IBPS Probationary Officer (PO) · Topic Collection

Reasoning PYQs

Verbal and non-verbal reasoning, analogies, syllogisms, number series, coding-decoding, blood relations, and analytical puzzles.

1315 Total Questions38 Official PapersYears: 2021–2026Search in Reasoning
Showing questions 681–700 of 1315Page 35 of 66
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 2·Reasoning Ability
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Question 681

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the questions given below:

Eight persons—B, C, D, E, G, H, I and J—were born in eight different years: 1963, 1974, 1976, 1983, 1991, 1998, 2003 and 2005. Their ages are calculated taking the base year as 2023. Each person likes a different colour: Red, Blue, Green, Yellow, Black, White, Pink and Orange.

All the information is not necessarily in the same order.

Age of H is a multiple of 4 but H was not born before 1991. Three persons were born between H and the one who likes Black colour. B was born immediately after the person who likes Black Colour. Two persons are born between the ones who like Black Colour and Orange Colour. More than two persons were born between D and the one who likes Orange Colour. J was born either two persons after or two persons before D. The number of persons born after J is the same as the number of persons born before G. Age of I is a multiple of 5 but doesn’t like Orange Colour. Two persons were born between the ones who like Pink and Red. As many persons were born before G as after the one who likes Green Colour. C was born after J and likes White Colour. Age of the one who likes Blue Colour is a multiple of 7. Neither the youngest nor the eldest person likes Red Colour.

Who among the following persons was born three persons after the one who was born in the year 1983?

  1. AOption (a)

    The one who likes Red Colour

  2. BOption (b)

    J

  3. COption (c)

    The one who was born immediately before the one who likes Pink Colour.

  4. DOption (d)

    D

  5. EOption (e)

    I

View answer & explanation

Correct answer

Answer: (c)C.

The one who was born immediately before the one who likes Pink Colour.

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 2·Reasoning Ability
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Question 682

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the questions given below:

Eight persons—B, C, D, E, G, H, I and J—were born in eight different years: 1963, 1974, 1976, 1983, 1991, 1998, 2003 and 2005. Their ages are calculated taking the base year as 2023. Each person likes a different colour: Red, Blue, Green, Yellow, Black, White, Pink and Orange.

All the information is not necessarily in the same order.

Age of H is a multiple of 4 but H was not born before 1991. Three persons were born between H and the one who likes Black colour. B was born immediately after the person who likes Black Colour. Two persons are born between the ones who like Black Colour and Orange Colour. More than two persons were born between D and the one who likes Orange Colour. J was born either two persons after or two persons before D. The number of persons born after J is the same as the number of persons born before G. Age of I is a multiple of 5 but doesn’t like Orange Colour. Two persons were born between the ones who like Pink and Red. As many persons were born before G as after the one who likes Green Colour. C was born after J and likes White Colour. Age of the one who likes Blue Colour is a multiple of 7. Neither the youngest nor the eldest person likes Red Colour.

Who among the following persons like Green and Yellow Colour respectively?

  1. AOption (a)

    H and E

  2. BOption (b)

    I and G

  3. COption (c)

    J and G

  4. DOption (d)

    H and J

  5. EOption (e)

    J and E

View answer & explanation

Correct answer

Answer: (c)C.

J and G

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 2·Reasoning Ability
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Question 683

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the questions given below:

Eight persons—B, C, D, E, G, H, I and J—were born in eight different years: 1963, 1974, 1976, 1983, 1991, 1998, 2003 and 2005. Their ages are calculated taking the base year as 2023. Each person likes a different colour: Red, Blue, Green, Yellow, Black, White, Pink and Orange.

All the information is not necessarily in the same order.

Age of H is a multiple of 4 but H was not born before 1991. Three persons were born between H and the one who likes Black colour. B was born immediately after the person who likes Black Colour. Two persons are born between the ones who like Black Colour and Orange Colour. More than two persons were born between D and the one who likes Orange Colour. J was born either two persons after or two persons before D. The number of persons born after J is the same as the number of persons born before G. Age of I is a multiple of 5 but doesn’t like Orange Colour. Two persons were born between the ones who like Pink and Red. As many persons were born before G as after the one who likes Green Colour. C was born after J and likes White Colour. Age of the one who likes Blue Colour is a multiple of 7. Neither the youngest nor the eldest person likes Red Colour.

