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QUESTION: 1

Six digits - 3, 4, 6, 2, 8 and 1 - are arranged in a 2 x 3 matrix such that each cell of the matrix has exactly one digit. The odd digits are not in the same column. The sum of the digits in row I is 2 more than that in row II. The difference between any two digits in a row is not more than 5. The sum of the digits in columns I, II and III are consecutive integers in ascending order. What is the difference between the digit in row I, column III and row II, column I?

Solution:

The sum of digits in Row I is 2 more than that in Row II.

The difference between any two numbers in a row is not more than 5.

But there are no possible combinations satisfying both the above conditions.

Hence, option 4.

QUESTION: 2

Group Question

Answer the following question based on the information given below.

Seven people - A, B, C, D, E, F and G - are to be divided in two groups P and Q such that number of people in groups P and Q is 3 and 4 respectively.

Further it is known that:

1. A and C should not be in the same group.

2. B and G should be in the same group.

3. If E and F are in the same group, then A and D should be in the same group.

4. If C and B are in the same group, then E should not be in the same group as A.

*Q. In how many different ways can the two groups be made?*

Solution:

The number of people in groups P and Q is 3 and 4 respectively.

Case 1 : B, G and C are in the same group.

So, E should not be in the same group as A.

Also, since C and A cannot be in the same group, E has to be in the same group as C.

So, B, C, G and E are in the same group i.e. group Q. Group Q: B, G, C, E

Group P: A, D, F

Case 2 : C is not in the same group as B and G.

Since A and C are in different groups, A should be in the same group as B and G.

If E and F are in the same group, then they have to be in group P as A and D have to be in the same group.

So, the possible sub-cases are: Sub Case 1 : Group Q: B, G, A and D

Group P: C, E and F Sub Case 2 : Group Q: B, G, A and E Group P: C, D and F Sub Case 2 : Group Q: B, G, A and F Group P: C, D and E Thus, the two groups can be formed in four ways. Hence, option 3.

QUESTION: 3

Seven people - A, B, C, D, E, F and G - are to be divided in two groups P and Q such that number of people in groups P and Q is 3 and 4 respectively.

Further it is known that:

1. A and C should not be in the same group.

2. B and G should be in the same group.

3. If E and F are in the same group, then A and D should be in the same group.

4. If C and B are in the same group, then E should not be in the same group as A.

*Q. If C and F are in the same group, how many people from D, B, E and A can individually be in that group?*

Solution:

Consider the solution to the previous question.

If C and F are in one group, either D or E can be individually part of that group.

Hence, option 2.

QUESTION: 4

Group Question

Answer the following question based on the information given below.

P, Q, R, S, T, U, V, W are four couples. X, a forgetful friend of these people, makes the following remarks:

I. (P, U) and (Q, S) are couples.

II. (P, V) and (R, T) are couples.

III. (R, V) and (Q, W) are couples.

IV. (S, T) and (U, W) are couples.

Y, another friend of these couples, tells that of the four statements made by X, one is totally correct, one is partially incorrect (one information is right, other is not) and the rest are totally incorrect.

*Who among the following cannot be married to Q?*

Solution:

Clearly there are four cases: Case 1: Statement I is totally correct.

Then, statement IV is totally incorrect, and one of the other two is partially incorrect..

Hence the third couple is either (R, T) or (R, V).

Hence, we have two possible solutions: (P, U), (Q, S), (R, T) and (V, W) (P, U), (Q, S), (R, V) and (T, W) Case 2: Statement II is fully correct.

Then (P, V) and (R, T) are couples.

Hence, one of (Q, S), (Q, W) or (U, W) should be a couple.

If (Q, S) is the 3rd couple, then (U, W) becomes the 4th couple.

But, this contradicts the given data and hence is not possible.

Now, if (U, W) is the 3rd couple then (Q, S) is also a couple.

This also contradicts the given data and hence is not possible.

Hence, (Q, W) is a couple.

Hence, we get one solution i.e. (P, V), (R, T), (Q, W) and (U, S).

Case 3: Statement III is fully correct. Then II is fully incorrect. Hence one of (P, U) or (S, T) can be a couple.

But if (P, U) is a couple, then (S, T) is also a couple and vice versa.

Hence, we get two partially incorrect statements.

Hence, this case has no solutions.

