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NMAT Quantitative Skills MCQ Quiz - 2


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NMAT Quantitative Skills MCQ Quiz - 2 - Question 1

In a race o f ‘x ’ m etres, R eem a beats Seem a and H ina b y 15 m and 1 8 m respectively. If in the same race, Seema beats Hina by 5 m, then find ‘x ’ (in m). 

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

L et the speed o f R eem a, Seem a and H in a be R, S and H respectively .
When Reemac overs xm , See ma and Hin acover (x -15) m and (x - 18) m .
As speed is directly proportional to distance,

When See m a covers x m , the n H in acover s (x -5) m .

From (i) and (ii),

(x - 15) (x - 5) = x (x - 18)

x2 - 20x + 75 = x2 - 18x
2x = 75

∴  x = 37.5 m

Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 2

Which of the following is the highest number that divides 1406, 974 and 638 leaving the same remainder in each case?

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

We need to find the highest number n, such that it divides 1406, 974 and 638 and leaves the same remainder.
If two numbers have the same remainder, then the difference of the two numbers will also be divisible by n.
In order to find out the highest number which leaves the same remainder we have to take the HCF of differences between the numbers (taken two at a time) as follows:

1406-974 = 432

974-638 = 336

1406-638 = 768

HCF of 432, 336 and 768 is 48.

Hence, option 1.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 3

For S = 1, 3, 6, 10, 15....... , which o f these is a valid expression for Tn ?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 3

Instead of creating an expression for Tn, consider a random value of n, and check the options. Identify the option that gives the same value of Tn as the terms of the given series.

n =1 implies T1 i.e. the first term.

For n = 1, T= 1 (from the series)

Options 1 and 2 can directly eliminated as they have a term (n - 1) which will make the entire expression 0 for n = 1 For option 3: n(n + l)/2 = (1 x 2)12 = 1 Hence, this may be a valid expression.

Observe that the expression in option 4 is twice the expression in option 3. Since option 3 matches the required value for T1, option 4 will not match.

Hence, option 4 can be eliminated.

Since there is an option for ‘None of the above’, check option 3 for other values of n.
For n = 2,

For n = 3

and so on.
Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 4

Group Question
Answer the following question based on the information given below. 50 players have been surveyed from a college. Their partially collected data is as shown below:

Q.

If the number of players who do not play any game is 40% of the number of players who play exactly two games, how many players play basketball?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 4

There are 50 players in all.

∴ People who play no game + People who play 1 game + People who play 2 games +

People who play 3 games = 50 Let the number of people who play exactly 2 games be x.

∴  0.4x + (12 + 11 + 10) + x + 3 = 50

∴ 1.4x + 36 = 50

∴  x = 10

Out of the 10 people who play exactly two games, 4 play cricket and tennis only.
Hence, the remaining 6 play basketball.

∴  Number of people who play basketball = 12 + 6 + 3 = 21
Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 5

Group Question
Answer the following question based on the information given below. 50 players have been surveyed from a college. Their partially collected data is as shown below:

Q.

If 21 players play basketball, what is the maximum number of people who  play cricket?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 5

The values currently given in the Venn diagram add up to 40.

Let the number of people who don’t play any game be n.

Since 21 players play basketball,

21 + l l + 4 + 1 0 + n = 50

∴ n = 4

So, there are 6 players who, in total, play basketball and cricket only or tennis and basketball only.

Since the number of cricket players is to be maximized, all 6 players can be assigned to the set who play basketball and cricket only.

∴ Maximum number o f cricket players = 1 1 + 4 + 3 + 6 = 24

Hence, option 1.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 6

Group Question
Answer the following question based on the information given below.
The following graph gives the sales revenue of five companies in the years from 2000 to 2004.

Q.

The maximum absolute decrease in the sales revenue of CD occurred between which of the following years?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 6

Note that the absolute decrease and not the percentage decrease is required.

The sales revenue for CD has decreased only twice, i.e. between 2001 and 2002 and between 2002 and 2003. Also, the sales revenue for CD in 2004 is more than the sales revenue in 2001.

Hence, options 1, 3 and 4 can be eliminated.
From the year 2001 to 2002, absolute decrease registered for CD = 7 5 - 5 0 = 25

From 2002 to 2003, the absolute decrease = 50 - 0 = 50

∴ The absolute decrease in sales value of CD is maximum from 2002 to 2003.
Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 7

Group Question
Answer the following question based on the information given below.
The following graph gives the sales revenue of five companies in the years from 2000 to 2004.

Q.

The absolute difference between the sales revenue of GH and IJ was the least in the year

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 7

The absolute difference between the sales revenue of GH and IJ for each year is given below.

For 2000= 100-50 = 50

For 2001 = 125-75 = 50

For 2002= 100-100 = 0

For 2003 = 125-75 = 50

For 2004 = 100 - 75 = 25

∴ The absolute difference between the sales revenue of GH and IJ was the least in the year 2002.
Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 8

Group Question
Answer the following question based on the information given below.
The following graph gives the sales revenue of five companies in the years from 2000 to 2004.

Q.

