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CAT Practice Test: Week 17 - CAT MCQ


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30 Questions MCQ Test - CAT Practice Test: Week 17

CAT Practice Test: Week 17 for CAT 2024 is part of CAT preparation. The CAT Practice Test: Week 17 questions and answers have been prepared according to the CAT exam syllabus.The CAT Practice Test: Week 17 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT Practice Test: Week 17 below.
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CAT Practice Test: Week 17 - Question 1
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If x = 2 is a root of the quadratic equation 3x2 – px – 2 = 0, then the value of ‘p’ is

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CAT Practice Test: Week 17 - Question 2
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Detailed Solution for CAT Practice Test: Week 17 - Question 2

Here, the degree is 2, therefore it is a quadratic equation.

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CAT Practice Test: Week 17 - Question 3
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If p = – 7 and q = 12 and x2+px+q=0, then the value of ‘x’ is

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CAT Practice Test: Week 17 - Question 4
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The roots of a quadratic equation x2−4px+4p2−q2=0 are
Detailed Solution for CAT Practice Test: Week 17 - Question 4

CAT Practice Test: Week 17 - Question 5
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The two numbers whose sum is 27 and their product is 182 are
Detailed Solution for CAT Practice Test: Week 17 - Question 5

Explanation:Let the one number be xx .As the sum  of numbers is 27 , then the other number will be (27−x)(27−x)                                                                                                                                    According to question

CAT Practice Test: Week 17 - Question 6
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The common root of 2x2+x−6 = 0 and x2−3x−10 = 0 is
Detailed Solution for CAT Practice Test: Week 17 - Question 6

CAT Practice Test: Week 17 - Question 7
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In a cricket match Kumble took three wickets less than twice the number of wickets taken by Srinath. The product of the number of wickets taken by these two is 20, then the number of wickets taken by Kumble is
Detailed Solution for CAT Practice Test: Week 17 - Question 7

 

Explanation:

Let the number of wickets taken by Srinath be x then the number of wickets taken by Kumble will be 2x−3
According to question, x(2x−3)=20

CAT Practice Test: Week 17 - Question 8
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(x2 + 1)2 - x2 = 0 has
Detailed Solution for CAT Practice Test: Week 17 - Question 8

CAT Practice Test: Week 17 - Question 9
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If the sum and product of the roots of the equation kx2 + 6x + 4k = 0 are equal, then k = 
Detailed Solution for CAT Practice Test: Week 17 - Question 9

CAT Practice Test: Week 17 - Question 10
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The product of two successive integral multiples of 5 is 1050. Then the numbers are
Detailed Solution for CAT Practice Test: Week 17 - Question 10

Explanation:

Let one multiple of 5 be x then the next consecutive multiple of will be (x+5) According to question,

Then the number are 30 and 35.

CAT Practice Test: Week 17 - Question 11
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Which of the following statements is/are definitely true?
Detailed Solution for CAT Practice Test: Week 17 - Question 11

Given that every player spoke exactly two false statements, hence they all spoke one true statement. Let the first statement of Stanley be true. Hence, the other two must be false. Therefore, Stanley is not playing for Team-A. Owen is not a mid-fielder and Geoffrey is not playing for Team-C.
Owen's second statement is, therefore, true. Hence, his first and third statements must be false, which means that Owen is not a defender and Stanley is not a mid-fielder. Owen has to be a goalkeeper. Stanley should be a defender. Geoffrey must be a mid-fielder.
Hence, Geoffrey's last statement is true. But Geoffrey's first statement is also true. Since this is not possible, Stanley's first statement cannot be true.
Let the second statement of Stanley be true. Therefore. Owen is a mid-fielder. From his other two statements, we can say that Stanley is from Team-A and Geoffrey is from the Team-B. Hence, Owen is from the Team-C. Owen's second statement is true. His first and third statements are false. Geoffrey's second statement is true. His first and third statements must be false. Therefore, Stanley must be a goalkeeper and Geoffrey must be a defender. This is one possible case.
Let Stanley's third statement be true. Geoffrey must be from Team-C. According to his first statement, Stanley must be from Team-A. Therefore, Owen must be from Team-B. Owen is not a mid-fielder.
Owen's second statement and Geoffrey's second statement are false. The only case possible in which both Owen and Geoffrey tell one true statement each is when Owen's first statement and Geoffrey's third statement are true. Hence, Owen is a defender, Geoffrey is a mid-fielder and Stanley is a goalkeeper. This is another possible case.
The possible cases are presented in the following table:

Hence, all are true. 

CAT Practice Test: Week 17 - Question 12
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The person who supports Barcelona is 
Detailed Solution for CAT Practice Test: Week 17 - Question 12

After going through all statements made by Graeme, Harry, and Mathew, one can make out that Mathew's second statement is either a true statement of a truth-teller or a false statement of an alternator, irrespective of which Mathew's first and third statements have to be true. This gives us the following result:

Based on above, we can determine that Graeme's first statement is false and second one is true. As the three of them have to be either a truth-teller, a liar, or an alternator, we can conclude that Graeme is an alternator and her third statement is hence false (which means Mathew is not an alternator). This leads us to the conclusion that Mathew is a truth-teller. Thus, Mathew's second statement can also be marked as true.
Hereafter, when we analyse Harry's statements, we realise that they all are false; so Harry must be a liar. With 'T' standing for true and 'F' for false, the nature of the statements will be as follows:

Hence, Harry supports Barcelona.

CAT Practice Test: Week 17 - Question 13
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Who among the following is a liar?
Detailed Solution for CAT Practice Test: Week 17 - Question 13

After going through all statements made by Graeme, Harry, and Mathew, one can make out that Mathew's second statement is either a true statement of a truth-teller or a false statement of an alternator, irrespective of which Mathew's first and third statements have to be true. This gives us the following result:

Based on above, we can determine that Graeme's first statement is false and second one is true. As the three of them have to be either a truth-teller, a liar, or an alternator, we can conclude that Graeme is an alternator and her third statement is hence false (which means Mathew is not an alternator). This leads us to the conclusion that Mathew is a truth-teller. Thus, Mathew's second statement can also be marked as true.
Hereafter, when we analyse Harry's statements, we realise that they all are false; so Harry must be a liar. With 'T' standing for true and 'F' for false, the nature of the statements will be as follows:

Harry is a liar.

CAT Practice Test: Week 17 - Question 14
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Which of the following statements is/are false?
Detailed Solution for CAT Practice Test: Week 17 - Question 14

After going through all statements made by Graeme, Harry, and Mathew, one can make out that Mathew's second statement is either a true statement of a truth-teller or a false statement of an alternator, irrespective of which Mathew's first and third statements have to be true. This gives us the following result:

Based on above, we can determine that Graeme's first statement is false and second one is true. As the three of them have to be either a truth-teller, a liar, or an alternator, we can conclude that Graeme is an alternator and her third statement is hence false (which means Mathew is not an alternator). This leads us to the conclusion that Mathew is a truth-teller. Thus, Mathew's second statement can also be marked as true.
Hereafter, when we analyse Harry's statements, we realise that they all are false; so Harry must be a liar. With 'T' standing for true and 'F' for false, the nature of the statements will be as follows:
All the above statements are false.

CAT Practice Test: Week 17 - Question 15
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Who among the following supports Arsenal?
Detailed Solution for CAT Practice Test: Week 17 - Question 15

After going through all statements made by Graeme, Harry, and Mathew, one can make out that Mathew's second statement is either a true statement of a truth-teller or a false statement of an alternator, irrespective of which Mathew's first and third statements have to be true. This gives us the following result:

Based on above, we can determine that Graeme's first statement is false and second one is true. As the three of them have to be either a truth-teller, a liar, or an alternator, we can conclude that Graeme is an alternator and her third statement is hence false (which means Mathew is not an alternator). This leads us to the conclusion that Mathew is a truth-teller. Thus, Mathew's second statement can also be marked as true.
Hereafter, when we analyse Harry's statements, we realise that they all are false; so Harry must be a liar. With 'T' standing for true and 'F' for false, the nature of the statements will be as follows:

Hence, Mathew supports Arsenal.