Case 4: Statement IV is fully correct. Then I is fully incorrect. Then the third couple can be (P, V) or (R, V), hence two solutions. (S, T), (U, W), (P, V), (Q, R)

(S, T), (U, W), (R, V), (P, Q)

Combining all four cases, we get these five solutions: (P, U), (Q, S) (R, T) and (V, W) (P, U), (Q, S), (R, V) and (T, W) (P, V), (R, T), (Q, W) and (U, S) (S, T), (U, W), (P, V) and (Q, R) (S, T), (U, W), (R, V) and (P, Q). Hence, Q can be married to S, W, R or R Hence, option 2

QUESTION: 5

P, Q, R, S, T, U, V, W are four couples. X, a forgetful friend of these people, makes the following remarks:

I. (P, U) and (Q, S) are couples.

II. (P, V) and (R, T) are couples.

III. (R, V) and (Q, W) are couples.

IV. (S, T) and (U, W) are couples.

Y, another friend of these couples, tells that of the four statements made by X, one is totally correct, one is partially incorrect (one information is right, other is not) and the rest are totally incorrect.

*Q. If (P, U) is a couple, which of the following is always true?*

Solution:

From the solution to the previous question of this set, we see that if (P, U) is a couple, we get the following two cases: (P, U), (Q, S), (R, T) and (V, W) (P, U), (Q, S), (R, V) and (T, W) Hence, options 1,2 and 3 are not always true.

Hence, option 4.

QUESTION: 6

P, Q, R, S, T, U, V, W are four couples. X, a forgetful friend of these people, makes the following remarks:

I. (P, U) and (Q, S) are couples.

II. (P, V) and (R, T) are couples.

III. (R, V) and (Q, W) are couples.

IV. (S, T) and (U, W) are couples.

Y, another friend of these couples, tells that of the four statements made by X, one is totally correct, one is partially incorrect (one information is right, other is not) and the rest are totally incorrect.

*Q. If (Q, W) is a couple, then which of the following statement(s) is/are true?*

Solution:

From the solution to the first question of this set, we can see that, if (Q, W) is a couple, we have the following case: (P, V), (R, T), (Q, W) and (U, S) Hence, options 1,2 and 3 are true.

Hence, option 4.

QUESTION: 7

P, Q, R, S, T, U, V, W are four couples. X, a forgetful friend of these people, makes the following remarks:

II. (P, V) and (R, T) are couples.

III. (R, V) and (Q, W) are couples.

IV. (S, T) and (U, W) are couples.

*Q. Who among the following cannot be married to W?*

Solution:

From the solution to the 1st question of this set, W can be married to U, V, Q and T.

Hence, option 3.

QUESTION: 8

Group Question

Answer the following question based on the information given below.

Six people - Arnav, Binal, Clark, Enna, Fenil and Dinesh - are participating in a 1 km race. The scenario when only 100 m are left for the race to get over is:

a. Enna is immediately behind Binal, who is behind Dinesh and ahead of Clark.

b. There is exactly one person between Enna and Fenil, who is in the last place.

*Q. Clark speeds up such that when he ends the race, he has crossed 3 people who were ahead of him at the 900 m point. Who is ahead of Clark at this stage? (Assume that the other people retain their speed).*

Solution:

At 900 m:

Fenil is last and there is exactly one person between Enna and Fenil. So, Enna is fourth.

Since Enna is immediately behind Binal, Binal is third.

Also, since Enna is in front of Clark, Clark is fith.

Arnav and Dinesh are first and second (in no specific order). This is also shown below:

Now, if Clark has crossed 3 people when he finishes the race (such that the others retain their relative positions), he becomes second.

However, either Arnav or Dinesh has finished before Clark and so can be said to be ahead of him at this stage.

Hence, the correct person cannot be determined.

Hence, option 4.

QUESTION: 9

Six people - Arnav, Binal, Clark, Enna, Fenil and Dinesh - are participating in a 1 km race. The scenario when only 100 m are left for the race to get over is:

a. Enna is immediately behind Binal, who is behind Dinesh and ahead of Clark.

b. There is exactly one person between Enna and Fenil, who is in the last place.

*Q. Who is second last in the race at the 900 m mark?*

Solution:

Consider the solution to the previous question. Clark is second last in the race at the 900 m mark. Hence, option 1.

QUESTION: 10

In a certain language;

1. ‘mys mis mysc’ means ‘Gift is life’

2. ‘misc mys mes’ means ‘Earth is good’

3. ‘mese misc mysc’ means ‘Always good gift’

4. ‘mis mos misc’ means ‘Life was good’

What can be the code for ‘Earth always life wasi’?

Solution:

From statements 1 and 2, ‘mys’ means ‘is’.

From statements 2, 3 and 4, ‘misc’ means ‘good’.

Hence, in statement 2, ‘mes’ means ‘earth’.

From statements 1 and 3, ‘mysc’ means ‘gift’.