In which of the following years was the ratio of the sales revenue of GH to 3 that of EF the maximum?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 8

The ratio of the sales revenue of GH to that of EF for each year is shown below.

For 2000: 100/25 = 4 

For 2001 : 125/50 = 2.5 

For 2002: 100/75= 1.33 

For 2003 : 75/50= 1.5

For 2004 : 75/75 = 1

∴ The ratio of the sales revenue of GH to that of EF was maximum in the year 2000.
Hence, option 1.

Note: This question can be answered by direct observation as well. It is evident from the bar chart that the ratio is the highest in 2000.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 9

Group Question
Answer the following question based on the information given below.
The following graph gives the sales revenue of five companies in the years from 2000 to 2004.

Q.

What is the average sales turnover, in lakhs of rupees per year, for company AB?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 9

Average sales turnover per year for company AB = (75+75 + 125 + 75 + 125)/5 = 95 lakhs

Hence, option 5.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 10

Group Question
Answer the following question based on the information given below.
The following graph gives the sales revenue of five companies in the years from 2000 to 2004.

Q.

What is th elength of the tan g en t draw n from origin (0, 0) to the circle 3x2 + 3y2+9 x + 4y + 6 = 0?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 10

Theequationofthecirclecanbewrittenas:

Expressitas(x-a)2+(y-b)2=r2where(a,b)aretheco-ordinatesofthecentreandristheradiusofthecircle.

So,co—ordinatesofthecentreare 

andlengthoftheradiusis 5/6

LetthetangentbedrawnfrompointP.

Distance between P and centre of circle (d)=

The tangent, radius and circle can be drawn as shown below:

Using Pythagoras theorem:

Hence, option 1.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 11

In the above figure, AB is the diameter and CD is parallel to AB. Also BC = AD = 2. AB = 8. What is the length of CD?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 11

From the figure, O is the center of a circle and CE is perpendicular to OB. 
Let EB = x

∴ OE = 4 - x

Applying Pythagoras theorem to ΔOCE, we get,

Applying Pythagoras theorem to ΔCEB, we get,

But CD = AB - 2x = 8 -1 = 7

Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 12

Anokhi and Bihari appeared for an examination. The probability that Anokhi will qualify the examination is 0.06 and that Bihari will qualify the examination is 0.09. The probability that both will qualify the examination is 0.03. What is the probability that both Anokhi and Bihari will not qualify the examination?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 12

Let A and B denote the events that Anokhi and Bihari will qualify the examination respectively.

Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 13

A number lies between the cubes of 15 and 16. If the number is divisible by 7 as well as the square of 12, what is the number?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 13

122 x 7 = 1 4 4 x 7 = 1008

Since the required number is divisible by 144 and 7, it has to be a multiple of 1008 i.e. 1008, 2016, 3024, 4032, 5040 etc

Among the four numbers given, only 4032 satisfies this condition.

Also, 153 = 3375 and 163 = 4096

3375 < 4032 < 4096 

Hence, option 2.

Alternatively,
Since 122 = 144 = 16 x 9, the required number also has to be divisible by 9.

For a number to be divisible by 9, sum of its digits = multiple of 9

Observe that 3468 and 3864 will have same sum of digits. 3 + 4 + 6 + 8 = 21; 4 + 0 + 4 + 6 = 14 and4 + 0 + 3 + 2 = 9

Hence, 3468, 3864 and 4046 cannot be divisible by 9; and hence cannot be divisible by 144.

Hence, options 1, 3 and 4 can be eliminated. 4032 is divisible by 9 and hence, may be divisible by 144. 4032/9 = 448

Since 144 = 16 x 9, check if 448 is divisible by 16. 448/16 = 28

Thus, 4032 is divisible by 144.

Also, 4032/7 = 576

Thus, 4032 is divisible by 7.

Finally, 153 = 3375 and 163 = 4096

3375 < 4032 < 4096 
Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 14

Each question is followed by two quantities, A and B. Answer each question using the following instructions: Mark (1) if quantity A is greater than quantity B.
Mark (2) if quantity B is greater than quantity A.
Mark (3) if the two quantities are equal.
Mark (4) if it is impossible to determine a relationship.

Mark (5) if the greater quantity cannot be determined but the two quantities are definitely not equal.

 to infinity.

 to infinity.

For S1 and S2, x 1 and 0 < x < 1.
A. S1
B. S2

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 14

 to infinity.

S1 is in G.P.
Here, a = x and r = x2

S2 is also in G.P.
Here, a = x2 and r = x2

Now, x 1.
For an infinite G.P., x < 1. When x < 1,S2 < S1 Thus, quantity A is greater than quantity B.
Hence, option 1.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 15

Each question is followed by two statements, I and II. Answer each question 3 using the following instructions:

Mark (1) if the question can be answered by using statement I alone but not by using statement II alone.
Mark (2) if the question can be answered by using statement II alone but not by using statement I alone.
Mark (3) if the question can be answered by using either of the statements alone.
Mark (4) if the question can be answered by using both the statements together but not by either of the statements alone.
Mark (5) if the question cannot be answered by using any of the statements.

