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Practice Test for NMAT - 11 - CAT MCQ


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30 Questions MCQ Test - Practice Test for NMAT - 11

Practice Test for NMAT - 11 for CAT 2024 is part of CAT preparation. The Practice Test for NMAT - 11 questions and answers have been prepared according to the CAT exam syllabus.The Practice Test for NMAT - 11 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Practice Test for NMAT - 11 below.
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Practice Test for NMAT - 11 - Question 1
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If A = log 1 + log 2 + log 3 + .......... log n and B = log ((n - 1)!), which of the following must be true? n is a natural number.

Detailed Solution for Practice Test for NMAT - 11 - Question 1

A = log 1 + log 2 + log 3 + ..........+ log n = log (1 * 2 * 3 x 4 x ... x n) = log(n!)
B = log ((n - 1)!)
Since n is a natural number,
for any n > 1, A > B
For n = 1, A = log (1!) = log 1 and B = log (0!) = log 1
i.e. A = B
Thus, A > B
Hence, option 4.

Practice Test for NMAT - 11 - Question 2
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A dart board is made of three concentric circles such that hitting the area of the innermost circle will give 10 points, hitting the area of the second circle excluding the area of the innermost circle will give 5 points and hitting the area of the outermost circle excluding the area of the second circle will give 2 points. If in 6 shots 15 points have been earned then in how many ways could that have been done?

Detailed Solution for Practice Test for NMAT - 11 - Question 2

Number of ways of scoring 15 points:
10 + 5 + 0 + 0 + 0 + 0: 6C2 X 2! = 30 
5 + 5 + 5 + Q + 0 + 0: 6C3= 20 
2 + 2 + 2 + 2 + 2 + 5: 6C1 = 6
Total number of ways = 30 + 20 + 6 = 56
Hence, option 1.

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Practice Test for NMAT - 11 - Question 3
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G is the centroid of AABC. D and E are the mid-point of BC and AB respectively.If A(ΔAGC) - A(ΔBDG) = 6 sq.cm, what is the area of AABC (in sq.cm)?

Detailed Solution for Practice Test for NMAT - 11 - Question 3

Let A(ΔABC) = x sq.cm
Since D is the midpoint of BC, AD divides ΔABC into two triangles of equal areas.

Since G is the centroid, it divides AD in the ratio 2:1 i.e. AG : GD = 2 : 1
In ΔADC, ΔAGC and ΔDGC have the same height and their bases are in the ratio 2:1. Hence, their areas are also in the same ratio.
Similarly, in ΔADB, ΔAGB and ΔDGB have the same height and their bases are in the ratio 2:1. Hence, their areas are also in the same ratio.


A(ΔABC) = 36 sq.cm
Hence, option 3.

Practice Test for NMAT - 11 - Question 4
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A cuboid-shaped hall has marble tiles only on its floor. All the other surfaces, including the roof, are painted. The roof is supported by six pillars, each of diameter 21 cm. The length, breadth and height of the hall are 8 m, 9 m and 5 m respectively. If a painter has quoted Rs. 45 per sq.m to paint the hall again, what is the cost of painting the hall (including the roof and pillars)?
Detailed Solution for Practice Test for NMAT - 11 - Question 4

Since the floor of the hall is tiled, it is not to be painted.
∴ Total area to be painted = Area of 4 walls + Area of roof + Curved surface area of 6 pillars - Area of contact of the pillars with the roof = 2(lh + bh) + lb + 6(2πrh) - 6πr2

= 170 + 72 + 6(3.3) - 6(0.03465)
= 261.59 sq.m
∴ Cost of re-painting the hall = 261.59 * 45 = Rs. 11,771.
Hence, option 2.

Practice Test for NMAT - 11 - Question 5
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How many numbers between 101 and 1001 are divisible by 6 but not by 15?
Detailed Solution for Practice Test for NMAT - 11 - Question 5

The LCM of 6 and 15 is 30. Hence, a number divisible by 30 is also divisible by 6 and 15.
Hence, the required count = number of multiples of 6 between 101 and 1001 - number of multiples of 30 between 101 and 1001
Now, 6 x 17 = 102 and 6 x 166 = 996
∴ Number of multiples of 6 between 101 and 1001 = 166-17 + 1 =150
Similarly, 30 x 4 = 120 and 30 x 33 = 990
∴ Number of multiples of 30 between 101 and 1001 = 33 - 4 + 1 = 30
∴ Count of numbers between 101 and 1001 divisible by 6 but not by 15 = 150 - 30 = 120
Hence, option 5.

