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NMAT Quantitative Skills MCQ Quiz - 1 - CAT MCQ


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NMAT Quantitative Skills MCQ Quiz - 1 - Question 1

Group Question

Answer the following question based on the information given below.

In an MBA entrance exam, questions are classified into two sections - Quants and Verbal. The number of questions in Quants is less than 100 while that in Verbal is not less than 75. Within each section, the questions are classified into Easy or Difficult based on the number of concepts involved. An easy question requires not more than 1 concept, while a difficult question requires 2 or more concepts to solve.Further, a question could be lengthy (atleast 3 minutes to solve) or non- lengthy (less thanl minute to solve).

Based on the following data, answer the subsequent questions.

1. The number of difficult, non-lengthy questions in Verbal is 10 less than half the number of easy, non-lengthy questions in Quants.

2. The ratio of number of easy, lengthy questions in Quants to number of difficult, lengthy questions in Verbal is 5:3.

3. The number of non-lengthy, difficult questions in Quants is 5 less than thrice the number of lengthy, easy questions in Verbal.

4. The number of lengthy questions in Verbal is 35 less than the number of easy questions in Quant.

5. The number of non-lengthy questions in Quants is 30 more than the number of difficult questions in Verbal.

6. The number of easy, non lengthy question in Verbal is thrice the number of lengthy, difficult questions in Quant.

7. Each sub-section had atleast 5 questions.

 

Q.What is the number of easy, but lengthy questions in the Verbal section?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 1

Represent Quant-lengthy-easy as Q-L-E, Verbal-non-lengthy-difficult as V-NL-D and so on.
Let Q-L-E = 5x, Q-NL-E = 2z, Q-L-D = K and V-L-E = y

V-L-D = 3x (from 2), V-NL-D = z - 10 (from 1), V-NL-E = 3K (from 6) and Q-NL-D = 3y - 5 (from 3)

Now, the questions in Quants and Verbal can be classified as easy/difficult or lengthy/non-lengthy as shown below.


The number of non-lengthy questions in Quants is 30 more than the number of difficult questions in Verbal.

2z + 3y - 5 = (3x + z — 10) + 30

3y + z - 3x = 15 ...(i)

The number of lengthy questions in Verbal section is 35 less than the number of easy questions in Quant.

y + 3x = (5x + 2z) - 35

2x - y + 2z = 35 ...(ii)

From (i) and (ii)

7y - 8x = 15

(x,y) = (6, 9) or (13, 17) or (20, 25) etc.

Corresponding value for z = 16 or 13 or 10 etc..
Since each sub-section has at least 5 qestions, the number of non-lengthy, difficult question in the verbal section
(z - 10) > 5.
> 15
z = 16
Thus, (x,y ,z) = (6, 9, 16) Also,the number of question in Quants is less than 100 while that in verbal is not less than 75.
Number o f questions in Quants = 5x + 2z + (3y - 5 ) + K = M + K < 100 

NMAT Quantitative Skills MCQ Quiz - 1 - Question 2

In an MBA entrance exam, questions are classified into two sections - Quants and Verbal. The number of questions in Quants is less than 100 while that in Verbal is not less than 75. Within each section, the questions are classified into Easy or Difficult based on the number of concepts involved. An easy question requires not more than 1 concept, while a difficult question requires 2 or more concepts to solve.Further, a question could be lengthy (atleast 3 minutes to solve) or non- lengthy (less thanl minute to solve).

Based on the following data, answer the subsequent questions.

1. The number of difficult, non-lengthy questions in Verbal is 10 less than half the number of easy, non-lengthy questions in Quants.

2. The ratio of number of easy, lengthy questions in Quants to number of difficult, lengthy questions in Verbal is 5:3.

3. The number of non-lengthy, difficult questions in Quants is 5 less than thrice the number of lengthy, easy questions in Verbal.

