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CAT Practice Test: Week 3 - CAT MCQ


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30 Questions MCQ Test - CAT Practice Test: Week 3

CAT Practice Test: Week 3 for CAT 2024 is part of CAT preparation. The CAT Practice Test: Week 3 questions and answers have been prepared according to the CAT exam syllabus.The CAT Practice Test: Week 3 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT Practice Test: Week 3 below.
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CAT Practice Test: Week 3 - Question 1
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A group of friends have some money which was in an increasing GP. The total money with the first and the last friend was Rs 66 and the product of the money that the second friend had and that the last but one friend had was Rs 128. If the total money with all of them together was Rs 126, then how many friends were there?

Detailed Solution for CAT Practice Test: Week 3 - Question 1

The sum of money with the first and the last friend = 66. This can be used as a hint. Let us assume the first friend was having Rs 2 and the last friend was having Rs 64. So, the money can be in the sequence 2, 4, 8, 16, 32, 64. It satisfies the given conditions. Alternatively, this can be done by using the formula for tn of GP also.

CAT Practice Test: Week 3 - Question 2
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The AM o f two given positive numbers is 2. I f the larger number is increased by 1, the GM of the numbers becomes equal to the AM of the given numbers. Then the HM of the given numbers is

Detailed Solution for CAT Practice Test: Week 3 - Question 2

Let the numbers be a and b. let a be the larger.

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CAT Practice Test: Week 3 - Question 3
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A GP consists of 1000 terms. The sum of the terms occupying the odd places is Pj and the sum of the terms occupying the even places is P2. Find the common ratio of this GP.

Detailed Solution for CAT Practice Test: Week 3 - Question 3

Take any small sample of 4 terms of any GP viz. 1, 2, 4 and 8. Its common ratio = 2 = (8+2)/(1 +4) And this will be true for any number of terms as long as we are taking total number of terms as even(in this question, it is given as 1000). However, if the total number of terms is given as odd, we cannot find the common ratio in this way, because the number of odd terms ≠ number of even terms.

CAT Practice Test: Week 3 - Question 4
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 If the roots of x3 - 12x2 + 39x - 28 = 0 are in an AP then their common difference is
Detailed Solution for CAT Practice Test: Week 3 - Question 4

Factorize the equation and we get ( x - 1 ) ( x - 4 ) ( x - 7 )

CAT Practice Test: Week 3 - Question 5
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If the nth term of AP is m and the nth term of the same AP is m, then (m + n)th term of AP is
Detailed Solution for CAT Practice Test: Week 3 - Question 5
  • Tn = m = a + (n - l ) d
  • Tm = n= a + (m - l ) d
  • subtracting them we get d=-1
  • and a=m+n-1
  • Add the two and solve through the options given.
  • then (m + n)th term of AP= a+(m+n-1)d
  • Putting values of a and d in the solution, we get
  •                                         =  m+n-1+(m+n-1)x-1
  •                                         = 0
CAT Practice Test: Week 3 - Question 6
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If a, b and c are positive integers, then find the product of (a + b) (b + c) (c + a).
Detailed Solution for CAT Practice Test: Week 3 - Question 6

Put a= l, b = 2 c = 3 and check through options.

CAT Practice Test: Week 3 - Question 7
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The mid-points of the adjacent sides of a square are joined. Again the mid-points of the adjacent sides of the newly formed figure are connected and this process is repeated again and again. Calculate the sum of the areas of all such figures given that the diagonal of outermost square is 6√2cm.
Detailed Solution for CAT Practice Test: Week 3 - Question 7

The side of the outermost square is 6 cm. Area of the square one in G.P with first term 36 and common ratio = 1/2

CAT Practice Test: Week 3 - Question 8
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There are three numbers in arithmetic progression. If the two larger numbers are both increased by one, then the resulting numbers are prime. The product of these two primes and the smallest of the original numbers is 598. Find the sum of the three numbers.
Detailed Solution for CAT Practice Test: Week 3 - Question 8

Let three numbers are 2,12,22
Two larger numbers are increased by 1 : 13,23
New three numbers : 2,13,23
Product of these numbers is equal to 598.
=> 2*13*23 = 598
Sum of the three numbers = 2+13+23 
= 36

CAT Practice Test: Week 3 - Question 9
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In how many ways can we select three natural numbers out of the first 10 natural numbers so that they are in a geometric progression with the common ratio greater than 1?
Detailed Solution for CAT Practice Test: Week 3 - Question 9

1,2,4 is GP with first term 1 and common ratio 2(>1).
1,3,9 is GP with first term 1 and common ratio 3(>1).
2,4,8 is GP with first term 2 and common ratio 2(>1).
Only 3 ways.

