This is an IBM model placement paper on Logical Reasoning for placement preparation. This placement paper will cover logical reasoning questions that are asked in IBM recruitment drives and also strictly follows the pattern of questions asked in IBM interviews. It is recommended to solve each one of the following questions to increase your chances of clearing the IBM interview.

**Logical Reasoning**

- What will be the next number? 3, 5, 7, 11, 13, 17…….
- 21
- 19
- 23
- 20

**Answer:****19****Explanation:**

3, 5, 7, 11, 13, 17 is a prime number series.

Hence next prime number in this series is 19 - Find wrong number in series: 12, 25, 49, 99, 187, 395, 789
- 7789
- 187
- 99
- 49

**Answer:****187****Explanation:**12*2+1 =25

25*2-1 = 49

49*2+1 = 99

395*2-1 = 789 - If x, y are integers, then (x
^{2}+ y^{2})^{1/2}is an integer?

Statement I – x^{2}+ y^{2}is an integer

Statement II – x^{2}– 3y^{2}= 0- (a)
- (b)
- (c)
- (d)
- (e)

**Answer:****(b) data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.****Explanation:**

Given Statement II => x

^{2}– 3y^{2}= 0

=> x^{2}= 3y^{2}Putting the above in the question

=> (x^{2}+ y^{2})^{1/2}

=> (3y^{2}+ y^{2})^{1/2}

=> (4y^{2})^{1/2}

=> ((2y)^{2})^{1/2}

=> (2y)

which is an integer as y is an integer - What day is 14th of a month?

Statement I – 3rd Saturday of the month is seventeenth

Statement II – 2nd last day of the month is Tuesday- (a)
- (b)
- (c)
- (d)
- (e)

**Answer:****(a) data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.****Explanation:**Given Statement I, 17th, of the month, is Saturday.

Therefore 14th will be Wednesday - Consider the following phrase:

**Statement:**A line from Ram’s appointment letter is “you are hereby appointed as a systems engineer with a probation period of two years and your performance will be reviewed at the end of the period for confirmation.”

**Assumptions:**

**I.**At the time of appointment, the performance of one generally is not well known.

**II.**In the probation period, one tries to prove his worth generally.

Choose the correct option given below.- If only assumption I is implicit
- If only assumption II is implicit.
- If either I or II is implicit.
- If neither I nor II is implicit.
- If both I and II are implicit.

**Answer:****(e) Both I and II are implicit.****Explanation:**Both the statements are implicit because since Ram is newly appointed in this company, so at the time of appointment, the performance of Ram is not well known. Also, they have to test performance over a span of time. So Ram (systems engineer) tries to prove his worth generally in the probation period. So, option (E) is correct.

- Consider the following phrase:

**Statement:**The price for safeda mango is terribly priced at Rs. 200/kg.

**Assumptions:**

**I.**The price for other types of mangoes are decently priced.

**II.**Rs 200 is a very big amount to pay for a safeda mango.

Choose the correct option given below.- If only assumption I is implicit
- If only assumption II is implicit.
- If either I or II is implicit.
- If neither I nor II is implicit.
- If both I and II are implicit.

**Answer:****(b) Only assumption II is implicit.****Explanation:**The Assumption I might or might not be true according to the given Statement, but the Assumption II is definitely true. Hence only Assumption II is implicit.

**Statements:**

I – All mangoes are bananas.

II – Some bananas are a globe.

III – All globe are square.

**Conclusions:**

I. Some mangoes are square.

II. No mango is square.

**Choose the correct option given below:**- only conclusion I is true.
- only conclusion II is true.
- either conclusion I or conclusion II is true
- neither conclusion I nor conclusion II is true
- both conclusions I and II are true.

**Answer:****(c) either conclusion I or conclusion II is true****Explanation:****Statements:**

I – Some C are T

II – Some T are R

III – All R is M

**Conclusions:**

I. Some M are T

II. Some C are M

**Choose the correct option given below:**- only conclusion I is true.
- only conclusion II is true.
- either conclusion I or conclusion II is true
- neither conclusion I nor conclusion II is true
- both conclusions I and II are true.

**Answer:****(a) only conclusion I is true.****Explanation:**Some C might or might not be M. But some M are definitely T.