4. The number of lengthy questions in Verbal is 35 less than the number of easy questions in Quant.

5. The number of non-lengthy questions in Quants is 30 more than the number of difficult questions in Verbal.

6. The number of easy, non lengthy question in Verbal is thrice the number of lengthy, difficult questions in Quant.

7. Each sub-section had atleast 5 questions.

 

Q.Which sub-section has the minimum number of questions?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 2

Consider the solution to first question. Number of questions in each subsection given in the options is: Option 1: V-L-E =y = 9

Option 2: Q-NL-D = 3y - 5 = 3(9) - 5 = 22

Option 3: V-NL-E = 3K= 3(14) or 3(15) = 42 or 45

Option 4: Q-L-D = K= 14 or 15
Option 5: V-NL-D = z - 10 = 16 - 10 = 6 Hence, option 5.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 3

In an MBA entrance exam, questions are classified into two sections - Quants and Verbal. The number of questions in Quants is less than 100 while that in Verbal is not less than 75. Within each section, the questions are classified into Easy or Difficult based on the number of concepts involved. An easy question requires not more than 1 concept, while a difficult question requires 2 or more concepts to solve.Further, a question could be lengthy (atleast 3 minutes to solve) or non- lengthy (less thanl minute to solve).

Based on the following data, answer the subsequent questions.

1. The number of difficult, non-lengthy questions in Verbal is 10 less than half the number of easy, non-lengthy questions in Quants.

2. The ratio of number of easy, lengthy questions in Quants to number of difficult, lengthy questions in Verbal is 5:3.

3. The number of non-lengthy, difficult questions in Quants is 5 less than thrice the number of lengthy, easy questions in Verbal.

4. The number of lengthy questions in Verbal is 35 less than the number of easy questions in Quant.

5. The number of non-lengthy questions in Quants is 30 more than the number of difficult questions in Verbal.

6. The number of easy, non lengthy question in Verbal is thrice the number of lengthy, difficult questions in Quant.

7. Each sub-section had atleast 5 questions.

 

Q.Which among the following could be a possible value of total number of easy questions?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 3

Consider the solution to the first question.

Number of easy questions = 5x + 2z + y + 3K

(x,y,z) = (6, 9, 16)

Number of easy questions = 71 + 3K K= 14 or 15

Number of easy questions =113 or 116 Hence, option 1.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 4

In an MBA entrance exam, questions are classified into two sections - Quants and Verbal. The number of questions in Quants is less than 100 while that in Verbal is not less than 75. Within each section, the questions are classified into Easy or Difficult based on the number of concepts involved. An easy question requires not more than 1 concept, while a difficult question requires 2 or more concepts to solve.Further, a question could be lengthy (atleast 3 minutes to solve) or non- lengthy (less thanl minute to solve).

Based on the following data, answer the subsequent questions.

1. The number of difficult, non-lengthy questions in Verbal is 10 less than half the number of easy, non-lengthy questions in Quants.

2. The ratio of number of easy, lengthy questions in Quants to number of difficult, lengthy questions in Verbal is 5:3.

3. The number of non-lengthy, difficult questions in Quants is 5 less than thrice the number of lengthy, easy questions in Verbal.

4. The number of lengthy questions in Verbal is 35 less than the number of easy questions in Quant.

5. The number of non-lengthy questions in Quants is 30 more than the number of difficult questions in Verbal.

6. The number of easy, non lengthy question in Verbal is thrice the number of lengthy, difficult questions in Quant.

7. Each sub-section had atleast 5 questions.

 

Q.Find the maximum possible score of the topper, if each correct option fetches 4 marks?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 4

Consider the solution to the first question.
Total questions = 5x + 2z + K + 3 y ~ 5 + y + 3K +3 x + z - 10

= 8x + 4y + 3z + 4K - 15

(x,y,z) = (6, 9, 16)

Total questions = 8(6) + 4(9) + 3(16) + 4AT— 15 = 117 + 4K

K= 14 or 15

Maximum number of questions =117 +(4 x 15) =177

The score is maximized if the topper answers each question correctly.
Maximum score = 177 x 4 = 708 Hence, option 5.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 5

Which value of x does not satisfy

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 5

Since this is always true, x + 3 > 0 i.e. x > -3

Since this is never true, x + 3 is not less than 0.
Except for x = -4, all the other values satisfy x > -3.
Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 6

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 6


Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 7

What is the largest of three consecutive natural numbers if the cube of the first number is smaller than their product by 5, the cube of the second number is greater than their product by 2 and the square of the third number exceeds their product by 3.