How many persons were born between E and the one who likes White colour?

  1. AOption (a)

    Three

  2. BOption (b)

    Two

  3. COption (c)

    More than four

  4. DOption (d)

    One

  5. EOption (e)

    Four

View answer & explanation

Correct answer

Answer: (b)B.

Two

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 2·Reasoning Ability
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Question 684

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the questions given below:

Eight persons—B, C, D, E, G, H, I and J—were born in eight different years: 1963, 1974, 1976, 1983, 1991, 1998, 2003 and 2005. Their ages are calculated taking the base year as 2023. Each person likes a different colour: Red, Blue, Green, Yellow, Black, White, Pink and Orange.

All the information is not necessarily in the same order.

Age of H is a multiple of 4 but H was not born before 1991. Three persons were born between H and the one who likes Black colour. B was born immediately after the person who likes Black Colour. Two persons are born between the ones who like Black Colour and Orange Colour. More than two persons were born between D and the one who likes Orange Colour. J was born either two persons after or two persons before D. The number of persons born after J is the same as the number of persons born before G. Age of I is a multiple of 5 but doesn’t like Orange Colour. Two persons were born between the ones who like Pink and Red. As many persons were born before G as after the one who likes Green Colour. C was born after J and likes White Colour. Age of the one who likes Blue Colour is a multiple of 7. Neither the youngest nor the eldest person likes Red Colour.

Which among the following statement(s) is/are false?

I. B was born in 1974.

II. G is not 47 years old.

III. I was born after D but before J.

  1. AOption (a)

    Both I and II

  2. BOption (b)

    Only II

  3. COption (c)

    Only III

  4. DOption (d)

    Both II and III

  5. EOption (e)

    All I, II, and III

View answer & explanation

Correct answer

Answer: (d)D.

Both II and III

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 2·Reasoning Ability
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Question 685

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the questions given below:

Eight persons—B, C, D, E, G, H, I and J—were born in eight different years: 1963, 1974, 1976, 1983, 1991, 1998, 2003 and 2005. Their ages are calculated taking the base year as 2023. Each person likes a different colour: Red, Blue, Green, Yellow, Black, White, Pink and Orange.

All the information is not necessarily in the same order.

Age of H is a multiple of 4 but H was not born before 1991. Three persons were born between H and the one who likes Black colour. B was born immediately after the person who likes Black Colour. Two persons are born between the ones who like Black Colour and Orange Colour. More than two persons were born between D and the one who likes Orange Colour. J was born either two persons after or two persons before D. The number of persons born after J is the same as the number of persons born before G. Age of I is a multiple of 5 but doesn’t like Orange Colour. Two persons were born between the ones who like Pink and Red. As many persons were born before G as after the one who likes Green Colour. C was born after J and likes White Colour. Age of the one who likes Blue Colour is a multiple of 7. Neither the youngest nor the eldest person likes Red Colour.

Four of the following five pairs are alike in a certain way and hence form a group. Which among the following pair does not belong to that group?

  1. AOption (a)

    D - 2005 - Pink

  2. BOption (b)

    C - 2003 - White

  3. COption (c)

    B - 1974 - Blue

  4. DOption (d)

    J - 1976 - Black

  5. EOption (e)

    E - 1983 - Orange

View answer & explanation

Correct answer

Answer: (d)D.

J - 1976 - Black

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 686

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the questions given below:
Six persons, P, Q, R, S, T, and U have booked flights to six different countries - India, Pakistan, Australia, Canada, Brazil and Japan – on six different days starting from Monday to Saturday one after the another in the same week.
The flight to Australia is booked before Thursday. T’s flight is booked before the one who booked his flight to Pakistan. The flight to Brazil is booked four days before the flight to Japan. S’s flight is booked immediately after the flight to India. P’s flight is booked immediately before the Flight to Japan. The number of flights booked before P’s flight is one less than the number of flights booked after the flight to Canada. The flight to India is not booked on Wednesday. Two flights were booked between S’s flight and Q’s flight. R’s flight is booked before the flight booked for Australia. T doesn’t book a flight to Brazil and U doesn’t book a flight on the last day of the week.