Is x > y l

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 15

Using Statement I alone: |x| > [y|

Case 1: If x > y, then definitely |x| > |y|

Case 2: I f x < y , it is still possible to have |x| > |y| e.g. If, x = -5 and y = 3 Here,

x < y

However, |—5| > |3| i.e. |x| > |y|

Thus, the exact relationship between x andy can not be found.
Thus, the question cannot be answered using statement I alone.
Using Statement II alone: W=T

In this case, either x andy are equal in sign or opposite in sign, but equal in magnitude.

∴ x≤y Thus, x can never be greater than y.

Thus, the question can be answered using statement II alone.
Thus, the question can be answered using statement II alone but not by using statement I alone.
Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 16

Each question is followed by two statements, A and B. Answer each question using the following instructions:

Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.
Mark option (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark option (3) if the question can be answered by using either statement alone.
Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.
Mark option (5) if the question cannot be answered on the basis of the two statements.
Is 2x = y?

A.

B. (2x - 9)2 = (y - 9)

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 16

Hence, (2x + y)2 = &xy Thus, (2x - y)2 = 0 Or 2x = y
Hence statement A alone is sufficient to answer the question.

Consider statement B alone: (2x - 9)2 = (y - 9)2 Thus, 2x — 9 = y —9 or 2 x - 9 = 9 -y Hence, 2x = y or 2x = 18 -y Hence, no definite conclusion is possible.
Hence, we cannot answer the question using statement B alone.
Hence, option 1.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 17

Each question is followed by two statements, I and II. Answer each question  using the following instructions: 

Mark (1) if the question can be answered by using statement I alone but not by using statement II alone.
Mark (2) if the question can be answered by using statement II alone but not by using statement I alone.
Mark (3) if the question can be answered by using either of the statements alone.
Mark (4) if the question can be answered by using both the statements together but not by either of the statements alone.
Mark (5) if the question cannot be answered by using any of the statements. Which direction was Qarim facing initially?

I. Qarim has turned by 90° in the anticlockwise direction 1983862989 number of times.
II. Qarim was facing North after 127839th turn.

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 17

Using statement I alone:
We cannot conclude anything about Qarim as we do not know the direction he is facing.

Thus, statement I alone is not sufficient to answer the question.

Using statement II alone:
We know the number of times Qarim turned and his present direction.
But we don't know the angle at which he is turning.
Thus, statement II alone is not sufficient to answer the question.

Using statement I and II both:
We get the angle at which he is turning also the direction in which he is turning from statement I and his direction at 127839th turn.
As he is facing north after 127839.
After 4 turns in any direction, we will face the same direction as that of the initial.

So, 127839/4 , we get remainder as 3.
He is facing north after 3 anticlockwise turns.
∴ He is facing east initially.
Hence, both statements I and II are necessary to answer.
Hence, option 4.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 18

Each question is followed by two statements, A and B. Answer each question using the following instructions:

Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.
Mark option (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark option (3) if the question can be answered by using either statement alone.
Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.
Mark option (5) if the question cannot be answered on the basis of the two statements.

The marked price of a shirt is Rs. 900. What is the discount offered on it?

A. The marked price is 20% more than the cost price and the amount of discount offered on the shirt is same as the profit.
B. The cost price is Rs. 750 and the percentage discount is equal to the profit percent.

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 18

Marked price of the shirt (i.e.M.R) = Rs. 900 Using statement A alone:

M.R is 20% more than the cost price (C.R)

∴ C. P. = 900/1.2 = Rs. 750

Since the profit and amount of discount is the same, let profit = discount = Rs. x.

Selling price (S.R) = C.R + profit = M.P. - discount 

 ∴ 750 + x = 900 - x

∴ x = Rs. 75

Thus, the discount offered is Rs. 75
Thus, the question can be answered using statement A alone.

Using statement B alone:

Cost price (C.P.) = Rs. 750

Since the discount percent and profit percent are equal, let them be x%.

i.e.

Solving the above equation, x = 100/11

Since this discount percent is calculated on the marked price, the actual discount can be found.

Thus, the question can be answered using statement B alone.

Thus, the question can be answered using either statement alone.

Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 19

Each question is followed by two statements, A and B. Answer each 3 question using the following instructions:

Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.
Mark option (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark option (3) if the question can be answered by using either statement alone.
Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.
Mark option (5) if the question cannot be answered on the basis of the two statements.
What will be the average of the ages of Amar and Aditya 16 years from now?

A. The ratio of the present ages of Amar and Aditya is 3 : 7.
B. The ratio of the ages of Amar and Aditya will be 1 : 2 two years from now.

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 19

Using statement A alone:

Let the present age of Amar and Aditya be 3x and lx years respectively.
Their age after 16 years will be 3x + 16 and lx + 16 respectively.
So, the average of their ages will be 5x + 16.
However, this can take multiple values based on the value of x.
Thus, the question cannot be answered using statement A alone.

Using statement B alone:

Let the age of Amar and Aditya be x and 2x, 2 years from now.
So, their ages after 16 years will be x + 14 and 2x + 14.
So, the average of their ages will be 1.5x + 14.