Hence, in statement 3, ‘mese’ means ‘always’.

From statements 1 and 4, ‘mis’ means ‘life’.

Now, ‘mes’, ‘mese’ and ‘mis’ are present in all the options.

Hence, the code for ‘wasi’ may be ‘mos’, ‘misc’ or ‘mus’.

Since the word ‘wasi’ is not present in the original sentences, its code should also not be present in the sentences.

However, ‘mos’ and ‘misc’ are present in the given sentences. Hence, ‘wasi’ may have been coded as ‘mus’. Hence, option 3.

QUESTION: 11

Read the two statements given below and choose the statement that logically follows from the first two.

Statements:

A. Some softies are vanilla.

B. All vanilla are strawberry.

Conclusions:

I. Some strawberry are not softies.

II. All strawberry are not vanilla.

Solution:

If vanilla and strawberry are the same set, then we have the following.

In this case, all strawberry are softies.

Conclusion I is false.

Again, this case also means that all strawberry are vanilla. Conclusion II is false. Hence, option 4.

QUESTION: 12

Group Question

Answer the following question based on the information given below.

In a super market, Nalini bought at least 1 piece of each of the two items A and B. For every piece of A that she purchased, she purchased 2 pieces of B. Also, Nalini bought at least 1 piece of each of the two items C and D. For every piece of D that she purchased, she purchased 2 pieces of C. Nalini bought more number of items A compared to the number of items D. The prices of one piece of A, B, C, and D is Rs. 100, Rs. 200, Rs. 50 and Rs. 150 respectively.

*Q. If she spent Rs. 2000 in buying the four items A, B, C and D, then how many pieces of item C were purchased?*

Solution:

Let the number of pieces of A be y and those of D be x.

The pieces of B would be 2y and those of C would be 2x.

Now, 100y + 200 X 2y + 50 X 2x + 150x = 2000. 2y + x = 8.

The possible combinations of x andy are: x = 2,y = 3; x = 4,y = 2; x = 6 ,y = 1; Since y > x , x = 2 and y = 3.

The number of pieces of item C = 2x = 4

Hence, option 4.

QUESTION: 13

In a super market, Nalini bought at least 1 piece of each of the two items A and B. For every piece of A that she purchased, she purchased 2 pieces of B. Also, Nalini bought at least 1 piece of each of the two items C and D. For every piece of D that she purchased, she purchased 2 pieces of C. Nalini bought more number of items A compared to the number of items D. The prices of one piece of A, B, C, and D is Rs. 100, Rs. 200, Rs. 50 and Rs. 150 respectively.

*Q. If Nalini purchases 6 pieces of item B, then what is the maximum amount that she could have spent in buying the four items?*

Solution:

If 6 pieces of B are purchased, then the number of pieces of A purchased are 3.

The number of pieces of D is less than that of A, then maximum number of items D would be 2 pieces.

Total amount = 3 x 100 + 6 x 200 + 4 x 50 + 2 x 150 = 2000 Hence, option 3.

QUESTION: 14

In a super market, Nalini bought at least 1 piece of each of the two items A and B. For every piece of A that she purchased, she purchased 2 pieces of B. Also, Nalini bought at least 1 piece of each of the two items C and D. For every piece of D that she purchased, she purchased 2 pieces of C. Nalini bought more number of items A compared to the number of items D. The prices of one piece of A, B, C, and D is Rs. 100, Rs. 200, Rs. 50 and Rs. 150 respectively.

*Q. If Nalini purchases 6 pieces of item B, then she could have spent Rs. ________in buying the four items.*

Solution:

If 6 pieces of B are purchased, then the number of pieces of A purchased are 3.

Case 1:

D is less than A, then minimum number of items D would be 1.

Total amount = 3 x 100 + 6 x 200 + 2 x 50 + 1 x 150 = 1750

Case 2:

D is less than A, then maximum number of items D would be 2.

Total amount = 3 x 100 + 6 x 200 + 4 x 50 + 2 x 150 = 2000

Hence, option 1

QUESTION: 15

For the following question, read the statement and select the most appropriate course of action.

Statement:

The meteorological department of India has warned of a cyclone approaching the country’s Eastern coast.

Courses of Action:

I. Fishermen should be told not to venture out to sea.

II. People in the potentially affected areas should be adequately informed of the approaching cyclone.

III. All hospitals in the affected areas should be put on high alert.

Solution:

Course of Action I is valid as fishermen will be under threat if they venture out to sea. Course of Action II is valid as people will then be able to take remedial measures. Course of Action III is valid as there are likely to be some casualties once the cyclone arrives.