Who among the following has booked the flight to Australia?

  1. AOption (a)

    P

  2. BOption (b)

    The one who booked the flight on Tuesday.

  3. COption (c)

    S

  4. DOption (d)

    The one who booked the flight on Wednesday.

  5. EOption (e)

    The one who booked the flight on Monday.

View answer & explanation

Correct answer

Answer: (d)D.

The one who booked the flight on Wednesday.

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 687

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the questions given below:
Six persons, P, Q, R, S, T, and U have booked flights to six different countries - India, Pakistan, Australia, Canada, Brazil and Japan – on six different days starting from Monday to Saturday one after the another in the same week.
The flight to Australia is booked before Thursday. T’s flight is booked before the one who booked his flight to Pakistan. The flight to Brazil is booked four days before the flight to Japan. S’s flight is booked immediately after the flight to India. P’s flight is booked immediately before the Flight to Japan. The number of flights booked before P’s flight is one less than the number of flights booked after the flight to Canada. The flight to India is not booked on Wednesday. Two flights were booked between S’s flight and Q’s flight. R’s flight is booked before the flight booked for Australia. T doesn’t book a flight to Brazil and U doesn’t book a flight on the last day of the week.

On which among the following day did S booked a flight and to which country respectively?

  1. AOption (a)

    Monday, Japan

  2. BOption (b)

    Saturday, India

  3. COption (c)

    Saturday, Japan

  4. DOption (d)

    Friday, Japan

  5. EOption (e)

    Friday, India

View answer & explanation

Correct answer

Answer: (c)C.

Saturday, Japan

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 688

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the questions given below:
Six persons, P, Q, R, S, T, and U have booked flights to six different countries - India, Pakistan, Australia, Canada, Brazil and Japan – on six different days starting from Monday to Saturday one after the another in the same week.
The flight to Australia is booked before Thursday. T’s flight is booked before the one who booked his flight to Pakistan. The flight to Brazil is booked four days before the flight to Japan. S’s flight is booked immediately after the flight to India. P’s flight is booked immediately before the Flight to Japan. The number of flights booked before P’s flight is one less than the number of flights booked after the flight to Canada. The flight to India is not booked on Wednesday. Two flights were booked between S’s flight and Q’s flight. R’s flight is booked before the flight booked for Australia. T doesn’t book a flight to Brazil and U doesn’t book a flight on the last day of the week.

If T is related to U and in the same way Q is related to S then R is related to who among the following persons?

  1. AOption (a)

    The one who booked the flight immediately after Q’s flight.

  2. BOption (b)

    The one who booked to flight to Japan.

  3. COption (c)

    T

  4. DOption (d)

    The one who booked to flight to India.

  5. EOption (e)

    Q

View answer & explanation

Correct answer

Answer: (d)D.

The one who booked to flight to India.

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 689

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the questions given below:
Six persons, P, Q, R, S, T, and U have booked flights to six different countries - India, Pakistan, Australia, Canada, Brazil and Japan – on six different days starting from Monday to Saturday one after the another in the same week.
The flight to Australia is booked before Thursday. T’s flight is booked before the one who booked his flight to Pakistan. The flight to Brazil is booked four days before the flight to Japan. S’s flight is booked immediately after the flight to India. P’s flight is booked immediately before the Flight to Japan. The number of flights booked before P’s flight is one less than the number of flights booked after the flight to Canada. The flight to India is not booked on Wednesday. Two flights were booked between S’s flight and Q’s flight. R’s flight is booked before the flight booked for Australia. T doesn’t book a flight to Brazil and U doesn’t book a flight on the last day of the week.

How many persons have their flights after the flight booked to Canada?

  1. AOption (a)

    Three

  2. BOption (b)

    Two

  3. COption (c)

    Four

  4. DOption (d)

    Either Four or Five

  5. EOption (e)

    Five

View answer & explanation

Correct answer

Answer: (e)E.

