 magazines- India Today(IT), The Week(TW), Frontline(FL). These people were also surveyed for 3 FMCG brands- P&G, HUL and RB.
A) The number of natives in the city who like exactly two magazines is five times the number of natives who like all the magazines.
B) The sum of the number of natives who like IT and 42% of those who like TW but not IT is equal to the number of natives who like P&G.
C) The number of natives who like HUL is equal to the sum of 37.5% of the number of natives who like TW and 50% of those who like FL.
D) 30,000 natives like all the FMCG brands and 7,000 like all the magazines.
E) 37,000 natives like IT.
F) 28,000 natives do not like IT but like FL.
G) 22,000 natives like IT and exactly one more magazine.
H) 12,000 natives like only TW and the same number of natives like IT and FL but not TW.
I) The number of natives who like RB is same as the number of natives who like HUL.

...view full instructions

Find the minimum number of natives who like at least one of the three FMCG brands?

A
48000

B
52000

C
55000

D
Cannot be determined

Solution

In the question, it is given that 37000 natives like IT, 12000 natives like only TW, 12000 natives like IT and FL but not TW, and 7000 natives like all three magazines.

In the question, it is given that the number of natives in the city who like exactly two magazines is five times the number of natives who like all the magazines. Therefore, the number of natives who like exactly two magazines = 5*7000 = 35000
It is given, 22,000 natives like IT and exactly one more magazine.

(only IT and TW) + (only IT and FL) = 22000

only IT and TW = 22000 - 12000 = 10000

The number of natives who like exactly two magazines is 35000

Therefore, only TW and FL = 35000 - 12000 - 10000 = 13000

It is given that 28,000 natives do not like IT but like FL.

(only FL) + (only FL and TW) = 28000

only FL = 28000 - 13000 = 15000

Final arrangement:

The number of natives who like all FMCG brands is 30000.

The number of natives who like P&G = The number of natives who like IT + 42% of those who like TW but not IT = 37000 + 0.42(25000) = 47500

The number of natives who like HUL = 0.375(42000) + 0.5(47000) = 39250

The number of natives who like RB = 39250

S + D + T + N = 80000 ...... (1)

S + 2D + 3T = 47500+2(39250) = 126000 ...... (2)

S + 2D = 36000

To find the minimum number of natives who like at least one of the three FMCG brands, we need to maximise the number of natives who do not like any FMCG brand, i.e. maximise N.

(2)-(1) -> D + 2T - N = 46000

N - D = 14000

N = 14000 + D

Maximum value D can take is 18000

Therefore, maximum value N can take is 32000

The minimum number of natives who like at least one of the three FMCG brands = 80000 - 32000 = 48000

The answer is option A.
Question 18
3 / -1

Directions For Questions

A city consisting of 80000 people were surveyed for 3 magazines- India Today(IT), The Week(TW), Frontline(FL). These people were also surveyed for 3 FMCG brands- P&G, HUL and RB.
A) The number of natives in the city who like exactly two magazines is five times the number of natives who like all the magazines.
B) The sum of the number of natives who like IT and 42% of those who like TW but not IT is equal to the number of natives who like P&G.
C) The number of natives who like HUL is equal to the sum of 37.5% of the number of natives who like TW and 50% of those who like FL.
D) 30,000 natives like all the FMCG brands and 7,000 like all the magazines.
E) 37,000 natives like IT.
F) 28,000 natives do not like IT but like FL.
G) 22,000 natives like IT and exactly one more magazine.
H) 12,000 natives like only TW and the same number of natives like IT and FL but not TW.
I) The number of natives who like RB is same as the number of natives who like HUL.

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What is the minimum number of natives who do not like any FMCG company?

A
10000

B
12000

C
14000

D
8000

Solution

In the question, it is given that 37000 natives like IT, 12000 natives like only TW, 12000 natives like IT and FL but not TW, and 7000 natives like all three magazines.

In the question, it is given that the number of natives in the city who like exactly two magazines is five times the number of natives who like all the magazines. Therefore, the number of natives who like exactly two magazines = 5*7000 = 35000
It is given, 22,000 natives like IT and exactly one more magazine.

(only IT and TW) + (only IT and FL) = 22000

only IT and TW = 22000 - 12000 = 10000

The number of natives who like exactly two magazines is 35000

Therefore, only TW and FL = 35000 - 12000 - 10000 = 13000

It is given that 28,000 natives do not like IT but like FL.

(only FL) + (only FL and TW) = 28000

only FL = 28000 - 13000 = 15000

Final arrangement:

The number of natives who like all FMCG brands is 30000.