Practice Test for NMAT - 11 - Question 6
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A pipe P fills a tank in 5 hours. Due to dirt accumulating in the pipe, the rate of supplying water from the pipe reduces by 2 I/hr every 30 minutes. What percentage of the tank will be filled in 2.5 hours? The capacity of the tank is 100 I.
Detailed Solution for Practice Test for NMAT - 11 - Question 6


2.5 hours comprises 5 parts of 30 minutes each. So, the rate of filling water in each part (in I/hr) is 20, 18, 16, 14 and 12 respectively.
Hence, option 1.

Practice Test for NMAT - 11 - Question 7
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Group Question

Answer the following question based on the information given below.

Tanushree has been trying to seek admission into a good B-school by taking the Common Admissions Test for the last three years. Like past years, this year too she joined the test series of A and B coaching institutes for their mock tests, the iCATs and the eCATs respectively.
The table below gives information of Tanushree's performance in 8 iCATs and 8 eCATs of last three years. The numbers represent the number of questions attempted by her in every section for every year.
Total number of questions in all mock tests of the years 2006, 2007 and 2008 were 120, 75 and 75 respectively.

 

Q. What is the minimum total number of questions attempted by Tanushree in any iCAT or eCAT in the year 2006? 
Detailed Solution for Practice Test for NMAT - 11 - Question 7


From the table it is clear that in the year 2006 minimum total number of questions attempted by
Tanushree is 76 in eCAT 8.
Hence, option 2.

Practice Test for NMAT - 11 - Question 8
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Tanushree has been trying to seek admission into a good B-school by taking the Common Admissions Test for the last three years. Like past years, this year too she joined the test series of A and B coaching institutes for their mock tests, the iCATs and the eCATs respectively.
The table below gives information of Tanushree's performance in 8 iCATs and 8 eCATs of last three years. The numbers represent the number of questions attempted by her in every section for every year.
Total number of questions in all mock tests of the years 2006, 2007 and 2008 were 120, 75 and 75 respectively.

 

Q. In 2007, for how many tests was the number of questions attempted by Tanushree maximum?
Detailed Solution for Practice Test for NMAT - 11 - Question 8

From the table in the previous question it is clear that, maximum number of questions attempted by Tanushree in the year 2007 in iCAT 2, eCAT 7 and iCAT 8 was 54.
Hence, option 2.

Practice Test for NMAT - 11 - Question 9
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Tanushree has been trying to seek admission into a good B-school by taking the Common Admissions Test for the last three years. Like past years, this year too she joined the test series of A and B coaching institutes for their mock tests, the iCATs and the eCATs respectively.
The table below gives information of Tanushree's performance in 8 iCATs and 8 eCATs of last three years. The numbers represent the number of questions attempted by her in every section for every year.
Total number of questions in all mock tests of the years 2006, 2007 and 2008 were 120, 75 and 75 respectively.

 

Q. What is the difference in the total number of questions attempted by Tanushree in eCATs and iCATs in the year 2008?
Detailed Solution for Practice Test for NMAT - 11 - Question 9

Difference = Total number of questions attempted in the year 2008 in eCATs - Total number of questions attempted in the year 2008 in iCATs
∴ Difference = 316 - 307 = 9
Hence, option 2.

Practice Test for NMAT - 11 - Question 10
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Tanushree has been trying to seek admission into a good B-school by taking the Common Admissions Test for the last three years. Like past years, this year too she joined the test series of A and B coaching institutes for their mock tests, the iCATs and the eCATs respectively.
The table below gives information of Tanushree's performance in 8 iCATs and 8 eCATs of last three years. The numbers represent the number of questions attempted by her in every section for every year.
Total number of questions in all mock tests of the years 2006, 2007 and 2008 were 120, 75 and 75 respectively.