CAT Practice Test: Week 3 - Question 10
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If the sum of the first 2n terms of the AP 2, 5, 8... is equal to the sum of first n terms of the AP 57, 59, 6 . . . , then what is the value of nl
Detailed Solution for CAT Practice Test: Week 3 - Question 10

CAT Practice Test: Week 3 - Question 11
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Directions to Solve

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

Question -

2,2,5, 13,28,?
Detailed Solution for CAT Practice Test: Week 3 - Question 11

The pattern is + 0, + 3, + 8, + 15, ..... i.e. + (l2 - 1), + (22 - 1), + (32 - 1), + (42 - 1), .....

So, missing term = 28 + (52 - 1) = 28 + 24 = 52.

CAT Practice Test: Week 3 - Question 12
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Directions to Solve

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

Question -

0, 2, 8, 14, ?, 34
Detailed Solution for CAT Practice Test: Week 3 - Question 12

The pattern is + 2, + 6, + 6, + 10, + 10,.....

So, missing term = 14 + 10 = 24.

CAT Practice Test: Week 3 - Question 13
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Directions to Solve

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

Question -

1, 5, 14, 30, 55, 91, ?
Detailed Solution for CAT Practice Test: Week 3 - Question 13

The pattern is + 4, + 9, + 16, + 25, + 36, ..... i.e. + 22, + 32, + 42, + 52, + 62,.....

So, missing term = 91 + 72 = 91 + 49 = 140.

CAT Practice Test: Week 3 - Question 14
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Directions to Solve

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

Question -

In the series 10, 17, 24, 31, 38,.....which of the following will be a number of the series ?
Detailed Solution for CAT Practice Test: Week 3 - Question 14

The given series consists of numbers each of which, on dividing by 7, leaves a remainder 3.

No other number except 346 satisfies the property.

CAT Practice Test: Week 3 - Question 15
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Directions to Solve

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

Question -

240, ?, 120, 40, 10, 2
Detailed Solution for CAT Practice Test: Week 3 - Question 15

The pattern followed is

240÷1=240

240÷2=120

120÷3=40

40÷4=10

10÷5=2

Hence the number is 240

CAT Practice Test: Week 3 - Question 16
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Directions to Solve

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

Question -

2,3,8,27, 112,?
Detailed Solution for CAT Practice Test: Week 3 - Question 16

The pattern is:

(a*1) + 1, (a*2) + 2, (a*3) + 3, (a*4) + 4, (a*5) + 5

So, missing term = 112 x 5 + 5 = 565.

CAT Practice Test: Week 3 - Question 17
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Directions to Solve

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

Question -

6, 17, 39, 72, ?
Detailed Solution for CAT Practice Test: Week 3 - Question 17

The pattern is + 11, + 22, + 33, .....

So, missing term = 72 + 44 = 116.

CAT Practice Test: Week 3 - Question 18
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Directions to Solve

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

Question -

20, 20, 19, 16, 17, 13, 14, 11, ?, ?
Detailed Solution for CAT Practice Test: Week 3 - Question 18

Let the missing terms of the series be x1 and x2.

Thus, the sequence 20, 20, 19, 16, 17, 13, 14, 11, xv x2 is a combination of two series :

I. 20, 19, 17, 14, x1 and II. 20, 16, 13, 11, x2

The pattern in I is - 1, - 2, - 3,......So, missing term, x1 = 14 - 4 = 10.

The pattern in II is - 4, - 3, - 2,......So, missing term, x2 = 11 - 1 = 10.

CAT Practice Test: Week 3 - Question 19
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Directions to Solve

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

Question -

24, 60, 120, 210, ?
Detailed Solution for CAT Practice Test: Week 3 - Question 19

The pattern is + 36, + 60, + 90,.....i.e. + [6 x (6 + 0)], + [6 x (6 + 4)], + [6 x (6 + 9)],...
So, missing term = 210 + [6 x (6 + 15)] = 210 + 126 = 336.

CAT Practice Test: Week 3 - Question 20
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Directions to Solve

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

Question -

625, 5, 125, 25, 25, ?, 5
Detailed Solution for CAT Practice Test: Week 3 - Question 20

The given sequence is a combination of two series :

I. 625, 125, 25, 5 and II. 5, 25, ?

The pattern in I is ? 5, while that in II is x 5. So, missing term = 25 x 5 = 125.