- Find wrong number in series: 23, 29, 31, 33, 41, 43, 47
- 29
- 33
- 41
- 47

**Answer:****33****Explanation:**The given series is prime numbers from 23

- Find wrong number in series: 8, 24, 12, 36, 18, 54, 26
- 12
- 24
- 18
- 26

**Answer:****Explanation:**Mixture of two alternate series:

8*3=24

24/2=12

12*3=36

36/2=18

18*3=54

54/2=27 **Find wrong number in series:**

2, 3, 6, 0, 8, -3, 14, -6- 3
- 0
- 8
- 3

**Answer:****C****Explanation:**Two alternate series:

2 + 4 = 6,

3 – 3 = 0

6 + 4 = 10,

0 – 3 = -3

10 + 4 = 14

-3 – 3 = -6- 9848 x 125 = ?
- 1232000
- 1242000
- 1231000
- 1233000

**Answer:****1231000****Explanation:**9848 x 125

= 9848 x 53

= 9848 x (10 / 2)^{3}

= 9848 x (10^{3}/ 2^{3})

= 9848 x (1000/8)

= 1231000 **Is x + y = 0?**

Statement I – x.y < 0

Statement II – x^{2}= y^{2}- (a)
- (b)
- (c)
- (d)
- (e)

**Answer:****(e) if the data in both Statements I and II together are necessary to answer the question.****Explanation:**For x + y = 0, there are 2 cases:

Case 1:

x and y are of opposite sign.

This can be inferred from x.y < 0Case 2:

x = y = 0

This can be inferred from x^{2}= y^{2}Hence the data in both Statements I and II together

are necessary to answer the question.**What is the probability that x**^{3}– 8 = 0 when x is selected from a set of 8 integers?

Statement I. The smallest number in the set is -11

Statement II. The arithmetic mean of the set is 1/8.- (a)
- (b)
- (c)
- (d)
- (e)

**Answer:****(d) if the data even in both Statements I and II together are not sufficient to answer the question.**- Consider the following phrase:

**Statement:**All C are J.

All J are B.

No B is R.

**Conclusions:**

**I.**All B are C.

**II.**Some J are C

**Choose the correct option given below:**- only conclusion I is true.
- only conclusion II is true.
- either conclusion I or conclusion II is true
- neither conclusion I nor conclusion II is true
- both conclusions I and II are true.

**Answer:****(b) only conclusion II is true.****Explanation:**All B are not C

- Consider the following phrase:

**Statement:**It is advantageous to start schooling of child at the age of 5 or so.

**Assumptions:**

**I.**At the age of the child reaches appropriate level of development and is ready to learn.

**II.**After 6 yrs of age schools do not admit children

Choose the correct option given below.- If only assumption I is implicit
- If only assumption II is implicit.
- If either I or II is implicit.
- If neither I nor II is implicit.
- If both I and II are implicit.

**Answer:****(a) Only assumption I is implicit** - Consider the following phrase:

**Statement:**Medicine M is a drug which is causing ripples in the medical field.

**Assumptions:**

**I.**M is not a great drug

**II.**No other drug is causing ripples in the medical field

Choose the correct option given below.- If only assumption I is implicit
- If only assumption II is implicit.
- If either I or II is implicit.
- If neither I nor II is implicit.
- If both I and II are implicit.

**Answer:****(a) Only assumption I is implicit** **Statements:**

I – Some S are L

II – Some C are P

III – All P is R

**Conclusions:**

I. Some P are L

II. Some C are R

**Choose the correct option given below:**- only conclusion I is true.
- only conclusion II is true.
- either conclusion I or conclusion II is true
- neither conclusion I nor conclusion II is true
- both conclusions I and II are true.

**Answer:****(d) neither conclusion I nor conclusion II is true**

**Directions to solve Question 3 and 4: Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question.
Read both the statements and Give answer
(a) if the data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.
(b) if the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.
(c) if the data in each Statement I and Statement II alone is sufficient to answer the question.
(d) if the data even in both Statements I and II together are not sufficient to answer the question.
(e) if the data in both Statements I and II together are necessary to answer the question.**

**Directions to solve Question 13 and 14: Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question.
Read both the statements and Give answer
(a) if the data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.
(b) if the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.
(c) if the data in each Statement I and Statement II alone is sufficient to answer the question.
(d) if the data even in both Statements I and II together are not sufficient to answer the question.
(e) if the data in both Statements I and II together are necessary to answer the question.**

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