However, this can take multiple values based on the value of x.
Thus, the question cannot be answered using statement B alone.

Using statements A and B together:

The present ages of Amar and Aditya will be 3x and lx respectively. After two years,

∴ x = 2
So, their present ages are 6 years and 14 years.
Once their present age is known, their age after 16 years can be found and so, the average can be found.
Thus, the question can be answered using both statements together but not by using either statement alone.

Hence, option 4.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 20

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 20

Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 21

A tank is installed on the terrace of the B wing of Pyramid Business Park. Two pipes are connected to the tank. Pipe A fills the tank with BMC water while pipe B supplies water to the main tap in wing B. At any given instant, only one of these pipes is kept open. Pipe A can completely fill the empty tank in 10 hours. However, both pipes were once opened simultaneously, and the empty tank was fully filled for the first time after 12 hours. In how much time can Pipe B empty half the fully-filled tank?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 21

Let the volume of the tank be 120 units (i.e. the LCM of 10 and 12).

∴ Pipe A fills = 120/10 = 12 litres per hour Similarly, pipes A and E together fill = 120/12= 10 litres per hour

A and B fill less water per hour than A alone as B removes water.

∴ B empties 12-10 = 2 litres per hour

∴  Time taken by B to empty half the tank = = 3 0 hours

Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 22

Group Question

Answer the following question based on the information given below.
The table below gives the comparison of five models of washing machines manufactured by two companies A and B. The comparisons are made on the basis of manufacturing costs, sales and percentage markup. The percentage growth in sales by value over last year is also provided.
The selling price of each model is obtained by marking up the total manufacturing cost by the percentage markup.

Q.

Which of the following models of company B yields the maximum profit per unit?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 22

Profit = Manufacturing cost x Mark up percentage

∴ Profit on one unit of Model 1 produced by company B

Calculating similarly for all the models we have,

∴ The maximum profit is on Model 5.
Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 23

Group Question

Answer the following question based on the information given below.
The table below gives the comparison of five models of washing machines manufactured by two companies A and B. The comparisons are made on the basis of manufacturing costs, sales and percentage markup. The percentage growth in sales by value over last year is also provided.
The selling price of each model is obtained by marking up the total manufacturing cost by the percentage markup.

Q.

Which of the following models of company B is sold at the least price?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 23

The selling price of each unit of any model =

Comparing the models and the price per unit, we have

In the above models, Model 2 is sold at the least price.
Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 24

Group Question

Answer the following question based on the information given below.
The table below gives the comparison of five models of washing machines manufactured by two companies A and B. The comparisons are made on the basis of manufacturing costs, sales and percentage markup. The percentage growth in sales by value over last year is also provided.
The selling price of each model is obtained by marking up the total manufacturing cost by the percentage markup.

Q.

Which of the following models of company A has the least fabrication cost per unit manufactured? 

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 24

Fabrication cost per unit manufactured = Fabrication cost as percentage of manufacturing cost x Cost price per unit

Model 5 of company A has the least fabrication cost.

Hence, option 1.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 25

Group Question

Answer the following question based on the information given below.
The table below gives the comparison of five models of washing machines manufactured by two companies A and B. The comparisons are made on the basis of manufacturing costs, sales and percentage markup. The percentage growth in sales by value over last year is also provided.
The selling price of each model is obtained by marking up the total manufacturing cost by the percentage markup.

Q.

Which of the following models of company B consumes the maximum cost in ‘Sub-assemblies’ by value?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 25

In company B, to find the model that consumes the most ‘sub-assemblies’ cost, let the total sales be 100.

The cost for Model 1 = 0.30 x 0.15 x 100 =4.5

The cost for Model 2 = 0.10 x 0.15 x 100 = 1.5

The cost for Model 3 = 0.25 x 0.25 x 100 = 6.25

The cost for Model 4 = 0.20 x 0.30 x 100 = 6

The cost for Model5  = 0.15 x 0.40 x 100 =6

∴ Model 3 consumes the maximum cost in ‘Sub-assemblies’ by value.
Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 26

Group Question

Answer the following question based on the information given below.
The table below gives the comparison of five models of washing machines manufactured by two companies A and B. The comparisons are made on the basis of manufacturing costs, sales and percentage markup. The percentage growth in sales by value over last year is also provided.
The selling price of each model is obtained by marking up the total manufacturing cost by the percentage markup.

Q.

On a certain sum, the ratio of the compound interest for the 19th year to the compound interest for the 20th year is 4 : 5. At what rate of compound interest is the amount placed?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 26

Consider an amount P placed at a compound interest at r% per annum.

∴ Amount at the end of 2 years = 

∴ Compound interest for second year =

Now, the amount at the end of 2 years becomes the principal for the third year.