CAT Practice Test: Week 17 - Question 16
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Who among the following spoke the maximum number of truths?
Detailed Solution for CAT Practice Test: Week 17 - Question 16

Each person alternates between a truth and a lie, then for three statements given by any person, the nature of the statements could be:
True, False, True
or
False, True, False
(i) Assume that the three statements given by Walter are in the order, True, False, True. Then, we get the following arrangement:

Here, all the three statements given by Neil become false. Hence, we'll try the second combination.
(ii) Assume that the three statements given by Walter are in the order False, True, False.
Then, we get the following arrangement:


Thus, it can be concluded that Gavin spoke spoke the maximum number of truths, i.e. 2.
Hence, answer option 4 is correct.

CAT Practice Test: Week 17 - Question 17
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Which of the following statements must be false?
Detailed Solution for CAT Practice Test: Week 17 - Question 17

Each person alternates between a truth and a lie, then for three statements given by any person, the nature of the statements could be:
True, False, True
or
False, True, False
(i) Assume that the three statements given by Walter are in the order, True, False, True. Then, we get the following arrangement:

Here, all the three statements given by Neil become false. Hence, we'll try the second combination.
(ii) Assume that the three statements given by Walter are in the order False, True, False.
Then, we get the following arrangement:


It can be observed from the arrangement made above that option (4) is false.

CAT Practice Test: Week 17 - Question 18
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Which train coach is Hugh travelling in?
Detailed Solution for CAT Practice Test: Week 17 - Question 18

 Let Henry be the truth-teller. From Henry's first statement, Daniel is not the alternator. Hence, Daniel must be the liar. As per Henry's second statement, Henry must be travelling in Coach-B because he is the truth-teller.
Since Daniel is a liar, from his first statement, the alternator is not travelling in Coach-C. Hence, the alternator must be travelling in Coach-A. The liar must be travelling in Coach-C. In this case, Hugh must be the alternator. Hugh's second statement is false and first statement is true. Hence, this is one possible case.
Let Daniel be the truth-teller. From Daniel's first statement, the alternator is travelling in Coach-C. Since Daniel is the truth-teller, Henry's first statement is true. Hence, Henry must be the alternator. His second statement must be false. Hence, the truth-teller is not travelling in Coach-B. Since the alternator is travelling in Coach-C, the truth-tellers is travelling in Coach-A and the liar must be travelling in Coach-B. Since Daniel is the truth-teller and Henry is the alternator, Hugh must be the liar. However, Hugh's first statement is true as Henry is not travelling in Coach-A (since Henry is the alternator, he must be travelling in Coach-C). Hence, Hugh cannot be the liar. Therefore, this case is not possible.
Let Hugh be the truth-teller. Daniel is the alternator and Henry is the liar. Daniel's second statement is false and hence, his first statement must be true. Therefore, the alternator is travelling in Coach-C. Since Henry is the liar, the truth-teller cannot be travelling in Coach-B. Hence, the truth-teller must be travelling in Coach-A and the liar must be travelling in Coach-B. This is one possible case.

Thus, it can be concluded that Hugh is travelling in Coach-A.
Hence, answer option 1 is correct.

