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CAT Practice Test: Week 2 - CAT MCQ


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30 Questions MCQ Test Daily Test for CAT Preparation - CAT Practice Test: Week 2

CAT Practice Test: Week 2 for CAT 2024 is part of Daily Test for CAT Preparation preparation. The CAT Practice Test: Week 2 questions and answers have been prepared according to the CAT exam syllabus.The CAT Practice Test: Week 2 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT Practice Test: Week 2 below.
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CAT Practice Test: Week 2 - Question 1
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LCM of first 100 natural numbers is N. What is the LCM of first 105 natural numbers?

Detailed Solution for CAT Practice Test: Week 2 - Question 1

N is the LCM of first 100 natural numbers.
Now 101 is a prime number, so 101 and N do not have any common factors. Hence their LCM = 101 X N
102= 2 X 51, since 2 < 100 and 51 < 100, 102 divides N
103 is a prime number, no common factors between 103 and N
104= 52 X 2; since 2 < 100 and 52 < 100, 105 divides N 
105 = 21 X 5; since 5 < 100 and 21 < 100, 105 divides N 
Hence, LCM of first 105 natural number is N X 101 X 103

CAT Practice Test: Week 2 - Question 2
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The total number of 3 digit numbers which have two or more consecutive digits identical is:

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

In each set of 100 numbers, there are 10 numbers whose tens digit and unit digit are same. Again in the same set there are 10 numbers whose hundreds and tens digits are same. But one number in each set of 100 numbers whose Hundreds, Tens and Unit digit are same as 111, 222, 333, 444 etc
Hence, there are exactly (10 + 10 - 1) = 19 numbers in each set of 100 numbers. Further there are 9 such sets of numbers
Therefore such total numbers = 19 × 9 = 171

Alternatively,
9 × 10 × 10 - 9 × 9 × 9 = 900 - 729 = 171

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CAT Practice Test: Week 2 - Question 3
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Find the last non zero digit of 96!

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

4*z(96/5)*z(6)

=4*z(19)*8

=8*(4*z(19/5)*z(9))

=8*(4*z(3)*8)

=8*(4*6*8)

=1536 i.e last digit is 6

CAT Practice Test: Week 2 - Question 4
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Two players A and B are playing a game of putting ‘+’ and signs in between any two integers written from 1 to 100. A starts the game by putting a plus sign anywhere between any two integers. Once all the signs have been put, the result is calculated. If it is even then A wins and if it is odd then B wins, provided they are putting signs by taking turns one by one and either of them can put any sign anywhere between any two integers. Who will win at the end?
Detailed Solution for CAT Practice Test: Week 2 - Question 4

Whatever is the sign between two consecutive integers starting from 1 to 100, it will be odd. So, we are getting 50 sets of odd numbers. Now, whatever calculation we do among 50 odd numbers, result will always be even. So, A will win always.

CAT Practice Test: Week 2 - Question 5
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How many divisors of 105 will have at least one zero at its end?
Detailed Solution for CAT Practice Test: Week 2 - Question 5

In order for a divisor (or any number) to have a zero at its end, it must have a 10 as a factor, i.e., a 2-and-5 pair. Notice that

10^5 = 2^5 x 5^5 = (2^4 x 5^4) x (2 x 5)

Therefore, any divisors of 2^4 x 5^4 will have a zero at its end when multiplied by 2 x 5. Since 2^4 x 5^4 has (4 + 1)(4 + 1) = 25 divisors, 10^5 has 25 divisors that have at least one zero at its end.

CAT Practice Test: Week 2 - Question 6
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Find the remainder when 496 is divided by 6.
Detailed Solution for CAT Practice Test: Week 2 - Question 6

 496/6, We can write it in this form
(6 - 2)96/6
Now, Remainder will depend only the powers of -2. So,
(-2)96/6, It is same as
([-2]4)24/6, it is same as
(16)24/6
Now,
(16 * 16 * 16 * 16..... 24 times)/6
On dividing individually 16 we always get a remainder 4.
So,
(4 * 4 * 4 * 4............ 24 times)/6.
Hence, Required Remainder = 4.
NOTE: When 4 has even number of powers, it will always give remainder 4 on dividing by 6.

