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CAT Practice Test: Month (January) - CAT MCQ


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30 Questions MCQ Test - CAT Practice Test: Month (January)

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CAT Practice Test: Month (January) - Question 1
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Twenty-five boxes of sweets are delivered to Mr Roy’s home. Mr Roy had ordered sweets of three different types. What is the minimum number of boxes of sweets which are having sweets of same type?

Detailed Solution for CAT Practice Test: Month (January) - Question 1

According to the question, 

Given information is, Twenty-five boxes of sweets are delivered to Mr Roy's home. Mr Roy had ordered three different types of sweets. What is the minimum number of boxes of sweets that are having sweets of same type?

Since Mr Roy has ordered for 25 boxes and there different types of sweets, minimum 9 boxes of sweets will have the same type of sweets.

Hence, the answer is 9.

CAT Practice Test: Month (January) - Question 2
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Find the remainder when 73 * 75 * 78 * 57 * 197 * 37 is divided by 34.

Detailed Solution for CAT Practice Test: Month (January) - Question 2

Remainder,
(73 * 75 * 78 * 57 * 197 * 37)/34 ===> (5 * 7 * 10 * 23 * 27 * 3)/34
[We have taken individual remainder, which means if 73 is divided by 34 individually, it will give remainder 5, 75 divided 34 gives remainder 7 and so on.]
(5 * 7 * 10 * 23 * 27 * 3)/34 ===> (35 * 30 * 23 * 27)/34 [Number Multiplied]
(35 * 30 * 23 * 27)/34 ===> (1 * -4 * -11 * -7)/34
[We have taken here negative as well as positive remainder at the same time. When 30 divided by 34 it will give either positive remainder 30 or negative remainder -4. We can use any one of negative or positive remainder at any time.]

(1 * -4 * -11 * -7)/34 ===> (28 * -11)/34 ===> (-6 * -11)/34 ===> 66/34 ===R===> 32.
Required remainder = 32.

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CAT Practice Test: Month (January) - Question 3
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Three distinct prime numbers, less than 10 are taken and all the numbers that can be formed by arranging all the digits are taken. Now, difference between the largest and the smallest number formed is equal to 495. It is also given that sum of the digits is more than 13. What is the product of the numbers?

Detailed Solution for CAT Practice Test: Month (January) - Question 3

Prime numbers less than 10 = 2, 3, 5, 7 So, option (d) cannot be the answer.
Sum of digits is more than 13 - so, set of [2, 3, 5] is not possible.
So, option (a) cannot be the answer.
Now check for options (b) and (c) by taking the values.

CAT Practice Test: Month (January) - Question 4
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What will be remainder when 1212121212... 300 times, is being divided by 99?
Detailed Solution for CAT Practice Test: Month (January) - Question 4

This number 1212121212... 300 times is divisible by 9. So, we can write 1212121212...300 times = 9 N, where N is the quotient obtained when divided by 9. Now this question is like -
1212121212... 300 times / 99 
= Remainder 9 / 9 x 134680...written 50 times / 11
[121212 = 13468 x 9]

Now we will have to find the reminder obtained when 134680134680.. . 50 times is divided by 11.
For this, we are supposed to use the divisibility rule of 11 from right hand side. [Using the divisibility rule from left hand side might give us the wrong remainder, like if we find out the remainder obtained when 12 is divided by 11, remainder = 1 = (2-1)≠(1 - 2)]
Remainder 134680...written 50 times / 11 = 2
So, the total remainder = 18

Alternatively, divisibility rule of 10" - 1, n = 2 can be used to find the remainder in this case.

 

CAT Practice Test: Month (January) - Question 5
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Which of the following would always divide a six-digit number of the form ababab?
Detailed Solution for CAT Practice Test: Month (January) - Question 5

Number = ababab

=ab×10000+ab×100+ab

=ab(10000+100+1)

=ab(10101)

CAT Practice Test: Month (January) - Question 6
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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 left in photograph?
Detailed Solution for CAT Practice Test: Month (January) - Question 6

Seema is sitting second from the left in photograph.

CAT Practice Test: Month (January) - Question 7
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Directions to Solve

Six friends are sitting in a circle and are facing the centre of the circle. Deepa is between Prakash and Pankaj. Priti is between Mukesh and Lalit. Prakash and Mukesh are opposite to each other.

Question - Who is sitting right to Prakash?
Detailed Solution for CAT Practice Test: Month (January) - Question 7

Hence, Lalit is sitting right to Prakash.