Five

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 690

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the questions given below:
Six persons, P, Q, R, S, T, and U have booked flights to six different countries - India, Pakistan, Australia, Canada, Brazil and Japan – on six different days starting from Monday to Saturday one after the another in the same week.
The flight to Australia is booked before Thursday. T’s flight is booked before the one who booked his flight to Pakistan. The flight to Brazil is booked four days before the flight to Japan. S’s flight is booked immediately after the flight to India. P’s flight is booked immediately before the Flight to Japan. The number of flights booked before P’s flight is one less than the number of flights booked after the flight to Canada. The flight to India is not booked on Wednesday. Two flights were booked between S’s flight and Q’s flight. R’s flight is booked before the flight booked for Australia. T doesn’t book a flight to Brazil and U doesn’t book a flight on the last day of the week.

How many persons have their flights booked between R’s flight and P’s flight?

  1. AOption (a)

    None

  2. BOption (b)

    One

  3. COption (c)

    Two

  4. DOption (d)

    Three

  5. EOption (e)

    Four

View answer & explanation

Correct answer

Answer: (c)C.

Two

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 691

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the given questions:
In a certain code language:
“Man is reading book” is coded as “pq mn uv xy”
“Canvas painting is interesting activity” is coded as “fg ij pq ab kl”
“Book activity lecture toy” is coded as “cd fg uv de”
“Reading is interesting lecture” is coded as “de pq kl mn”

The code “cd” is coded for?

  1. AOption (a)

    lecture

  2. BOption (b)

    activity

  3. COption (c)

    book

  4. DOption (d)

    None of these

  5. EOption (e)

    toy

View answer & explanation

Correct answer

Answer: (e)E.

toy

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 692

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the given questions:
In a certain code language:
“Man is reading book” is coded as “pq mn uv xy”
“Canvas painting is interesting activity” is coded as “fg ij pq ab kl”
“Book activity lecture toy” is coded as “cd fg uv de”
“Reading is interesting lecture” is coded as “de pq kl mn”

What is the code for the word pairs “interesting lecture” in the given code language?

  1. AOption (a)

    ij de

  2. BOption (b)

    pq cg

  3. COption (c)

    kl de

  4. DOption (d)

    cg de

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (c)C.

kl de

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 693

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the given questions:
In a certain code language:
“Man is reading book” is coded as “pq mn uv xy”
“Canvas painting is interesting activity” is coded as “fg ij pq ab kl”
“Book activity lecture toy” is coded as “cd fg uv de”
“Reading is interesting lecture” is coded as “de pq kl mn”

What is the code for the word “man” in the given code language?

  1. AOption (a)

    mn

  2. BOption (b)

    pq

  3. COption (c)

    xy

  4. DOption (d)

    cd

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (c)C.

xy

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 694

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the given questions:
In a certain code language:
“Man is reading book” is coded as “pq mn uv xy”
“Canvas painting is interesting activity” is coded as “fg ij pq ab kl”
“Book activity lecture toy” is coded as “cd fg uv de”
“Reading is interesting lecture” is coded as “de pq kl mn”

The code “uv fg” is coded for the word pairs?

  1. AOption (a)

    lecture book

  2. BOption (b)

    toy book

  3. COption (c)

    painting book

  4. DOption (d)

    canvas toy

  5. EOption (e)

    book activity

View answer & explanation

Correct answer

Answer: (e)E.

book activity

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 695

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the given questions:
In a certain code language:
“Man is reading book” is coded as “pq mn uv xy”
“Canvas painting is interesting activity” is coded as “fg ij pq ab kl”
“Book activity lecture toy” is coded as “cd fg uv de”
“Reading is interesting lecture” is coded as “de pq kl mn”

Which of the following combination is correct?

  1. AOption (a)

    Reading - pq

  2. BOption (b)

    Is - mn

  3. COption (c)

    activity- ab

  4. DOption (d)

    book-uv

  5. EOption (e)

    Both (c) and (d)

View answer & explanation

Correct answer

Answer: (d)D.

book-uv

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 696

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the given questions below.
Nine boxes – R, S, T, U, V, W, X, Y and Z are arranged in stacks one after the another, but not necessarily in the same order.
Box Z is above placed Box Y which is not adjacent to Box W. Five boxes are placed between Box S and Box U. Box X is placed two boxes above Box S. The number of boxes placed above Box X is three less than the number box placed below Box T. Two boxes are placed between Box X and Box V. Box W is placed four boxes above Box V. Box R is placed exactly between Box W and Box V.