CAT Practice Test: Week 2 - Question 7
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Tatto bought a notebook containing 96 pages leaves and numbered them which came to 192 pages. Tappo tore out the latter 25 leaves of the notebook and added the 50 numbers she found on those pages. Which of the following is not true?
Detailed Solution for CAT Practice Test: Week 2 - Question 7

Information Given:

  • The notebook has 96 leaves, which means it has 192 pages (since each leaf has two pages).
  • The pages are numbered from 1 to 192.
  • Tappo tore out the last 25 leaves of the notebook. Since each leaf has 2 pages, she tore out 50 pages.

Step 1: Determine the page numbers torn out

The last 25 leaves correspond to the last 50 pages in the notebook. Since the total number of pages is 192, the page numbers torn out would be from 143 to 192.

Step 2: Calculate the sum of the torn-out pages

The sum of an arithmetic series (in this case, the page numbers) is given by:

For the torn-out pages from 143 to 192:

  • First term (aaa) = 143
  • Last term (lll) = 192
  • Number of terms (nnn) = 50

So, the sum is:

Step 3: Analyze each option

  1. Option 1: She could have found the sum of pages as 1990.

    • To find if this is possible, subtract 1990 from the total sum of all pages (1 to 192):

    • Since the remaining sum does not match with any realistic remaining pages, this option is not possible.

  2. Option 2: She could have found the sum of pages as 1275.

    • Subtracting 1275 from the total sum: Remaining sum=18528−1275=17253
    • The sum is possible and reasonable, so this option is possible.

  3. Option 3: She could have found the sum of pages as 1375.

    • Subtracting 1375 from the total sum: Remaining sum=18528−1375=17153
    • The sum is possible and reasonable, so this option is possible.

Conclusion:

Option 1: She could have found the sum of pages as 1990 is not true because the sum 1990 cannot realistically be the sum of the pages torn out in this context.

Answer: Option 1

CAT Practice Test: Week 2 - Question 8
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There are 50 integers a1, a2,........, a50, not all of them necessarily different. Let the greatest integer of these 50 integers be referred to as G, and the smallest integer is referred to as L. The integers a1 through a24 form sequence S1, and the rest form sequence S2. Each member of S1 is less than or equal to each member of S2.
Every element of S1 is made greater than or equal to every element of S2 by adding to each element of S1 an integer x. Then, x cannot be less than:
Detailed Solution for CAT Practice Test: Week 2 - Question 8

The smallest integer of the series is 1 and greatest integer is 50. If each element of S1 is made greater of equal to every element of S2, then the smallest element 1 should be added to (50 - 1) = 49. Hence option (G-L) is the correct answer.

As this is a variable based question: the word "ANY" can be used.

Let the series of integers a1,a2,.......,a50 be 1,2,3,4,5,.......,50.

S1=1,2,3,4,.........24, S2=25,26,27,..........50.

CAT Practice Test: Week 2 - Question 9
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Srini wrote his class 10th board examination this year. When the result came out he searched for his hall ticket to see his roll number but could not trace it. He could remember only the first three digits of the 6 digit number as 267. His father, however, remembered that the number was divisible by 11. His mother gave the information that the number was also divisible by 13. They tried to recollect the number when all of a sudden Srini told that the number was a multiple of 7. What was the unit digits of the number?
Detailed Solution for CAT Practice Test: Week 2 - Question 9

His roll number is divisible by 1001 and the first three digits are 267. Hence the last three digits will also be 267.

CAT Practice Test: Week 2 - Question 10
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When 7179 and 9699 are divided by another natural number N , remainder obtained is same. How many values of N will be ending with one or more than one zeroes?
Detailed Solution for CAT Practice Test: Week 2 - Question 10

When 7179 and 9699 are divided by another natural number N, remainder obtained is same.
 Let remainder is R, then (7179 — R) and (9699 — R) are multiples of N and {(9699 — R) — (7179 — R)} is multiple of N. Then 2520 is multiple of N or the largest value of N is 2520. Total factors of N which are multiples of 10 is 18. 

CAT Practice Test: Week 2 - Question 11
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A, P, R, X, S and Z are sitting in a row. S and Z are in the centre. A and P are at the ends. R is sitting to the left of A. Who is to the right of P ?
Detailed Solution for CAT Practice Test: Week 2 - Question 11

The seating arrangement is as follows:

Therefore, right of P is X.