CAT Practice Test: Week 3 - Question 21
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Find out the Synonym of the following word:

FAKE
Detailed Solution for CAT Practice Test: Week 3 - Question 21
  • Meaning of Fake: Not genuine, imitation or counterfeit.
  • Meaning of Original: present or existing from the beginning; first or earliest
  • Meaning of Trustworthy: able to be relied on as honest or truthful
  • Meaning of Loyal: giving or showing firm and constant support or allegiance to a person or institution
CAT Practice Test: Week 3 - Question 22
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Find out the Synonym of the following word:

INDICT
Detailed Solution for CAT Practice Test: Week 3 - Question 22
  • Meaning of Indict: Formally accuse of or charge with a crime.
  • Meaning of Condemn: express complete disapproval of; censure.
  • Meaning of Reprimand: a formal expression of disapproval
  • Meaning of Allege: claim or assert that someone has done something illegal or wrong, typically without proof
CAT Practice Test: Week 3 - Question 23
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Find out the Synonym of the following word:

STRINGENT
Detailed Solution for CAT Practice Test: Week 3 - Question 23
  • Meaning of Stringent: Strict, precise, and exacting.
  • Meaning of Dry: free from moisture or liquid; not wet or moist
  • Meaning of Strained: showing signs of nervous tension or tiredness
  • Meaning of Rigorous: extremely thorough and careful
  • Meaning of Shrill: (of a voice or sound) high-pitched and piercing
CAT Practice Test: Week 3 - Question 24
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Find out the Synonym of the following word:

LAMENT
Detailed Solution for CAT Practice Test: Week 3 - Question 24
  • Lament has two meanings out of which one is 'to complain'.
  • Meaning of Complaint: a statement that something is unsatisfactory or unacceptable
  • Meaning of Comment: a verbal or written remark expressing an opinion or reaction
  • Meaning of Condone: accept (behaviour that is considered morally wrong or offensive)
  • Meaning of Console: comfort (someone) at a time of grief or disappointment
CAT Practice Test: Week 3 - Question 25
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Find out the Synonym of the following word:

HESITATED
Detailed Solution for CAT Practice Test: Week 3 - Question 25
  • Meaning of Hesitated: Pause in indecision before saying or doing something.
  • Meaning of Stopped: (of an event, action, or process) come to an end; cease to happen.
  • Meaning of Paused: interrupt action or speech briefly
  • Meaning of Slowed: reduce one's speed or the speed of a vehicle or process
  • Meaning of Postponed: cause or arrange for (something) to take place at a time later than that first scheduled
CAT Practice Test: Week 3 - Question 26
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Foremost :
Detailed Solution for CAT Practice Test: Week 3 - Question 26

Hindmost : furthest back, latest or ultramodern.
Disposed : inclined or willing.
Mature : fully developed physically, full-grown.
Unimportant : lacking in importance or significance.
Foremost : most prominent in rank, importance, or position.

So, antonym is Unimportant.
 

CAT Practice Test: Week 3 - Question 27
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EXTRICATE
Detailed Solution for CAT Practice Test: Week 3 - Question 27
Definition:
Extricate means to free or release someone or something from a difficult or tangled situation.
Explanation:
To identify the correct answer, let's look at the meanings of the other options:
- Manifest: This means to display or show something clearly. It does not have the same meaning as extricate.
- Palpable: This means easily perceived or noticeable. It does not have the same meaning as extricate.
- Release: This means to set free or let go. It is a synonym of extricate and could be a possible answer.
- Entangle: This means to tangle or involve someone or something in difficulties or complications. It is the correct synonym of extricate and is the correct answer.
Therefore, the correct answer is D: Entangle.
CAT Practice Test: Week 3 - Question 28
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REPRESS
Detailed Solution for CAT Practice Test: Week 3 - Question 28
Explanation:
The word "repress" means to restrain, suppress, or hold back. The question is asking for a word that is the opposite in meaning to "repress." Let's examine the given options:
A. Inhibit: This word means to hinder, restrain, or prevent. It is similar in meaning to "repress," so it is not the correct answer.
B. Liberate: This word means to set free, release, or emancipate. It is the opposite of "repress" and is the correct answer.
C. Curb: This word means to control, limit, or restrain. It is similar in meaning to "repress," so it is not the correct answer.
D. Quell: This word means to suppress, calm, or pacify. It is similar in meaning to "repress," so it is not the correct answer.
Therefore, the correct answer is B. Liberate.
CAT Practice Test: Week 3 - Question 29
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ACQUITTED
Detailed Solution for CAT Practice Test: Week 3 - Question 29

In this sentence we would be selecting the word which is opposite to "acquitted" from the given options.
Acquit means to decide that someone is not guilty of a crime. Thus, the opposite would be to blame someone or charge someone guilty of a crime.
If we look into the options:
Entrusted means to give someone the responsibility of doing something
Convicted means to prove someone guilty of a crime. It is the correct option.
Burdened means heavily laden or encumbered or someone who has been given a lot of lead. 
Freed means not held physically.
 

CAT Practice Test: Week 3 - Question 30
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PROVOCATION
Detailed Solution for CAT Practice Test: Week 3 - Question 30

Provocation : action or speech that makes someone angry, especially deliberately.
Destruction : the action or process of causing so much damage to something that it no longer exists or cannot be repaired.
Peace : freedom from disturbance; tranquillity.
Pacification : an attempt to create or maintain peace.
Vocation : a strong feeling of suitability for a particular career or occupation.

Antonym of Provocation is Pacification.
 

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