 

Q. For which test, the number of questions attempted by Tanushree as a percentage of total number of questions is approximately the same for all the three years?
Detailed Solution for Practice Test for NMAT - 11 - Question 10

From the table given in the solution to the first question of the set it is clear that in eCAT 4 the number of questions attempted by Tanushree as a percentage of total number of question is approximately same in all the three years i.e. 64.16%, 64% and 64%.
Hence, option 4.

Practice Test for NMAT - 11 - Question 11
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Group Question

Answer the following question based on the information given below.

The graph below shows the market value (in Rs.) of four shares at the end of each month in a period from January to June.

All values are in multiples of 5.

 

Q. Which of these sale transactions would yield the highest revenue for a person owning only these 4 shares?
Detailed Solution for Practice Test for NMAT - 11 - Question 11

The revenue in each transaction is as shown below:
Option 1: (25 x 75) + (40 x 100) = Rs. 5,875
Option 2: 70 x (40 + 50 + 50) = Rs. 9,800
Option 3: (90 x 115) + (10 x 55) = Rs. 10,900
Option 4: 25 x (50 + 55 + 70 + 95) = Rs. 6,750
Hence, option 3.

Practice Test for NMAT - 11 - Question 12
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The graph below shows the market value (in Rs.) of four shares at the end of each month in a period from January to June.

All values are in multiples of 5.

 

Q. Falguni invested Rs. 12,000 in January in the four shares in the ratio 6 : 9 : 7 : 2 and sold all these shares in May. What was her actual profit/loss (in Rs.)? Assume that she did not transact at all apart from this purchase and sale.
Detailed Solution for Practice Test for NMAT - 11 - Question 12

Amount invested in share A in Jan = (6/24) x 12000 = Rs. 3,000
Similarly, amount invested (in Rs.) in shares B, C and D respectively in Jan = 4500, 3500 and 1000
∴ Number of shares of A purchased in Jan = 3000/40 = 75
Similarly, number of shares of B, C and D respectively bought in Jan = 75, 50 and 10
∴ Falguni’s revenue in May (in Rs.) = (45 x 75) + (60 x 75) + (80 x 50) + (100 x 10) = 3375 + 4500 + 4000 + 1000 = 12875
∴ Required profit (in Rs.) = 12875 - 12000 = 875
Hence, option 1.

Practice Test for NMAT - 11 - Question 13
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The graph below shows the market value (in Rs.) of four shares at the end of each month in a period from January to June.

All values are in multiples of 5.

 

Q. Prashant earned Rs. 17,360 by selling all his shares in April. If he had only A, B, C and D in the ratio 3 : 2 : 4 : 5, what was the total number of shares that he sold? 
Detailed Solution for Practice Test for NMAT - 11 - Question 13

Let Prashant have 3x, 2x, 4x and 5x shares of A, B, C and D respectively.
∴ Prashant sold 3x + 2x + 4x + 5x = 14x shares in April
∴ Prashant’s revenue in April = 3x(40) + 2x(70) + 4x(75) + 5x(105) = 1085x = 17360 
∴ x = 16
∴ Number of shares sold by Prashant in April = 14x16 = 224
Hence, option 2

Practice Test for NMAT - 11 - Question 14
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The graph below shows the market value (in Rs.) of four shares at the end of each month in a period from January to June.

All values are in multiples of 5.

 

Q. Jay wants to sell 1 share each of C and D to buy 1 share of A at the end of a month. Which of these months would be the least profitable for Jay? 
Detailed Solution for Practice Test for NMAT - 11 - Question 14

Calculate the profit/loss for each month: Feb: 70 + 9 5 - 5 0 = 115
Mar: = 75+ 115-50 = 140
Apr: 75+ 105-40 = 140
May: 80 + 100-45 = 135
Jun: 80 + 110-45 = 145

Thus, February would be the least profitable.
Hence, option 1.

Practice Test for NMAT - 11 - Question 15
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Group Question

Answer the following question based on the information given below.

The pie charts show expenditure of two companies Hero and Honda in five different sectors - A, B, C, D and E. Study the pie charts carefully and answer the questions.



Total expenditure of Hero = Rs. 4230 crore
Total expenditure of Honda = Rs. 5640 crore

 

Q. How much is the difference between the expenditures of Honda and Hero in sector C? 
Detailed Solution for Practice Test for NMAT - 11 - Question 15

Expenditure of Hero in sector C = 23% of 4230 crore = (0.23 x 4230) crore = 972.9 crore
Expenditure of Honda in sector C = 0.17 x 5640 crore = 958.8 crore
∴ The required difference = (972.9 - 958.8) crore =14.1 crore
Hence, option 2.