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 7

The largest number cannot be 1 or 2 as is the largest of three consecutive natural numbers.
Now, consider the options.
If the largest number is 3, the numbers are 1,2 and 3. Their product is 6. It exceeds the cube of 1 by 5, is less than the cube of 2 by 2 and is less than the square of 3 by 3.
Thus 3 satisfies all the conditions.
Hence, option 1.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 8

From a block of ice cream in the shape of a cuboid of length, breadth and height as a, b, c units respectively, two scoops of ice cream are taken out and served per person. The scoop is in the shape of a hemisphere of radius R. If there is no wastage, how many people get the ice cream?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 8

Total volume of the block of ice-cream = (Volume of the hemispherical scoop) x 2 x (no. of people served)

Let x people get the ice cream.

Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 9

If Rohan was born on 29th March 1990 on Thursday, on what day on the week will his 25th birthday fall?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 9

Rohan’s 25th birthday will be on 29th March 2015.
Now, the first 2000 completed years comprise 5 sets of 400 years each. Since there are 0 odd days in 400 years, there are 0 odd days in the first 2000 years as well.
The 14 completed years from 2000 to 2014 have 3 leap years (2004, 2008 and 2012) and 11 non-leap years.
Since a non-leap year has 1 odd day and a leap year has 2 odd days,

Total odd days in these 14 years = 11(1) + 3(2) = 17 = 7(2) + 3 i.e. 3 odd days.

Total number of days in 2015 (upto 29th March) = 31 + 28 + 29 = 88 days (as 2015 is not a leap year).
Number of odd days in this period = 7(12) + 4 i.e. 4 odd days.
So, total odd days till Rohan’s birthday = 3 + 4 = 7 i.e. 0 odd days.
Hence, Rohan’s 25th birthday will fall on a Sunday.
Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 10

An Ant is at (2, 4) and wants to go to (9, 14) but in the process it has to carry food lying on the x-axis. Where should it touch the x-axis, so that it has to cover minimum distance in the entire journey?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 10

If we try to solve this problem by using distance formula, it will require a lot of calculations.
Let us approach this problem in a different way.

‘C’ is the mirror image of B(9, 14)

Now the path taken by the ant is APB, where P(x, 0).
We know that PE = PC

We can safely say that path taken by the ant is APC.
And we need to find minimum length of APC.
APC will be minimum if A, P, C lie on a same straight line,

i.e. AC = AP + PC

Equation of line AC is:  

 

 

Hence, option 4.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 11

Group Question

Answer the following question based on the information given below.

The first pie chart below shows the percentage distribution of three components the weight of a human being while the second pie chart shows the percentage distribution of protein (in terms of weight) across different body parts.

 

Q.If Zebesco, a professional wrestler, weighs 21 stone, how much of his body weight (in pounds) does not come from protein in tissue? 

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 11

 Weight of Zebesco that does not come from protein in tissue = 21 -1.638 = 19.362 stone

Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 12

The first pie chart below shows the percentage distribution of three components the weight of a human being while the second pie chart shows the percentage distribution of protein (in terms of weight) across different body parts.

 

Q.‘Other nutrients’ in the body comprises minerals, carbohydrates, fats and vitamins in the ratio 2 : 4 : 1 : 3. What is the maximum possible difference (in stone) between the weight contributed by protein in skin and fats for a gymnast weighing 52 kg?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 12

Weight contributed by protein in skin = 0.08 x 0.15 x 52 = 0.624 kg

The difference between this value and the weight contributed by fat can be maximized when fat contributes the least to ‘other nutrients’.

 Weight contributed by fat = (1/10) x 0.15 x 52 = 0.78 kg

Maximum difference = 0.78 - 0.624 = 0.156 kg = (0.156/6.3) stone ~ 0.02 stone

Hence, option 1.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 13

The first pie chart below shows the percentage distribution of three components the weight of a human being while the second pie chart shows the percentage distribution of protein (in terms of weight) across different body parts.

 

Q.Gaurav weighs 65 kg. What percentage of his body weight comes from muscles?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 13

The weight due to protein in muscles can be found. However, it is not known if water or other nutrients also contribute to muscle weight, and if so, in what proportion.
Hence, the body weight due to muscles cannot be found.
Hence, option 5.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 14

The first pie chart below shows the percentage distribution of three components the weight of a human being while the second pie chart shows the percentage distribution of protein (in terms of weight) across different body parts.

 

Q.Which of these is the heaviest component? 