∴ Amount at the end of 3 years = 

∴ Compound interest for third year =

∴ Compound interest for third year = Compound interest for second year X

In general,
Compound interest for (n + 1 )th year = Compound interest for nth year X 

∴ 500 = 400 + 4r

∴ r = 25
So, the amount is placed at 25% compound interest.
Hence, option 1.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 27

I f the roots o f the equation x 2 - 4ax + 4a2 - 4a + 8 are real and less than 5, what is the range of values for a?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 27

Since the roots are real, b2 - 4ac > 0

∴ (4a)2 -4(4a 2 - 4a + S ) >0

∴ 16a - 32 > 0

∴ a > 2 .........(I)

Now, let the roots be p and q.
Hence, the equation can be written as (x - p) (x - q).
For f(5),x = 5 Since both the roots are less than 5 , x > p and x > q when x = 5 Hence, f(5) is the product of two positive numbers and is, therefore, positive.

Hence, option 1

NMAT Quantitative Skills MCQ Quiz - 2 - Question 28

A triangle ABC has integral sides in the ratio 1 : 2.4 : 2.6. If the area of the triangle is 1080 sq.cm, what is its perimeter (in cm)?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 28

Since the triangle has integral sides, convert the given ratio to an integral form by multiplying it by 5 (or 10).

Hence, ratio o f sides = ( 1 x 5 ) : (2.4 x 5 ) : (2.6 x 5) = 5 : 12 : 13 Any triangle with ratio of sides as 5 : 12 : 13 is a right triangle.

So, if the sides (in cm) are 5x, 12x and 13x respectively, 5x and 12x become the base and height (in any order).

Since the area of the triangle is 1080 sq.cm,

∴ 3Ox2 = 1080

∴ x2 = 36

∴ x = 6

Thus, the perimeter = 5x + 12x + 13x = 3Ox = 180 cm

Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 29

If a dictionary only contains the alphabets of the word DANG, at what position will the word NAGD be in this dictionary?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 29

In a dictionary, words are arranged in the alphabetical order.

If A is the 1st letter, the remaining 3 places can be filled in 3! ways by the letters D, N and G.

Similarly, the number of words with D as the 1st letter is 3! and the number of words with G as the 1st letter is 3!

Now, when N is the 1st letter, the sequence of words is:

NADG
NAGD
.........
.........
..........

Hence, the position of the word NAGD = 3! + 3! + 3!+2
= 6 + 6 + 6 + 2
= 20

Thus, the word NAGD is at the 20th position in this dictionary.
Hence, option 4.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 30

Answer the following question based on the information given below.
A food company manufactures 4 products - P, Q, R, and S. Based on their quality, they are graded A, B, C or D every year with A denoting the best quality and D the worst. If the intial grade of any product is A, the selling price of product P, Q, R and S is Rs. 100, Rs. 120, Rs. 140 and Rs. 150 respectively. However, if a product has some other grade in 2001, then the selling price increases by 10% for every increase in grade. Also with every decrease in grade of quality, the selling price reduces by 10%. Each year, 100 pieces of each product are sold.The table below shows some of the grades obtained from 2001 to 2004.

Also
• No two products have the same grade in the year 2001
• Q and R have got the A grade exactly once whereas S and P have achieved this twice.
• All products, except Q, have seen their grade fall to D at least once.
• Grade B is present five times in the table.

Q.

If the company earns Rs. 42758.28 in all by selling only product Q for all 3 4 years, what grade did product Q get in 2001?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 30

Q and R cannot get grade A in 2001 as no grade is repeated in 2001. Also, since Q and R got grade A exactly once, Q got it in 2003 while R got it in 2004.

S got grade A twice, one of which was in 2003. Since S also could not have grade A in 2001 (as explained for Q and R), S got its second grade A in 2002. Also, each product saw its grade fall to D atleast once. Hence, S would have got grade D in 2001.

Since no grade was repeated in 2001, Q and R would have got grades B and C (in no specific order).

Finally, P would have got grade B in 2002 (as there are 5 grade Bs in the whole table).

Thus, the filled-in table is as shown below.

Each year, 100 units of each product and the selling price of a product increases/decreases by 10% with every increase/decrease in grade.

Case 1: Q got grade B in 2001

Hence, Q’s grades are B, B, A, B

∴ Total earnings = 100 x [(120 x 0.9) + (120 x 0.9) + (120 x 0.9 x 1.1) + (120 x 0.9 x 1.1 x 0.9)

= 100 x (108 + 108 + 118.8 + 106.92)

= Rs. 44,172

This is not possible as the total earnings from Q were Rs. 42,758.28 over the period.
Hence, Q got grade C in 2001.
Hence, option 3.

Note: You need not calculate the earnings for grade C, but if verify, you will get the given value.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 31

Answer the following question based on the information given below.
A food company manufactures 4 products - P, Q, R, and S. Based on their quality, they are graded A, B, C or D every year with A denoting the best quality and D the worst. If the intial grade of any product is A, the selling price of product P, Q, R and S is Rs. 100, Rs. 120, Rs. 140 and Rs. 150 respectively. However, if a product has some other grade in 2001, then the selling price increases by 10% for every increase in grade. Also with every decrease in grade of quality, the selling price reduces by 10%. Each year, 100 pieces of each product are sold.The table below shows some of the grades obtained from 2001 to 2004.