CAT Practice Test: Month (January) - Question 8
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Directions to Solve

Six friends are sitting in a circle and are facing the centre of the circle. Deepa is between Prakash and Pankaj. Priti is between Mukesh and Lalit. Prakash and Mukesh are opposite to each other.

Question - Who is just right to Pankaj?
Detailed Solution for CAT Practice Test: Month (January) - Question 8

Hence, Deepa is sitting just right to Pankaj.

CAT Practice Test: Month (January) - Question 9
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Directions to Solve

Six friends are sitting in a circle and are facing the centre of the circle. Deepa is between Prakash and Pankaj. Priti is between Mukesh and Lalit. Prakash and Mukesh are opposite to each other.

Question - Who are the neighbours of Mukesh?
Detailed Solution for CAT Practice Test: Month (January) - Question 9

Hence, Priti and Pankaj are the neighbours of Mukesh.

CAT Practice Test: Month (January) - Question 10
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Directions to Solve

Six friends are sitting in a circle and are facing the centre of the circle. Deepa is between Prakash and Pankaj. Priti is between Mukesh and Lalit. Prakash and Mukesh are opposite to each other.

Question - Who is sitting opposite to Priti?
Detailed Solution for CAT Practice Test: Month (January) - Question 10

Hence, Deepa is sitting opposite to Priti.

CAT Practice Test: Month (January) - Question 11
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Given that (m +1l)th, (n + 1)th and (r +1l)th term of an AP are in GP and m , n , r are in HP, then find the ratio of the first term of the AP to its common difference in terms of n.
Detailed Solution for CAT Practice Test: Month (January) - Question 11

Since the (m + 1)th, (n + 1)th and (r + 1)th term of an A.P are in G.P. so,

CAT Practice Test: Month (January) - Question 12
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Detailed Solution for CAT Practice Test: Month (January) - Question 12

CAT Practice Test: Month (January) - Question 13
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If a geometric mean of two non-negative numbers is equal to their harmonic mean, then which of the following is necessarily true?I. One of the numbers is zero.II. Both the numbers are equal.III. One of the numbers is one.
Detailed Solution for CAT Practice Test: Month (January) - Question 13

CAT Practice Test: Month (January) - Question 14
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A series in which any term is the sum of the preceding two terms is called a Fibonacci series. The first two terms are given initially and together they determine the entire series. If the difference of the squares of the ninth and the eighth terms of a Fibonacci series is 715 then, what is the 12th term of that series?
Detailed Solution for CAT Practice Test: Month (January) - Question 14

The series is like 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
The difference is 715 and the 12th term is 144.

CAT Practice Test: Month (January) - Question 15
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The first term of an AP = the common ratio of a GP and the first term of the GP = common difference of the AP. If the sum of the first two terms of the GP is equal to the sum of the first 2 terms of the AP, then the ratio of the first term of the GP to the first term of an AP is
Detailed Solution for CAT Practice Test: Month (January) - Question 15

This is independent of the first term of GP.

CAT Practice Test: Month (January) - Question 16
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Directions for questions: Based on the series of numbers given in the question, find the next / missing number in the series.

3, 9, 36, 180, ?
Detailed Solution for CAT Practice Test: Month (January) - Question 16

The given series follows the pattern x 3 , x 4 , x 5  and so on.
Hence last term will be 180 x 6 = 1080. 

CAT Practice Test: Month (January) - Question 17
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Directions for questions: Based on the series of numbers given in the question, find the next / missing number in the series.

100, 50, ? , 12.5, 6.25
Detailed Solution for CAT Practice Test: Month (January) - Question 17

Each term is divided by 2 to get the next term.
Hence missing term will be 50 / 2 = 25. 

CAT Practice Test: Month (January) - Question 18
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Directions for questions: Based on the series of numbers given in the question, find the next / missing number in the series.

5, 7, 11, 13, 17, ?
Detailed Solution for CAT Practice Test: Month (January) - Question 18

Here the pattern is + 2, + 4 , + 2, + 4  and so on.
Hence last term will be 17 + 2 = 19. 

CAT Practice Test: Month (January) - Question 19
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Directions for questions: Based on the series of numbers given in the question, find the next / missing number in the series.

81, 100, 121, 144, ?
Detailed Solution for CAT Practice Test: Month (January) - Question 19

The given series is set of perfect squares starting from 9.
Hence last term will be 132 = 169. 

CAT Practice Test: Month (January) - Question 20
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Directions for questions: Based on the series of numbers given in the question, find the next / missing number in the series.

99, 91, 75, 67, 51, 43, ?
Detailed Solution for CAT Practice Test: Month (January) - Question 20

The terms are formed by subtracting 8 and 16 alternately from the previous term.
Hence the required term will be (43 – 16)= 27. 