The number of natives who like P&G = The number of natives who like IT + 42% of those who like TW but not IT = 37000 + 0.42(25000) = 47500

The number of natives who like HUL = 0.375(42000) + 0.5(47000) = 39250

The number of natives who like RB = 39250

S + D + T + N = 80000 ...... (1)

S + 2D + 3T = 47500+2(39250) = 126000 ...... (2)

S + 2D = 36000

(2)-(1) -> D + 2T - N = 46000

N - D = 14000

N = 14000 + D

Minimum value of N is 14000 when D = 0

The answer is option C.
Question 19
3 / -1

Directions For Questions

A city consisting of 80000 people were surveyed for 3 magazines- India Today(IT), The Week(TW), Frontline(FL). These people were also surveyed for 3 FMCG brands- P&G, HUL and RB.
A) The number of natives in the city who like exactly two magazines is five times the number of natives who like all the magazines.
B) The sum of the number of natives who like IT and 42% of those who like TW but not IT is equal to the number of natives who like P&G.
C) The number of natives who like HUL is equal to the sum of 37.5% of the number of natives who like TW and 50% of those who like FL.
D) 30,000 natives like all the FMCG brands and 7,000 like all the magazines.
E) 37,000 natives like IT.
F) 28,000 natives do not like IT but like FL.
G) 22,000 natives like IT and exactly one more magazine.
H) 12,000 natives like only TW and the same number of natives like IT and FL but not TW.
I) The number of natives who like RB is same as the number of natives who like HUL.

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Find the total number of people who like only one of the FMCG brand if the total number of people who like only 2 FMCG brands is 15000.

A
4000

B
6000

C
10000

D
Cannot be determined

Solution

In the question, it is given that 37000 natives like IT, 12000 natives like only TW, 12000 natives like IT and FL but not TW, and 7000 natives like all three magazines.

In the question, it is given that the number of natives in the city who like exactly two magazines is five times the number of natives who like all the magazines. Therefore, the number of natives who like exactly two magazines = 5*7000 = 35000
It is given, 22,000 natives like IT and exactly one more magazine.

(only IT and TW) + (only IT and FL) = 22000

only IT and TW = 22000 - 12000 = 10000

The number of natives who like exactly two magazines is 35000

Therefore, only TW and FL = 35000 - 12000 - 10000 = 13000

It is given that 28,000 natives do not like IT but like FL.

(only FL) + (only FL and TW) = 28000

only FL = 28000 - 13000 = 15000

Final arrangement:

The number of natives who like all FMCG brands is 30000.

The number of natives who like P&G = The number of natives who like IT + 42% of those who like TW but not IT = 37000 + 0.42(25000) = 47500

The number of natives who like HUL = 0.375(42000) + 0.5(47000) = 39250

The number of natives who like RB = 39250

It is given that the total number of people who like only 2 FMCG brands is 15000, i.e. D = 15000
S + D + T + N = 80000 ...... (1)

S + 2D + 3T = 47500+2(39250) = 126000 ...... (2)

S + 2D = 36000

S + 2(15000) = 36000
S = 6000
Tthe total number of people who like only 1 FMCG brand is 6000.
The answer is option B.
Question 20
3 / -1

Directions For Questions

A city consisting of 80000 people were surveyed for 3 magazines- India Today(IT), The Week(TW), Frontline(FL). These people were also surveyed for 3 FMCG brands- P&G, HUL and RB.
A) The number of natives in the city who like exactly two magazines is five times the number of natives who like all the magazines.
B) The sum of the number of natives who like IT and 42% of those who like TW but not IT is equal to the number of natives who like P&G.
C) The number of natives who like HUL is equal to the sum of 37.5% of the number of natives who like TW and 50% of those who like FL.
D) 30,000 natives like all the FMCG brands and 7,000 like all the magazines.
E) 37,000 natives like IT.
F) 28,000 natives do not like IT but like FL.
G) 22,000 natives like IT and exactly one more magazine.
H) 12,000 natives like only TW and the same number of natives like IT and FL but not TW.
I) The number of natives who like RB is same as the number of natives who like HUL.

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If it is known that none of the natives liked exactly one FMCG brands, find the number of natives who liked P&G and HUL?

A
38750

B
387504

C
387507

D
387509

Solution

In the question, it is given that 37000 natives like IT, 12000 natives like only TW, 12000 natives like IT and FL but not TW, and 7000 natives like all three magazines.

In the question, it is given that the number of natives in the city who like exactly two magazines is five times the number of natives who like all the magazines. Therefore, the number of natives who like exactly two magazines = 5*7000 = 35000
It is given, 22,000 natives like IT and exactly one more magazine.

(only IT and TW) + (only IT and FL) = 22000

only IT and TW = 22000 - 12000 = 10000

The number of natives who like exactly two magazines is 35000

Therefore, only TW and FL = 35000 - 12000 - 10000 = 13000

It is given that 28,000 natives do not like IT but like FL.

(only FL) + (only FL and TW) = 28000

only FL = 28000 - 13000 = 15000

Final arrangement:

The number of natives who like all FMCG brands is 30000.

The number of natives who like P&G = The number of natives who like IT + 42% of those who like TW but not IT = 37000 + 0.42(25000) = 47500

The number of natives who like HUL = 0.375(42000) + 0.5(47000) = 39250

The number of natives who like RB = 39250

S + D + T + N = 80000 ...... (1)

S + 2D + 3T = 47500+2(39250) = 126000 ...... (2)

S + 2D = 36000

It is given, S = 0, i.e. a = b = c = 0
D = d + e + f = 18000 ...... (3)
d + e = 17500 ...... (4)
(3)-(4) -> f = 500
HUL = 39250
d + b + f + 30000 = 39250
d = 8750
Similarly, we get e = 8750
The number of natives who liked P&G and HUL = 30000 + 8750 = 38750