CAT Practice Test: Week 17 - Question 19
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Who among the following definitely made at least one true statement?
Detailed Solution for CAT Practice Test: Week 17 - Question 19

 Let Henry be the truth-teller. From Henry's first statement, Daniel is not the alternator. Hence, Daniel must be the liar. As per Henry's second statement, Henry must be travelling in Coach-B because he is the truth-teller.
Since Daniel is a liar, from his first statement, the alternator is not travelling in Coach-C. Hence, the alternator must be travelling in Coach-A. The liar must be travelling in Coach-C. In this case, Hugh must be the alternator. Hugh's second statement is false and first statement is true. Hence, this is one possible case.
Let Daniel be the truth-teller. From Daniel's first statement, the alternator is travelling in Coach-C. Since Daniel is the truth-teller, Henry's first statement is true. Hence, Henry must be the alternator. His second statement must be false. Hence, the truth-teller is not travelling in Coach-B. Since the alternator is travelling in Coach-C, the truth-tellers is travelling in Coach-A and the liar must be travelling in Coach-B. Since Daniel is the truth-teller and Henry is the alternator, Hugh must be the liar. However, Hugh's first statement is true as Henry is not travelling in Coach-A (since Henry is the alternator, he must be travelling in Coach-C). Hence, Hugh cannot be the liar. Therefore, this case is not possible.
Let Hugh be the truth-teller. Daniel is the alternator and Henry is the liar. Daniel's second statement is false and hence, his first statement must be true. Therefore, the alternator is travelling in Coach-C. Since Henry is the liar, the truth-teller cannot be travelling in Coach-B. Hence, the truth-teller must be travelling in Coach-A and the liar must be travelling in Coach-B. This is one possible case.

In both the cases, Hugh spoke at least one true statement.
Hence, answer option 3 is correct.

CAT Practice Test: Week 17 - Question 20
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If Henry is not the liar, then who is the truth-teller?
Detailed Solution for CAT Practice Test: Week 17 - Question 20

 Let Henry be the truth-teller. From Henry's first statement, Daniel is not the alternator. Hence, Daniel must be the liar. As per Henry's second statement, Henry must be travelling in Coach-B because he is the truth-teller.
Since Daniel is a liar, from his first statement, the alternator is not travelling in Coach-C. Hence, the alternator must be travelling in Coach-A. The liar must be travelling in Coach-C. In this case, Hugh must be the alternator. Hugh's second statement is false and first statement is true. Hence, this is one possible case.
Let Daniel be the truth-teller. From Daniel's first statement, the alternator is travelling in Coach-C. Since Daniel is the truth-teller, Henry's first statement is true. Hence, Henry must be the alternator. His second statement must be false. Hence, the truth-teller is not travelling in Coach-B. Since the alternator is travelling in Coach-C, the truth-tellers is travelling in Coach-A and the liar must be travelling in Coach-B. Since Daniel is the truth-teller and Henry is the alternator, Hugh must be the liar. However, Hugh's first statement is true as Henry is not travelling in Coach-A (since Henry is the alternator, he must be travelling in Coach-C). Hence, Hugh cannot be the liar. Therefore, this case is not possible.
Let Hugh be the truth-teller. Daniel is the alternator and Henry is the liar. Daniel's second statement is false and hence, his first statement must be true. Therefore, the alternator is travelling in Coach-C. Since Henry is the liar, the truth-teller cannot be travelling in Coach-B. Hence, the truth-teller must be travelling in Coach-A and the liar must be travelling in Coach-B. This is one possible case.

If Henry is not the liar, then Henry is the truth-teller.
Hence, answer option 2 is correct.

CAT Practice Test: Week 17 - Question 21
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Directions: Four parts of the sentence given below have been underlined. Identify the part having an error. 
Detailed Solution for CAT Practice Test: Week 17 - Question 21

The visitors ‘had left’. When two events in the past are in sequence, the earlier event is put in the past perfect tense. The visitors had left before he returned to office.

CAT Practice Test: Week 17 - Question 22
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Directions: Four parts of the sentence given below have been underlined. Identify the part having an error. 