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 14

1 stone > 1 kg > 1 pound

Also 1 stone =14 pounds

Convert all the weights given into a common unit, say stone.
Option 1: 52% of 15% of 13.5 stone Option 2: 40% of 15% of some amount less than 10 stone (because 10 stone  kg)

Option 3: 70% of 10.3 stone

Option 4: 30% o f some amount less than 9 stone (because 9 stone = 9 x 1 4 pounds =126 pounds)

Option 5: 23% of 15% of some amount less than 8 stone (as explained in option 4).
By observation itself, options 2, 4 and 5 will be less than option 3.
Also, option 3 is nearly 7 stone while option 1 is not even 2 stone.
Hence, the weight in option 3 is the greatest.
Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 15

Group Question

Answer the following question based on the information given below.

Cereal consumption of Maharashtra state in 000 ton

 

Q.What is the approximate ratio of the difference between the maximum and minimum monthly wheat consumption for 2011 and the difference between the maximum and minimum monthly rice consumption for 2012?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 15

Minimum monthly wheat consumption in 2011 = 15100 tons

Maximum monthly wheat consumption in 2011 = 17400 tons

Difference between the maximum and minimum wheat consumption for 2011 = 2300 tons

Minimum monthly rice consumption in 2012 = 18200 tons

Maximum monthly rice consumption in 2012 = 25500 tons

Difference between the maximum and minimum rice consumption in 2012 = 7300 tons

Hence, the required ratio = 23 : 73  1 : 3

Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 16

Answer the following question based on the information given below.

Cereal consumption of Maharashtra state in 000 ton

 

Q.Which month has highest cereal consumption in 2012?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 16

Consider the monthly cereal consumption ( in 000 tons) in 2012 for only the five months mentioned in the answer options.

 Aug = 18.1 + 13.9 + 25.5 = 57.5

Sep = 17.4 + 13.8 + 23.4 = 54.6

Oct = 17.6 + 14.3 + 24.5 = 56.4

Nov = 17.8 + 15.3 + 23.6 = 56.7

Dec = 16.1 + 15.2 + 25.1 = 56.4

Hence August has the maximum cereal consumption in 2012.
Hence, option 5.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 17

Answer the following question based on the information given below.

Cereal consumption of Maharashtra state in 000 ton

 

Q.Which of the following cases shows the maximum instances of a negative percentage change in the monthly consumption? 

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 17

A negative percentage change in the monthly consumption basically implies that the consumption in a particular month is less than the consumption in the previous month.
The number of times there is a negative percentage change for each option is:
Wheat in 2011 : 4 times - Mar, June, Sept, and Dec

Jwari in 2011 : 2 times - April and Oct Rice in 2012 : 5 times - Mar, April, Jun, Sept and Nov

Jwari in 2012 : 5 times - June, Jul, Aug, Sept and Dec

Thus, the rice consumption in 2012 as well as the jwari consumption in 2012 both show the most instances of a negative percentage change.
Hence, option 5.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 18

Answer the following question based on the information given below.

Cereal consumption of Maharashtra state in 000 ton

 

Q.What is the maximum percentage change in the rice consumption for the year 2011?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 18

Here, observe that the absolute change in the rice consumption in 2011 was less than 2000 tons for every consecutive month apart from December.
Between November and December, the rice consumption increased by 2400 tons.

It can be verified that the percentage change in all other months was less than this value.
Hence, option 1.

NMAT Quantitative Skills MCQ Quiz - 1 - Question 19

There is a field which is in the shape of a quarter circle. A cow is tied on the field such that the circle formed by its grazing is exactly inscribed in the quarter. What is the ratio of area which is grazed and that which is not?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 19

The figure is as shown below.

The cow is grazing along the circle with centre as P while the field is a quarter with centre at O. Let the smaller circle touch the bigger circle along its circumference at Z.

Now, let the radius of bigger circle be R and that of smaller circle be r.
Now, CP = DP = r

Now, if we extend line OP to meet the circle at Z, then

 

 

NMAT Quantitative Skills MCQ Quiz - 1 - Question 20

A toy is made by mounting a hemisphere of radius 7 cm over a right circular cylinder of the same radius. (Flat surface of hemisphere coincides with that of the right circular cylinder.) Height of the clinder is 10 cm. What will be the cost of painting the entire toy except the base, if the cost of painting is Rs. 14 per cm2?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 1 - Question 20

Note that we need to paint only curved surface areas of hemisphere and cylinder.
Curved Surface Area of the hemisphere = 2πr2