Practice Test for NMAT - 11 - Question 16
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The pie charts show expenditure of two companies Hero and Honda in five different sectors - A, B, C, D and E. Study the pie charts carefully and answer the questions.



Total expenditure of Hero = Rs. 4230 crore
Total expenditure of Honda = Rs. 5640 crore

 

Q. In how many sectors the expenditure of Honda is more than that of Hero?
Detailed Solution for Practice Test for NMAT - 11 - Question 16

If we calculate the expenditures for the two companies, we get the following values (in Rs. crore).


Thus, the expenditure of Honda is more than that of Hero in sector D and sector E.
Hence, option 4.

Practice Test for NMAT - 11 - Question 17
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The pie charts show expenditure of two companies Hero and Honda in five different sectors - A, B, C, D and E. Study the pie charts carefully and answer the questions.



Total expenditure of Hero = Rs. 4230 crore
Total expenditure of Honda = Rs. 5640 crore

 

Q. Expenditure of Honda in sector A is how many percent more/less than the expenditure of Hero in sector B?
Detailed Solution for Practice Test for NMAT - 11 - Question 17

Expenditure of Honda in sector A = Rs. 620.4 crore
Expenditure of Hero in sector B = Rs. 507.6 crore

∴ Expenditure of Honda in sector A is more than the expenditure of Hero in sector B by:

Hence, option 5.

Practice Test for NMAT - 11 - Question 18
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The pie charts show expenditure of two companies Hero and Honda in five different sectors - A, B, C, D and E. Study the pie charts carefully and answer the questions.



Total expenditure of Hero = Rs. 4230 crore
Total expenditure of Honda = Rs. 5640 crore

 

Q. If the incomes of Hero and Honda were in the ratio 5 : 6 and their profits were same, then what must be the profit earned by Honda? (Note: Profit = Income - Expenditure)
Detailed Solution for Practice Test for NMAT - 11 - Question 18

Let the profits of both the companies be Rs. x crore.
Profit = Income - Expenditure
Income = Expenditure + Profit
Income of Hero = Rs. (4230 + x) crore
Income of Honda = Rs. (5640 + x) crore
The ratio of income of Hero and Honda is 5 : 6,

Solving the above equation we get x = Rs. 2820 crore
Profit earned by Honda = Rs. 2820 crore
Hence, option 1.

Practice Test for NMAT - 11 - Question 19
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If March 1,1651 was a Wednesday, then what day of the week was March 1,1752?
Detailed Solution for Practice Test for NMAT - 11 - Question 19

In 100 years, there are 5 odd days.
Therefore, March 1,1751 was a Monday.
1752 being a leap year has 29 days in February. So there are 366 days from March 1,1751 to March 1, 1752.
366 days have 2 odd days.
March 1,1752 was thus a Wednesday.
Hence, option 1.

Practice Test for NMAT - 11 - Question 20
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Two stations A and B are 920 km apart. A train T-|, which stops for 5 minutes at every town-station and for 3 minutes at every village-station started from A with a speed of 60 km/hr towards B and at the same time a train T2 with a speed of 80 km/hr which does not stop in any intermediate station started from B towards A. They met at C which is 560 km away from B. If the number of town-stations between A and C is less than the number of village-stations, then at least how many stations - town or village - are there between A and C? Assume T-| stops only at town or village-stations.
Detailed Solution for Practice Test for NMAT - 11 - Question 20

Train T2 covered 560 km with a speed of 80 kmph in 7 hours.
Train T1 covered 920 - 560 = 360 km in 7 hours. The speed of train T1 = 60 km/hr
Thus T1 traveled only for 6 hours (360/60) and it must have halted for a total of 60 minutes.
Suppose the number of town-stations are x and the number of village-stations are y and x < y, then: 5x + 3y = 60
We get three combinations of (x, y) satisfying the conditions for this equation: (3, 15), (6, 10) or (0, 20).
Thus there are at least 6 + 10 = 16 stations between A and C.
Hence, option 4.