CAT Practice Test: Month (January) - Question 21
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The average of the first ten prime numbers, which are odd, is
Detailed Solution for CAT Practice Test: Month (January) - Question 21

Required average = (3 + 5 + 7 + 11 + 13 + 17 + 19
+ 23 + 29 + 31)/10 = 158/10 = 15.8.

CAT Practice Test: Month (January) - Question 22
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The average weight of 3 boys A, B and C is 74 kg. Another boy D joins the group and the average now becomes 70 kg. If another boy E, whose weight is 3 kg more than that of D, replaces A then the average weight of B, C, D and E becomes 75 kg. The weight of A is
Detailed Solution for CAT Practice Test: Month (January) - Question 22

D’s weight = 4 x 70 – 3 x 74 = 280 – 222 = 58.
E’s weight = 58 + 3 = 61.
Now, we know that A + B + C + D = 4 x 70 = 280
and B + C + D + E = 75 x 4 = 300. Hence, A’s
weight is 20 kg less than E ’s weight. A = 61 - 20
= 41 kg.

CAT Practice Test: Month (January) - Question 23
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The average of the first ten whole numbers is
Detailed Solution for CAT Practice Test: Month (January) - Question 23

Required average = (0 + 1 + 2 + … + 9)/10 = 45/10
= 4.5

CAT Practice Test: Month (January) - Question 24
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The average of the first ten odd numbers is
Detailed Solution for CAT Practice Test: Month (January) - Question 24

The sum of the first n odd numbers = n2. In this case n = 10 → Sum = 102 = 100.
Required average = 100/10 = 10.

CAT Practice Test: Month (January) - Question 25
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The average of the first ten composite numbers is
Detailed Solution for CAT Practice Test: Month (January) - Question 25

Required average = (4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18)/10 = 112/10 = 11.2.

CAT Practice Test: Month (January) - Question 26
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Directions to Solve

Each of these questions given below contains three elements. These elements may or may not have some inter linkage. Each group of elements may fit into one of these diagrams at (A), (B), (C), (D) and/or (E). You have to indicate the group of elements which correctly fits into the diagrams.

Question -

Which of the following diagrams indicates the best relation between Elephant, Carnivorous and Tiger ?
Detailed Solution for CAT Practice Test: Month (January) - Question 26

Tiger is carnivorous but Elephant is different from these two.

CAT Practice Test: Month (January) - Question 27
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Directions to Solve

Each of these questions given below contains three elements. These elements may or may not have some inter linkage. Each group of elements may fit into one of these diagrams at (A), (B), (C), (D) and/or (E). You have to indicate the group of elements which correctly fits into the diagrams.

Question -

Which of the following diagrams indicates the best relation between Furniture, Chairs and Tables ?
Detailed Solution for CAT Practice Test: Month (January) - Question 27

From above given question ,we know that
Chair is different from table, but both come under the class furniture.
From above it is clear that option ( C ) represents the best relationship between furniture, chairs and tables .As shown in venn - diagram .

CAT Practice Test: Month (January) - Question 28
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Directions to Solve

Each of these questions given below contains three elements. These elements may or may not have some inter linkage. Each group of elements may fit into one of these diagrams at (A), (B), (C), (D) and/or (E). You have to indicate the group of elements which correctly fits into the diagrams.

Question -

Which of the following diagrams indicates the best relation between Vegetables, Tomato and Fruits ?
Detailed Solution for CAT Practice Test: Month (January) - Question 28

Tomato is a fruit not a vegetable. So vegetable is different.

CAT Practice Test: Month (January) - Question 29
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Directions to Solve

Each of these questions given below contains three elements. These elements may or may not have some inter linkage. Each group of elements may fit into one of these diagrams at (A), (B), (C), (D) and/or (E). You have to indicate the group of elements which correctly fits into the diagrams.

Question -

Which of the following diagrams indicates the best relation between Class, Blackboard and School ?
Detailed Solution for CAT Practice Test: Month (January) - Question 29

Blackboard is in class and class is in the school.

CAT Practice Test: Month (January) - Question 30
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Directions to Solve

Each of these questions given below contains three elements. These elements may or may not have some inter linkage. Each group of elements may fit into one of these diagrams at (A), (B), (C), (D) and/or (E). You have to indicate the group of elements which correctly fits into the diagrams.

Question -

Which of the following diagrams indicates the best relation between Rabi-Crop, Paddy and Wheat ?
Detailed Solution for CAT Practice Test: Month (January) - Question 30

Wheat and Paddy are different from each other but Wheat is the Rabi-Crop.

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