CAT Practice Test: Week 2 - Question 12
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Amit, Bharati, Cheryl, Deepak and Eric are five friends sitting in a restaurant. They are wearing caps of five different colors — yellow, blue, green, white and red. Also they are eating five different snacks — burgers, sandwiches, ice cream, pastries and pizza.
The person wearing a red cap is eating pastries.
Amit does not eat ice cream and Cheryl is eating sandwiches. Bharati is wearing a yellow cap and Amit is wearing a blue cap. Eric is eating pizza and is not wearing a green cap.
Who is Wearing the white cap ?
Detailed Solution for CAT Practice Test: Week 2 - Question 12

There are five people in the scenario. And each person is associated with two properties. For instance those are Colour of the caps, and the dish they are eating. Hence the tabulation method is easier to apply.


 

Hence, The properties can be tabular form as it is shows in the given information.

We know that a person wearing a red cap is eating pastries. So There is only one place possible in the table to fit this combination. Therefore the person will be Deepak.


We also know that Eric is not wearing a green cap. Hence, the one who is wearing a green cap should be Cheryl. Since Amith does not eat Ice Cream, it should be Bharati who is eating it. That leaves us with the fact that Amith should be eating burgers. As that’s the only dish left. And hence, Eric should be wearing a white cap.

CAT Practice Test: Week 2 - Question 13
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A, B, C, D and E are sitting on a bench. A is sitting next to B, C is sitting next to D, D is not sitting with E who is on the left end of the bench. C is on the second position from the right. A is to the right of B and E. A and C are sitting together. In which position A is sitting ?
Detailed Solution for CAT Practice Test: Week 2 - Question 13

Therefore, A is sitting in between B and C.

CAT Practice Test: Week 2 - Question 14
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Directions to Solve

P, Q, R, S, T, U, V and W are sitting round the circle and are facing the centre:

  1. P is second to the right of T who is the neighbour of R and V.
  2. S is not the neighbour of P.
  3. V is the neighbour of U.
  4. Q is not between S and W. W is not between U and S.

Question - Which two of the following are not neighbours ?
Detailed Solution for CAT Practice Test: Week 2 - Question 14

CAT Practice Test: Week 2 - Question 15
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Directions to Solve

P, Q, R, S, T, U, V and W are sitting round the circle and are facing the centre:

  1. P is second to the right of T who is the neighbour of R and V.
  2. S is not the neighbour of P.
  3. V is the neighbour of U.
  4. Q is not between S and W. W is not between U and S.

Question - Which one is immediate right to the V?
Detailed Solution for CAT Practice Test: Week 2 - Question 15

T is immediate right to the V.

CAT Practice Test: Week 2 - Question 16
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Directions to Solve

P, Q, R, S, T, U, V and W are sitting round the circle and are facing the centre:

  1. P is second to the right of T who is the neighbour of R and V.
  2. S is not the neighbour of P.
  3. V is the neighbour of U.
  4. Q is not between S and W. W is not between U and S.

Question - Which of the following is correct?
CAT Practice Test: Week 2 - Question 17
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Directions to Solve

P, Q, R, S, T, U, V and W are sitting round the circle and are facing the centre:

  1. P is second to the right of T who is the neighbour of R and V.
  2. S is not the neighbour of P.
  3. V is the neighbour of U.
  4. Q is not between S and W. W is not between U and S.

Question - What is the position of S?
Detailed Solution for CAT Practice Test: Week 2 - Question 17

CAT Practice Test: Week 2 - Question 18
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Directions to Solve

Five girls are sitting on a bench to be photographed. Seema is to the left of Rani and to the right of Bindu. Mary is to the right of Rani. Reeta is between Rani and Mary.

Question - Who is sitting immediate right to Reeta?
Detailed Solution for CAT Practice Test: Week 2 - Question 18

Mary is sitting immediate right to Reeta.

CAT Practice Test: Week 2 - Question 19
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Directions to Solve

Five girls are sitting on a bench to be photographed. Seema is to the left of Rani and to the right of Bindu. Mary is to the right of Rani. Reeta is between Rani and Mary.

Question - Who is in the middle of the photograph?
Detailed Solution for CAT Practice Test: Week 2 - Question 19

Rani is in the middle of the photograph.

CAT Practice Test: Week 2 - Question 20
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Directions to Solve

Five girls are sitting on a bench to be photographed. Seema is to the left of Rani and to the right of Bindu. Mary is to the right of Rani. Reeta is between Rani and Mary.

Question - Who is second from the right?
Detailed Solution for CAT Practice Test: Week 2 - Question 20

Reeta is sitting second from the right.

CAT Practice Test: Week 2 - Question 21
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Directions: Read the passage having some numbered blanks.