Practice Test for NMAT - 11 - Question 21
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Which term is independent of x in the polynomial  (4x9 + 5/x7)32 ?
Detailed Solution for Practice Test for NMAT - 11 - Question 21

The (r +1)th term in the expansion of (x + y)n = nCr * xn - r * yr

For the term independent of x, the power of x must be zero
∴ 9(32 - r) - 7r = 0
r = 18
Hence, the 19th term is independent of x.
Hence, option 2.

Practice Test for NMAT - 11 - Question 22
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How many times does a typist have to press the keys of a keyboard to type the first five hundred positive integers?
Detailed Solution for Practice Test for NMAT - 11 - Question 22

The first five hundred positive integers are 1 to 500
The number of times the keys of the keyboard are pressed to type these integers is equal to the total number of digits present in the first five hundred integers.
From 1 to 9, there are 9 single-digit numbers, i.e., the keys are pressed 9 times.
From 10 to 99, there are 90 two-digit numbers, i.e., the keys are pressed 2 * 90 = 180 times.
From 100 to 500, there are 401 three-digit numbers, i.e., the keys are pressed 3 * 401 = 1203 times.
Total number of times the keys are pressed = 9 + 180 + 1203 = 1392
Hence, option 4.

Practice Test for NMAT - 11 - Question 23
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An amount, when kept at compound interest, amounts to Rs. 2,401 at the end of 6 years and Rs. 5,103 at the end of 9 years. At what rate has the amount been kept?
Detailed Solution for Practice Test for NMAT - 11 - Question 23

The amount accrued in compound interest at the end of n years is:

As per the given data,


Dividing (ii) by (i),




Hence, option 4.

Practice Test for NMAT - 11 - Question 24
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Sarah goes from P to Q in a boat and comes back to R which is exactly in between P and Q in 33 hours. The speed of the boat and the stream is 30km/hr and 20 km/hr respectively. If the river flows uniformly in one direction only, then how much time (in hours) will she take to go downstream from Q to P? 
Detailed Solution for Practice Test for NMAT - 11 - Question 24

Let the distance between P and Q be 2s km
∴ Distance between P and R = distance between Q and R = s km
Speed of the boat and the stream is 30 km/hr and 20 km/hr respectively.
∴ Speed of the boat upstream from P to Q = 30 - 20 = 10 km/hr
∴ Speed of the boat downstream from Q to R = 30 + 20 = 50 km/hr

 ∴ s = 150 km
∴  2s = 300 km

Hence, option 3.

Practice Test for NMAT - 11 - Question 25
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In how many ways can 12 apples be equally divided among 3 boys?
Detailed Solution for Practice Test for NMAT - 11 - Question 25

Since 12 apples are to be equally divided among 3 boys, each boy gets 4 apples.
The first group of 4 apples (say G1) can be selected from 12 apples in 12C4 ways
The second group of 4 apples (say G2) can be selected from the remaining 8 apples in 8C4 ways.
The remaining 4 apples automatically become the third group (say G3).
Since these are 3 groups, the number of ways in which these groups are picked = 3!

These groups can be distributed among three boys in 3! ways



Thus, 12 apples can be equally distributed among 3 boys in 34650 ways
Hence, option 2.
Alternatively,
If there are m objects that are to be equally divided among n people such that each person gets p objects,

Here, m = 12, n = 3 and p = 4

Hence, option 2.

Practice Test for NMAT - 11 - Question 26
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Group Question

Answer the following question based on the information given below.

Surveys were conducted in three years - 2003, 2004 and 2005 - to find out the likelihood of people investing in shares or real estate. Each year, exactly 500 people were surveyed and the results of the survey are given in the following table.
Persons likely to invest = persons somewhat likely to invest + persons very likely to invest
Persons unlikely to invest = persons somewhat unlikely to invest + persons very unlikely to invest
Additional Information for questions 4 and 5:
The same set of 500 persons were surveyed in each of the three given years.

 

Q. In the year 2003, at least how many of the persons surveyed are unlikely to invest in both shares and real estate?
Detailed Solution for Practice Test for NMAT - 11 - Question 26

As per the data given, the total number of persons surveyed who are unlikely to invest in shares and real estate in 2003 include those who are very unlikely and somewhat unlikely = 250 + 120 + 85 + 70 = 525
But the total number of persons surveyed = 500
∴ We are asked to find the least number of persons who are unlikely to invest in both shares and real estate we can calculate the required number of respondents = 525 - 500 = 25
Hence, option 1.