Turquoise, (1) which is found in microscopic crystals, is opaque with (2) a waxy luster, varying in (3) colours (4) from greenish grey to sky blue. 
Detailed Solution for CAT Practice Test: Week 17 - Question 22

It varies in `colour`, not `colours`. Here `colour` is used as a characteristic.

CAT Practice Test: Week 17 - Question 23
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Directions: Four parts of the sentence given below have been underlined. Identify the part having an error. 

(1) While studying the chemistry of (2) human body, Dr. Rosalyn Yalow won a Nobel Prize for the research she (3) conducted on the (4) role of hormones.
Detailed Solution for CAT Practice Test: Week 17 - Question 23

In case of two successive actions in the past tense, the action that occurs earlier uses past perfect tense (remember the example: the patient had died before the doctor came). 

CAT Practice Test: Week 17 - Question 24
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Directions: The sentence below is underlined or has an underlined part. The underlined part may have an error of grammar or syntax. There are five options that seek to correct the error (including an option that simply repeats the sentence). Select the option that best replaces the underlined part.

Even before the villagers could be shifted to a safer place the river has overflown its bank.
Detailed Solution for CAT Practice Test: Week 17 - Question 24

'Flown' is the past participle form of 'fly' while 'flowed' is the past participle form of 'flow'. The river does not fly; it flows. And when two past actions are in sequence, past perfect tense (had) should be used for the event that happens earlier. This option rectifies both the errors.

CAT Practice Test: Week 17 - Question 25
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Directions: Four parts of the sentence given below have been underlined. Identify the part having an error.

The door (1) is locked (2) from inside, someone (3) must have been (4) inside the room. 
Detailed Solution for CAT Practice Test: Week 17 - Question 25

'Must be' will be the correct use in place of 'must have been'. 'Must have been' refers to an action in the past.

CAT Practice Test: Week 17 - Question 26
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Directions: Fill in the blank with the most appropriate option.

The knee is ________ most other joints in the body because it cannot twist without injury.
Detailed Solution for CAT Practice Test: Week 17 - Question 26

The comparison is with `most other body joints`. Hence, `more likely than`.

CAT Practice Test: Week 17 - Question 27
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Directions: Identify the part having an error. 
Detailed Solution for CAT Practice Test: Week 17 - Question 27

If two events in the past are in sequence, the earlier event will use past perfect tense. Replace `was recorded` by `had been recorded`, to precede simple past `was difficult`.

CAT Practice Test: Week 17 - Question 28
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Directions: A part of the sentence that has been underlined has an error. The part has been rewritten under answer options 1 to 4. Select the option that is the most coherent and precise representation of the underlined part.

I could wait hardly and would always ask if I could go to play cricket.
Detailed Solution for CAT Practice Test: Week 17 - Question 28

This option corrects the error of placement of adverb. The adverb must be used before the word it modifies.

CAT Practice Test: Week 17 - Question 29
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Directions: Four parts of the sentence given below have been underlined. Identify the part having an error.

(1) Could I (2) have (3) any cookies (4) with some coffee, please?
Detailed Solution for CAT Practice Test: Week 17 - Question 29

Replace 'any' by 'some'. Generally any is used in negative sentences. We use 'could' as a polite way of telling or asking someone to do something. Can is less polite. 

CAT Practice Test: Week 17 - Question 30
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Directions: The sentence below is underlined or has an underlined part. The underlined part may have an error of grammar or syntax. There are four options that seek to correct the error (including an option that simply repeats the sentence). Select the option that best replaces the underlined part.

The criminals fled while the police reached the spot of crime.
Detailed Solution for CAT Practice Test: Week 17 - Question 30

The original sentence bears the error of faulty use of tense and conjunction. When two past actions are in sequence, past perfect tense should be used to refer to the earlier action. Therefore, the correct usage is 'had fled'. The conjunction `while` needs to be replaced by the conjunction `before` to emphasize that the criminals had fled before the police arrived at the scene. This option rectifies both the errors of tense and of incorrect word usage.

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