Hence, the correct answer is option 4.

QUESTION: 16

In the word “ABSENTMINDEDNESS”, as we go from left to right all the consonants immediately before a vowel are replaced by that particular vowel. This process is continued till we reach the last vowel of the word. Which letters are at positions 7 and 11 from the right in the new word formed?

Solution:

As we go from left to right, the first vowel is A. There are no consonants before the vowel A.

There are two consonants before the vowel E.

Hence, B and S get replaced by E and the word becomes AEEENTMINDEDNES S.

Now, N, T and M get replaced by I and the word becomes AEEEIIIINDEDNES S.

Now, N and D are replaced by E and then D and N are replaced by the next E.

So, the word becomes AEEEIIIIEEEEEESS.

The two S’s will remain the same, as there is no vowel after them.

Thus, the seventh letter from right is E and the eleventh letter is I.

Hence, option 1.

QUESTION: 17

Group Question

Answer the following question based on the information given below.

Five Civil Engineering students Vinit, Kapil, Adwait, Nikhil and Varun decided to study five towers for their course project. They decided to take up one tower each for study and analysis. The towers are Tower A, Tower B, Tower C, Tower D and Tower E and their heights (in ft) are 2700, 2250, 1768, 1345 and 1005, though not necessarily in the same order. The cities to which the towers belonged are Delhi, Mumbai, Bangalore, Hyderabad and Kolkata, in no specific order. Out of the five towers, two are residential, two are commercial and one is a government building. Further, the following information is known:

I. The tower which Kapil studied is in Kolkata and is shorter in height than at least two towers.

II. None of the commercial towers are the tallest out of the given five towers. Also they’re not situated in Bangalore or Delhi.

III. Tower D is the shortest in height out of the five towers and is not situated in Bangalore or Mumbai.

IV. The tower situated in Mumbai is not a commercial tower.

V. Tower B is not in Mumbai or Bangalore.

VI. Nikhil studied Tower C which is the second tallest tower out of the five towers and it is not situated in Hyderabad or Delhi.

VII. The Government tower is located in Bangalore.

VIII. The tower which Varun studied is neither Tower C nor Tower D and is taller than at least two out of the five towers.

IX. The tower which Adwait studied has height 1768 ft.

X. Tower E is a commercial tower and is situated in Hyderabad.

XI. The tower studied by Vinit is shorter than the tower studied by Kapil.

XII. Tower A which is situated in Mumbai is not studied by Kapil or Nikhil.

*Q. Varun studied Tower__and it is a ________ tower.*

Solution:

From statement I and IX, we can observe that the height of the tower which Kapil studied is either 1345ft or 1005ft.

From statement VI, we know that Tower C is situated in either Mumbai or Bangalore and its height is 2250ft.

From statement VIII and IX, we know that the height of the tower which Varun studied is 2700ft.

From statement I and XI, we can observe that the height of Kapil’s tower is 1345ft and the height of Vinit’s tower is 1005ft.

From statement III, we can infer that Vinit’s tower is Tower D.

From statement XII, we can infer that Tower A was studied by either Varun or Adwait. Also, Tower C is situated in Bangalore which is a Government tower. (Using statement VII) The above points can be summarized in the following table:

From statement II, we know that the tower which Varun studied is a Residential tower.

Using statement X, we can infer that the tower studied by Adwait is Tower E. Thus, tower D is in Delhi. Also, it can be inferred that the tower studied by Varun is in Mumbai. Using statement II, we can infer that the tower situated in Kolkata is a Commercial tower and thus, tower D is a Residential tower.

Also, from statement XII, Varun studied Tower A and Kapil studied Tower B.

The final arrangement can be shown in the following table:

Thus, Varan studied tower A which is Residential. Hence, option 2.

QUESTION: 18

Five Civil Engineering students Vinit, Kapil, Adwait, Nikhil and Varun decided to study five towers for their course project. They decided to take up one tower each for study and analysis. The towers are Tower A, Tower B, Tower C, Tower D and Tower E and their heights (in ft) are 2700, 2250, 1768, 1345 and 1005, though not necessarily in the same order. The cities to which the towers belonged are Delhi, Mumbai, Bangalore, Hyderabad and Kolkata, in no specific order. Out of the five towers, two are residential, two are commercial and one is a government building. Further, the following information is known:

I. The tower which Kapil studied is in Kolkata and is shorter in height than at least two towers.

II. None of the commercial towers are the tallest out of the given five towers. Also they’re not situated in Bangalore or Delhi.