Practice Test for NMAT - 11 - Question 27
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Surveys were conducted in three years - 2003, 2004 and 2005 - to find out the likelihood of people investing in shares or real estate. Each year, exactly 500 people were surveyed and the results of the survey are given in the following table.
Persons likely to invest = persons somewhat likely to invest + persons very likely to invest
Persons unlikely to invest = persons somewhat unlikely to invest + persons very unlikely to invest
Additional Information for questions 4 and 5:
The same set of 500 persons were surveyed in each of the three given years.

 

Q. In the year 2005, what is the least number of persons surveyed who are likely to invest in shares or real estate?
Detailed Solution for Practice Test for NMAT - 11 - Question 27

Those likely to invest in shares and real estate include those who are somewhat likely and very likely.
Those who are somewhat likely to invest in real estate are 170 and those in shares are 55.
The least number of those somewhat likely to invest in shares or real estate = max(170, 55) = 170.
Similarly the least number of respondents very likely to invest in shares or real estate = max(125, 35) = 120.
The required number of respondents = 170 + 125 = 295
Hence, option 3.

Practice Test for NMAT - 11 - Question 28
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Surveys were conducted in three years - 2003, 2004 and 2005 - to find out the likelihood of people investing in shares or real estate. Each year, exactly 500 people were surveyed and the results of the survey are given in the following table.
Persons likely to invest = persons somewhat likely to invest + persons very likely to invest
Persons unlikely to invest = persons somewhat unlikely to invest + persons very unlikely to invest
Additional Information for questions 4 and 5:
The same set of 500 persons were surveyed in each of the three given years.

 

Q. In the year 2004, if of the persons surveyed, exactly 70 persons said that they were undecided to invest either in shares or in real estate, what percentage of the total number of persons surveyed were undecided to invest both in shares and in real estate?
Detailed Solution for Practice Test for NMAT - 11 - Question 28

In 2004, number of persons undecided to invest in shares and real estate are respectively 60 and 25. Those who are undecided to invest either in shares or real estate is 70.
Number of respondents who were undecided to invest in shares and real estate = (60 + 25) - 70 = 15
The required percentage = (15/500) * 100 = 3%
Hence, option 4.

Practice Test for NMAT - 11 - Question 29
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Surveys were conducted in three years - 2003, 2004 and 2005 - to find out the likelihood of people investing in shares or real estate. Each year, exactly 500 people were surveyed and the results of the survey are given in the following table.
Persons likely to invest = persons somewhat likely to invest + persons very likely to invest
Persons unlikely to invest = persons somewhat unlikely to invest + persons very unlikely to invest
Additional Information for questions 4 and 5:
The same set of 500 persons were surveyed in each of the three given years.

 

Q. If the same set of 500 people were surveyed in all three years, the number of persons who responded with the same likelihood of investment in real estate in 2004 and 2005 is at most
Detailed Solution for Practice Test for NMAT - 11 - Question 29

Solution: In the year 2004, 90 were very unlikely to invest in real estate and in 2005 their number is 105. At the most, of these, 90 persons could have responded with the same likelihood.
In this way the maximum number of persons responding in the same likelihood of investment in real estate = 90 + 40 + 25 + 170 + 105 + 25 = 455
Hence, option 4.

Practice Test for NMAT - 11 - Question 30
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Group Question

Answer the following question based on the information given below.

The table below provides data about the expenditure (in lakhs) of two manufacturing companies, ABBA and BAAB for the years 2000 and 2001.

 

Q. By how many percentage points is the percentage decrease in raw material cost in 2001 compared to that in 2000, for ABBA less than that for BAAB.
Detailed Solution for Practice Test for NMAT - 11 - Question 30

Percentage decrease in raw material cost of ABBA = [(615 - 390)/615] * 100 36.6% Percentage decrease in raw material cost of BAAB = [(16278 - 6009)/16278] * 100 63%
The percentage point difference = 63 - 36.6 = 26.4% 26.5%
Hence, option 4.

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