Ram Singh was a _____(i)____ appointed in the army. He was known for the tremendous _____(ii)____ that he had shown on the battle grounds. Crime in any form was detested by him. A person accused of a minor ____(iii)____ or involved in a small _____(iv)______ was punished by him severely. This sternness was even depicted in his _____(v)_____ with his ____(vi)_____. He did not want to _____(vii)_____ in hurting anybody, but at times his talks like his deeds were very _____(viii)_____.

Select the most suitable word from the given options and fill blank (ii).
Detailed Solution for CAT Practice Test: Week 2 - Question 21

Only valour fits here, which means boldness or determination in facing great danger, especially in a battle.

CAT Practice Test: Week 2 - Question 22
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Directions: Select the word most opposite in meaning to the given word.  

PRUDENCE
Detailed Solution for CAT Practice Test: Week 2 - Question 22

`Prudence` refers to quality or fact of being cautious, careful. `Indiscretion` is the quality of lacking prudence and judgment. Hence, (C).

CAT Practice Test: Week 2 - Question 23
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Directions: Select the word most opposite in meaning to the given word.  

WAYWARD
Detailed Solution for CAT Practice Test: Week 2 - Question 23

`Wayward` is an unpredictable, erratic person.

CAT Practice Test: Week 2 - Question 24
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Directions: Choose the word opposite in meaning to the given word.

INGENUOUS
Detailed Solution for CAT Practice Test: Week 2 - Question 24

`Ingenuous` is a guileless person; `crafty` is an overly shrewd person.

CAT Practice Test: Week 2 - Question 25
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Directions: Select the option most similar in meaning to the word in bold letters.

NINCOMPOOP
Detailed Solution for CAT Practice Test: Week 2 - Question 25

It means a fool or simpleton.

CAT Practice Test: Week 2 - Question 26
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Directions: Read the sentence with the usage of the word in bold. Pick the meaning which is synonymous to the word in bold.

Abjure : In some countries people were forced to abjure their belief in God.
Detailed Solution for CAT Practice Test: Week 2 - Question 26

‘Abjure’ means a promise, usually in public, to give up something, including a belief or opinion. ‘Renounce’ in option (B) means just the same. Hence, (B) is the answer.

CAT Practice Test: Week 2 - Question 27
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Directions: The passage given below has certain blanks here and there you have to study it carefully and fill in the blank.

The entire __(i)__ of the party gave a very __(ii)__ look. A very light music was being played at the back and people were dancing with their partners with their masks on their faces to __(iii)__ their identity. There were some at the bar corner who were __(iv)__ away to glory. Sumptuous meal was well laid at one corner of the hall. We actually had __(v)__ food with us. But when it comes to food, I am a big __(vi)__ type. By the time it was 11:30, everybody felt something of an __(vii)__ but it was __(viii)__ towards the end. Everybody’s mood was __(ix)__ by a young man, who narrated a canto from Browning’s ‘My Last Dutches’.

Select the most suitable word from the given options and fill blank (ix).
Detailed Solution for CAT Practice Test: Week 2 - Question 27

The passage talks about the party getting cheerful and lively towards the end. It was boring earlier and was enlivened or rejuvenated by a young man's narration. So, option A is the correct answer.

CAT Practice Test: Week 2 - Question 28
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Directions: Select the option closest in meaning to the italicized word.

A taciturn host:
Detailed Solution for CAT Practice Test: Week 2 - Question 28

Taciturn refers to a person who is reserved or uncommunicative in speech. Hence, option (C) is correct.

CAT Practice Test: Week 2 - Question 29
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Directions: Choose from the given alternatives the one that will be a substitute for the underlined part in the following sentence and mark the answer accordingly.

The study of the cause of diseases should be the first step in our effort to find a cure for any disease.
Detailed Solution for CAT Practice Test: Week 2 - Question 29

'Aetiology' is the science of the causes or origin of diseases. 

CAT Practice Test: Week 2 - Question 30
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Directions: Choose from the given alternatives the one that will be a substitute for the underlined part in the following sentence and mark the answer accordingly.

Scant respect for literature and arts is a tendency noticeable in contemporary industrialized societies.
Detailed Solution for CAT Practice Test: Week 2 - Question 30

`Philistinism` is being pedantry, lacking in and indifferent to cultural and aesthetic values. Such a person would not have respect for literature and arts. Hence, option (A) is the answer.

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