III. Tower D is the shortest in height out of the five towers and is not situated in Bangalore or Mumbai.

IV. The tower situated in Mumbai is not a commercial tower.

V. Tower B is not in Mumbai or Bangalore.

VI. Nikhil studied Tower C which is the second tallest tower out of the five towers and it is not situated in Hyderabad or Delhi.

VII. The Government tower is located in Bangalore.

VIII. The tower which Varun studied is neither Tower C nor Tower D and is taller than at least two out of the five towers.

IX. The tower which Adwait studied has height 1768 ft.

X. Tower E is a commercial tower and is situated in Hyderabad.

XI. The tower studied by Vinit is shorter than the tower studied by Kapil.

XII. Tower A which is situated in Mumbai is not studied by Kapil or Nikhil.

*Q. Which of the following statement(s) is/are incorrect?*

*I. The tower situated in Mumbai is a Residential tower.
II. The height of tower E is 1768ft.
III. Tower A is in Hyderabad.*

Solution:

Consider the solution to the first question.

Statements I and II are correct while statement III is incorrect. Hence, option 3.

QUESTION: 19

Five Civil Engineering students Vinit, Kapil, Adwait, Nikhil and Varun decided to study five towers for their course project. They decided to take up one tower each for study and analysis. The towers are Tower A, Tower B, Tower C, Tower D and Tower E and their heights (in ft) are 2700, 2250, 1768, 1345 and 1005, though not necessarily in the same order. The cities to which the towers belonged are Delhi, Mumbai, Bangalore, Hyderabad and Kolkata, in no specific order. Out of the five towers, two are residential, two are commercial and one is a government building. Further, the following information is known:

I. The tower which Kapil studied is in Kolkata and is shorter in height than at least two towers.

II. None of the commercial towers are the tallest out of the given five towers. Also they’re not situated in Bangalore or Delhi.

III. Tower D is the shortest in height out of the five towers and is not situated in Bangalore or Mumbai.

IV. The tower situated in Mumbai is not a commercial tower.

V. Tower B is not in Mumbai or Bangalore.

VI. Nikhil studied Tower C which is the second tallest tower out of the five towers and it is not situated in Hyderabad or Delhi.

VII. The Government tower is located in Bangalore.

VIII. The tower which Varun studied is neither Tower C nor Tower D and is taller than at least two out of the five towers.

IX. The tower which Adwait studied has height 1768 ft.

X. Tower E is a commercial tower and is situated in Hyderabad.

XI. The tower studied by Vinit is shorter than the tower studied by Kapil.

XII. Tower A which is situated in Mumbai is not studied by Kapil or Nikhil.

*Q. Which of the following statement(s) is/are correct?*

*I. Vinit studied Tower D.
II. The tallest tower is a Commercial tower.
III. The tower which Nikhil studied is a Government tower.*

Solution:

Consider the solution to the first question.

Statements I and III are correct while statement II is incorrect.

Hence, option 2.

QUESTION: 20

Five Civil Engineering students Vinit, Kapil, Adwait, Nikhil and Varun decided to study five towers for their course project. They decided to take up one tower each for study and analysis. The towers are Tower A, Tower B, Tower C, Tower D and Tower E and their heights (in ft) are 2700, 2250, 1768, 1345 and 1005, though not necessarily in the same order. The cities to which the towers belonged are Delhi, Mumbai, Bangalore, Hyderabad and Kolkata, in no specific order. Out of the five towers, two are residential, two are commercial and one is a government building. Further, the following information is known:

II. None of the commercial towers are the tallest out of the given five towers. Also they’re not situated in Bangalore or Delhi.

III. Tower D is the shortest in height out of the five towers and is not situated in Bangalore or Mumbai.

IV. The tower situated in Mumbai is not a commercial tower.

V. Tower B is not in Mumbai or Bangalore.

VI. Nikhil studied Tower C which is the second tallest tower out of the five towers and it is not situated in Hyderabad or Delhi.

VII. The Government tower is located in Bangalore.

VIII. The tower which Varun studied is neither Tower C nor Tower D and is taller than at least two out of the five towers.

IX. The tower which Adwait studied has height 1768 ft.

X. Tower E is a commercial tower and is situated in Hyderabad.

XI. The tower studied by Vinit is shorter than the tower studied by Kapil.

XII. Tower A which is situated in Mumbai is not studied by Kapil or Nikhil.

*Q. What will be the correct arrangement if the students are arranged in descending order of the heights of the towers that they’re studying?*

Solution:

Consider the solution to the first question.

The arrangement of students in descending order of heights of towers that they’re studying is Varun, Nikhil, Adwait, Kapil, Vinit.

Hence, option 1.

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