Also
• No two products have the same grade in the year 2001
• Q and R have got the A grade exactly once whereas S and P have achieved this twice.
• All products, except Q, have seen their grade fall to D at least once.
• Grade B is present five times in the table.

Q.

Assuming the data from the first question, how many products yield more 3 than Rs. 45,000 to the company?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 31

Consider the solution to the first question.
Q has grade C and overall earnings through Q = Rs. 42758.28 i.e. less than Rs. 45,000.

Consider the other products.

P = 100 x [100 + (100 x 0.9) + (100 x 0.9 x 0.9 x 0.9) + (100 x 0.9 x 0.9 x 0.9 x 1.1 x 1.1 x U ) ]

100 x (100 + 90 + 72.9 + 97.03)

= Rs. 35,993 i.e. less than Rs. 45,000.
R = 100 x [(140 x 0.9) + (140 x 0.9 x 0.9) + (140 x 0.9 x 0.9 x 0.9) + (140 x 0.9 x 0.9 x 0.9 x 1.1 x 1.1 x 1.1)]
= 100 x (126 + 113.4 + 102.06 + 135.84)
= Rs. 477,30 i.e. more than Rs. 45,000.
S = 100 x [(150 x 0.9 x 0.9 x 0.9) + 2(150 x 0.9 x 0.9 x 0.9 x 1.1 x 1.1 x 1.1) + (150 x 0.9 x 0.9 x 0.9 x 1.1 x l.i x l.i x 0.9)]
= 100 x (109.35 + 291.09 + 130.99)
= Rs. 53,143 i.e. more than Rs. 45,000
Thus, two products (R and S) yield revenues more than Rs. 45,000.
Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 32

Answer the following question based on the information given below.
A food company manufactures 4 products - P, Q, R, and S. Based on their quality, they are graded A, B, C or D every year with A denoting the best quality and D the worst. If the intial grade of any product is A, the selling price of product P, Q, R and S is Rs. 100, Rs. 120, Rs. 140 and Rs. 150 respectively. However, if a product has some other grade in 2001, then the selling price increases by 10% for every increase in grade. Also with every decrease in grade of quality, the selling price reduces by 10%. Each year, 100 pieces of each product are sold.The table below shows some of the grades obtained from 2001 to 2004.

Also
• No two products have the same grade in the year 2001
• Q and R have got the A grade exactly once whereas S and P have achieved this twice.
• All products, except Q, have seen their grade fall to D at least once.
• Grade B is present five times in the table.

Q.

If Q got grade C in 2001, which product saw the maximum decrease in price from 2001 to 2002?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 32

Q and S can be directly eliminated as their price increases from 2001 to 2002.

The change in price of P and R is as shown below.

P: 100 to 90 i.e. decrease of Rs. 10

R: (140 x 0.9) to (140 x 0.9 x 0.9) i.e. decrease of Rs. 12.6

Hence, R saw the maximum decrease.
Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 33

Answer the following question based on the information given below.
A food company manufactures 4 products - P, Q, R, and S. Based on their quality, they are graded A, B, C or D every year with A denoting the best quality and D the worst. If the intial grade of any product is A, the selling price of product P, Q, R and S is Rs. 100, Rs. 120, Rs. 140 and Rs. 150 respectively. However, if a product has some other grade in 2001, then the selling price increases by 10% for every increase in grade. Also with every decrease in grade of quality, the selling price reduces by 10%. Each year, 100 pieces of each product are sold.The table below shows some of the grades obtained from 2001 to 2004.

Also
• No two products have the same grade in the year 2001
• Q and R have got the A grade exactly once whereas S and P have achieved this twice.
• All products, except Q, have seen their grade fall to D at least once.
• Grade B is present five times in the table.

Q.

If in 2005, the grades of all products increase by one compared to 2004, how many products have the same grade in 2005?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 33

If each product’s grade increases by one from 2004 to 2005, all products have grade A in 2005.
Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 34

Answer the following question based on the information given below.
The table below shows the month-wise breakup of the amount of fish (in tonnes) arriving at Sassoon Docks from different sources in a particular year. Fish is imported only in months when the demand is not met through these sources.

The table below shows the yield/boat (in kg) for each source for a few months.

Q.

Which of the following statements is correct?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 34

Note that the statements in options 3 and 4 can be verified directly by observation compared to the ones in options 1 and 2 (which require some calculation).

Start with option 3, as it is the most direct of the lot.

AP has supplied more than Guj exactly 7 times (Jan, Feb, Apr, May, Jun, Aug, Sep)

Thus, the statement in option 3 is true.
Hence, option 3.

Note: You need not check the other options but you can verify that they are false).

NMAT Quantitative Skills MCQ Quiz - 2 - Question 35

Answer the following question based on the information given below.
The table below shows the month-wise breakup of the amount of fish (in tonnes) arriving at Sassoon Docks from different sources in a particular year. Fish is imported only in months when the demand is not met through these sources.

The table below shows the yield/boat (in kg) for each source for a few months.

Q.