Which among the following boxes is placed five boxes below Box Z?

  1. AOption (a)

    Box X

  2. BOption (b)

    Box V

  3. COption (c)

    Box W

  4. DOption (d)

    Box Y

  5. EOption (e)

    Box R

View answer & explanation

Correct answer

Answer: (b)B.

Box V

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 697

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the given questions below.
Nine boxes – R, S, T, U, V, W, X, Y and Z are arranged in stacks one after the another, but not necessarily in the same order.
Box Z is above placed Box Y which is not adjacent to Box W. Five boxes are placed between Box S and Box U. Box X is placed two boxes above Box S. The number of boxes placed above Box X is three less than the number box placed below Box T. Two boxes are placed between Box X and Box V. Box W is placed four boxes above Box V. Box R is placed exactly between Box W and Box V.

If all the boxes are arranged in ascending order from bottom to top in alphabetical order, then position of which among the following box remain unchanged?

  1. AOption (a)

    Box T

  2. BOption (b)

    Box X

  3. COption (c)

    Box V

  4. DOption (d)

    Box W

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (d)D.

Box W

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 698

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the given questions below.
Nine boxes – R, S, T, U, V, W, X, Y and Z are arranged in stacks one after the another, but not necessarily in the same order.
Box Z is above placed Box Y which is not adjacent to Box W. Five boxes are placed between Box S and Box U. Box X is placed two boxes above Box S. The number of boxes placed above Box X is three less than the number box placed below Box T. Two boxes are placed between Box X and Box V. Box W is placed four boxes above Box V. Box R is placed exactly between Box W and Box V.

How many boxes are kept above Box X?

  1. AOption (a)

    One

  2. BOption (b)

    Two

  3. COption (c)

    Three

  4. DOption (d)

    Four

  5. EOption (e)

    Five

View answer & explanation

Correct answer

Answer: (d)D.

Four

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 699

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the given questions below.
Nine boxes – R, S, T, U, V, W, X, Y and Z are arranged in stacks one after the another, but not necessarily in the same order.
Box Z is above placed Box Y which is not adjacent to Box W. Five boxes are placed between Box S and Box U. Box X is placed two boxes above Box S. The number of boxes placed above Box X is three less than the number box placed below Box T. Two boxes are placed between Box X and Box V. Box W is placed four boxes above Box V. Box R is placed exactly between Box W and Box V.

Box R is placed on which position?

  1. AOption (a)

    Fourth from the top

  2. BOption (b)

    Third from the bottom

  3. COption (c)

    Fourth from the bottom

  4. DOption (d)

    Second from the bottom

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (c)C.

Fourth from the bottom

Explanation not yet available.
IBPS Probationary Officer (PO) 2023 Previous Year Paper Shift 4·Reasoning Ability
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Question 700

IBPS Probationary Officer (PO) 2023• Reasoning Ability• Reasoning Ability

Study the following information carefully and answer the given questions below.
Nine boxes – R, S, T, U, V, W, X, Y and Z are arranged in stacks one after the another, but not necessarily in the same order.
Box Z is above placed Box Y which is not adjacent to Box W. Five boxes are placed between Box S and Box U. Box X is placed two boxes above Box S. The number of boxes placed above Box X is three less than the number box placed below Box T. Two boxes are placed between Box X and Box V. Box W is placed four boxes above Box V. Box R is placed exactly between Box W and Box V.

How many boxes are placed between Box Y and Box T?

  1. AOption (a)

    As many are placed between Box Z and Box Y

  2. BOption (b)

    As many are placed between Box V and Box X

  3. COption (c)

    As many are placed between Box R and Box S

  4. DOption (d)

    As many are placed between Box U and Box V

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (d)D.

As many are placed between Box U and Box V

Explanation not yet available.

How should I prepare for Reasoning in IBPS Probationary Officer (PO)?

Solving previous year questions by topic helps identify recurring concepts, question patterns, and frequently asked sub-topics. Attempt each question, review the step-by-step explanation, and note down key formulas or facts for quick revision before the exam.