For how many months does supply exceed demand?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 35

Whenever imports are zero, supply ≥ demand.
This happens only in Jan and Apr.
However, even in these months, there is a possibility that supply = demand
Hence, the required value cannot be found.
Hence, option 5.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 36

Answer the following question based on the information given below.
The table below shows the month-wise breakup of the amount of fish (in tonnes) arriving at Sassoon Docks from different sources in a particular year. Fish is imported only in months when the demand is not met through these sources.

The table below shows the yield/boat (in kg) for each source for a few months.

Q.

What is the average yield imported (in tonnes) in the months when the demand exceeds the supply?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 36

The fish is imported only when demand exceeds the supply.

∴ Average yield imported (in tonnes) = (105 + 700 + 700 + 600 +15 + 24 + 42)/7 312 tonnes= 312000 kgs

Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 37

Answer the following question based on the information given below.
The table below shows the month-wise breakup of the amount of fish (in tonnes) arriving at Sassoon Docks from different sources in a particular year. Fish is imported only in months when the demand is not met through these sources.

The table below shows the yield/boat (in kg) for each source for a few months.

Q.

What is the approximate difference in the number of boats coming from AP in Jan and Apr?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 37

Number of boats x yield per boat ≥ fish coming in from that source

For Jan: n x 100 ≥ 10922 x 1000 

∴  n ≥ 109220

For Apr: n x 75 ≥ 56602 x 1000 

∴  n ≥ 754693.33

Since n is number of boats, minimum n = 754694 

∴ Required difference = 754694 - 109220 = 645474 

Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 38

A palace has 72 distinct floors. Each floor is of made of one of two materials (marble, granite), is of 1 of 3 sizes (small, medium, large), has 1 of 3 colors (black, white, grey) and is in 1 of 4 shapes (square, triangle, circle, hexagon). How many floors completely differ from the “marble large white circle” floor? e.g. the “granite small black hexagon” floor completely differs while the “granite small black circle” does not completely differ.

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 38

For a floor to completely differ from the “marble large white circle” floor, it has differ on each parameter. The number of choices available for each parameter are:

Material: 1 (granite)
Size: 2 (small, medium)
Colour: 2 (black, grey)
Shape: 3 (square, triangle, hexagon).

Hence, a floor can completely differ i n i x 2 x 2 > < 3 = 12 ways.
Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 39

Arif marks his goods at a% above the cost price and gives a discount of a% to it. If he sells his goods at a price of Rs. P, then which of the following statements is/are true?

I. Selling price of the goods is higher for higher value of a if cost price is constant.
II. Arif always incurs loss on his transaction III. The negative profit percentage is proportional to a2 and is independent of P. (Negative profit is financial loss)

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 39

Let the cost price of the goods be Rs. z.

Since he marks the price at a% above the cost price, his marked price is (1 + a)z.

He gives a discount of a% to the marked price.

∴ His selling price is (1 + a) z x (1 - a) = (1 - a2) z = P If cost price is constant, then selling price is lower for higher value of a.
Thus, I is false.

Thus, Arif always incurs a loss on his transaction.
Thus, II is true.

Thus, the profit percentage is proportional to a2 and is independent of P.
Thus, III is true.
Hence, option 4.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 40

Alord got an order from a garment manufacturer for 480 Denim Shirts. He brought 12 sewing machines and appointed some expert tailors to do the job. However, many didn’t report for duty. As a result, each of those who did, had to stitch 32 more shirts than originally planned by Alord, with equal distribution of work. How many tailors had been appointed earlier and how many had not reported for work?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 40

The number of tailors = x

∴ The number of shirts assigned to each tailor = 480/x

Let us say that n tailors did not report to the duty. Then,

Substituting the values of x and n from the answer options, we have option 3 to be correct.
When x = 10 and n = 4 the equation (i) gets satisfied perfectly.
Hence, option 3.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 41

I f x3 - y3 = 469 a n d x - y integers. 

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 41

x3 - y3 = 469

∴ (x - y ) ( x 2 + x y + y 2) = 469 

( x - y ) = 1

∴ x 2 + x y + y2 = 469 ... (1)

∵ ( x - y ) = 1 

∴ (x -y )2 = 12 x2 - 2xy + y2 = 1 ... (2)

(1) - (2) gives

3xy = 468

∴ xy = 156

Add xy on both the sides of (1)

∴ x2 + xy + y2 + xy = 469 + xy

∴ x2 + 2xy +y2 = 469 + 156

∴ (x +y)2 = 625

∴ + y = ± 25 Sincex an d y are positive integers,x + y = 25 Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 42

The ratio of the height of a right circular cone to its radius is 4 : 3. If the height and radius of the cone are halved, by what percent does the volume of the cone decrease?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 42

Let the height and radius of the right circular cone be 4x and 3x units 4 2
 respectively.

The new height and radius of the cone are 2x and 1.5x units respectively.

Hence, option 4.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 43

Group Question

Answer the following question based on the information given below.
The pie-charts show the sales of different types of cars in 2012 and the city wise distribution of Swift in 2012. The ratio of total sales of cars in the first, second, third and fourth quarter of the year 2012 was 1:2:3:4. The total sales of cars in the third quarter of 2012 was Rs 200 crore more than that in the first quarter.

Q.

If the sales of Swift in 2012 form x% of the total sales of cars in the second quarter, what is the value of x?.

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 43

Let the total sales of cars in 2012 be Rs p crores.

∴ 0.3p - p = 200

∴ p = 200/0.2 = Rs. 1,000 crores

∴ Total sales of cars in second quarter = 0.2p = 0.2 x 1000 = Rs. 200 crores

Total sales of Swift in 2012 = 25% of p = 0.25 x 1000 = Rs. 250 crores

∴ Required percentage = (250/200) x 100 = 125%
∴ x = 125 Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 44

Group Question

Answer the following question based on the information given below.
The pie-charts show the sales of different types of cars in 2012 and the city wise distribution of Swift in 2012. The ratio of total sales of cars in the first, second, third and fourth quarter of the year 2012 was 1:2:3:4. The total sales of cars in the third quarter of 2012 was Rs 200 crore more than that in the first quarter.

Q.

If the total sales of Honda City in Bangalore is same as that of Swift in Kolkata, then the total sales of Honda City in Bangalore is what percent of the total sales of cars in Bangalore?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 44

Consider the solution to the first question.

Total sales of Swift in 2012 = Rs. 250 crores and total sales of cars in 2012 = Rs. 1000 crores.

∴ Total sales of Swift in Kolkata = 10% of 250 i.e. Rs. 25 crores 

∴ Total sales of Honda City in Bangalore = Rs. 25 crores.

However, the total car sales in Bangalore are not known.

Hence, the required percentage cannot be found.
Hence, option 5.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 45

Group Question

Answer the following question based on the information given below.
The pie-charts show the sales of different types of cars in 2012 and the city wise distribution of Swift in 2012. The ratio of total sales of cars in the first, second, third and fourth quarter of the year 2012 was 1:2:3:4. The total sales of cars in the third quarter of 2012 was Rs 200 crore more than that in the first quarter.

Q.

If the total number of Swift sold in New Delhi in 2012 was 15% of the total number of Swift sold in 2012, then what is the ratio of average selling price of Swift in New Delhi and its overall average price?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 45

Let the total number of Swift sold in 2012 be y.

Hence, option 5

NMAT Quantitative Skills MCQ Quiz - 2 - Question 46

Group Question

Answer the following question based on the information given below.
The pie-charts show the sales of different types of cars in 2012 and the city wise distribution of Swift in 2012. The ratio of total sales of cars in the first, second, third and fourth quarter of the year 2012 was 1:2:3:4. The total sales of cars in the third quarter of 2012 was Rs 200 crore more than that in the first quarter.

Q.

If the total sales of Polo in Chennai is one-fifth of that of Swift in New Delhi, what was the total sales (in Rs. crore) of Polo in Chennai?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 46

Consider the solution to the first question.

Total sales of Polo in Chennai = 

Hence, option 2.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 47

Group Question

Answer the following question based on the information given below.
The pie-charts show the sales of different types of cars in 2012 and the city wise distribution of Swift in 2012. The ratio of total sales of cars in the first, second, third and fourth quarter of the year 2012 was 1:2:3:4. The total sales of cars in the third quarter of 2012 was Rs 200 crore more than that in the first quarter.

Q.

How many digits will a product o f a 19-digit number and a 17-digit number  have?

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 47

Let a 19-digit number be x and a 17-digit number be y.

1018 ≤ x < 1019

1016 ≤ y < 1017

1034 ≤ xy < 1036

1034 has 35 digits.

1036 has 37 digits.

∴ x x y can have 35 or 36 digits.
Hence, option 1.

NMAT Quantitative Skills MCQ Quiz - 2 - Question 48

Taps A and B are two types of taps connected to an empty tank. A can fill the tank in twice the number of hours that B would take to empty the tank. At time t = 00 hours, A was opened. At t = 08 hours, B was opened. At t = 12 hours, A was closed. K t t = T hours, the tank got emptied. What is the value of 77

Detailed Solution for NMAT Quantitative Skills MCQ Quiz - 2 - Question 48

Since A fills the tank in twice the time that B takes to empty it, B is twice as efficient as A.
Let A fill a litres of water per hour. So, B empties 2a litres of water per hour.
From t = 00 hours to t = 08 hours (i.e. for 8 hours), only A was opened.

∴ Amount of water filled in 8 hours = 8 x a = 8a litres

From t = 08 hours to t = 12 hours (i.e. for 4 hours), both A and B were opened.

 ∴ Amount o f water filled in 4 hours = 4 x ( a- 2a) = - 4a litres 

i.e. 4a litres of water were emptied in these 4 hours.

 ∴ Amount of water left in the tank at t = 12 hours = 8a - 4a = 4a litres 

From t -12 hours onwards, only B was open.

 ∴ Time taken by B to empty the tank = 4a/2a = 2 hours

Thus, tank got emptied at 7= 14 hours.

∴ T= 14
Hence, option 2.

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