Mock Test on Quantitative Techniques by CLATalogue

Mock Test on Quantitative Techniques by CLATalogue

Direction for Question​​ 1-8:​​ There are two pie charts given. In first one, the percentage breakup of no of children (under age 10) of six states is given and similarly in second pie chart, percentage breakup of number of children between 11 to 16 age is given. Also a table is attached giving the details about the boys:girls​​ sex ratio. Answer the following questions based on above information.​​ 

 

 

States

B:G​​ <10

B:G​​ (11-16)

Delhi

3:05

13:15

Karnataka

5:11

5:03

Assam

9:11

11:05

Gujarat

5:03

8:06

Jharkhand

7:05

11:09

UP

9:06

17:11

 

 

 

 

 

Q1: What is the difference between number of boys from Karnataka (under age 10) and​​ number of girls from Assam (between​​ age 11 to​​ 16)?

  • 102135  (b) 103125  (c) 104215  (d) ​​ 105115

Q2: If each state had equal number of children​​ up to​​ age 16, which state would have least number of children between 10-11 yrs age?

  • Jharkhand(b) Assam  (c) UP​​    (d) Cannot be determined

Q3: What is the​​ average number of girls for each state​​ (including both the age groups)?

  • 448895  (b) 458895  c) 448795  (d) 447895

Q4: What is the total number of boys in the given states?

  • 3306625(b) 3306725  (c) 3216725  (d) 3206675

Q5: Which two states have equal number of girls and in which age group?

  • Jharkhand & Assam in age group between 11-16

  • Karnataka & Gujarat ​​ in age group of under 10

  • Delhi & Gujarat in age group between 11-16

  • Gujarat and Jharkhand in age group under 10

Q6: Which state has the highest number of girls in total?

  • Karnataka(b) Assam  (c) Delhi​​   (d) Gujarat

Q7: Which state has the highest number of boys in age between 10-11 yrs?

  • Assam​​   (b) UP​​    (c) Gujarat  (d) Jharkhand

Q 8: Which two states have equal number of boys in any age group?

  • Delhi & Assam   (c) Karnataka & Assam​​ 

  • ​​ Karnataka & Delhi  (d) Gujarat & Jharkhand

Q9:​​ If Length of a rectangle is 4 times​​ the breadth, then find the area of square whose side is equal to average of length and breadth of the rectangle​​ if area of rectangle is 256 cm2.​​ ​​ 

  • 225cm2(b) 196cm2​​  (c) 256cm2​​  (d) 400cm2

Q10: In​​ the​​ previous question if a circle has to be made within the square such that its circumference touches the side of square, what will be the area of that square?

  • 314cm2(b) 209cm2(c) 156cm2(d) 254 cm2

Question 11-13: If Swapnil is earning interest on the principal amount of loan that he gave to Ram and Shyam @ of 15% in S.I and C.I respectively. The loan is given for 3 years. The difference between S.I and C.I is Rs.70.875. Answer the following questions.

Q11: What is the Principal amount lent by Swapnil?

  • 1005  (b) 1000  (c) 1050  (d) 1100

Q12: What would be the difference in S.I and C.I if the same amount of money is lent to both Ram and Shyam @10% for same time?

  • 100  (b) 75   (c) 10   (d) 31

Q13:​​ How much Swapnil should lent to Ram (in S.I. only) in order to earn same interest as he earns from Shyam @10% for 3 yrs?

  • 1100  (b) 1103  (c) 1200  (d) 1203

Question 14-15: ​​ Ojas owns a bookstore and makes a profit of 12.5% by selling books at certain price. His profit increases to 37.5% if he starts selling books at Rs.28 more than what he was usually charging. Answer the following question based on given information.

​​ Q14: What was Ojas’s original selling price?

  • 130  (b) 122   (c) 128   (d) 126

Q15: At what price Ojas purchased his books?

  • 112  (b) 115   (c) 122   (d) 110

Answers & Solutions:

Tips for solving data set Question 1 to 8:

  • The data set has two pie charts and one table which give gender details ok kids. Read the questions first then as per requirement fill up the table which will include columns with boys under age 10, girls under age 10 and boys and girls between 11-16 and rows will have different states. A table with all the numbers for reference but I​​ suggest​​ you first read questions and fill as per requirement only not just look at the solutions.

  • We will also require division of 25​​ lakh​​ and 35​​ lakh​​ children in different states so that boys girls division can be done​​ from that data.

  • The data set is vast and detailed but if done with calm mind you can score 8 marks with simple calculation. But remember to keep track of time. In exam if such a data set come first try read questions and attempt 4 easy one.

States

Children ​​ age <​​ 10

T=2500000

Children age​​ 11 to 16

T=3500000

Delhi

18%

450000

16%

560000

Karnataka

12%

300000

15%

525000

Assam

15%

375000

18%

630000

Gujarat

17%

425000

20%

700000

Jharkhand

15%

375000

17%

595000

UP

23%

575000

14%

490000

​​ ​​ 

States

B:G​​ <10

B

G

B:G​​ (11-16)

B

F

TB

TG

Delhi

3:05

168750

281250

13:15

260000

300000

428750

581250

Karnataka

5:11

93750

206250

5:03

328125

196875

421875

403125

Assam

9:11

168750

206250

11:05

433125

196875

601875

403125

Gujarat

5:03

265625

159375

8:06

400000

300000

665625

459375

Jharkhand

7:05

218750

156250

11:09

327250

267750

546000

424000

UP

9:06

345000

230000

17:11

297500

192500

642500

422500

 

  • Ans: (b) 103125

Sol: ​​ Number of Boys from Karnataka (age<10) =​​ 93750​​ 

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ Number of Girls from Assam (age 11-16) =​​ 196875

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ Difference between the boys from Karnataka and Girls from Assam = 196875 – 93750​​  

          ​​ ​​ ​​ ​​ ​​​​ = 103125

  • Ans: ​​ (d) Cannot be determined

Sol:​​ the question asks us to assume that all states have equal no. of children under age 16, even if we go by the assumption, the distribution of children among states under different age group is​​ different hence out of total 60 lakh (total under age of 16)​​ even each state with 10 lakh children, the sum of actual number of children is above 10 lakh. Hence It is not possible to answer the question with the given assumption as negative number of children is not practical situation correct answer.

  • Ans:​​ ​​ (a) 448895

Sol:​​ As total girls = 2693375 (sum of all the girls in both age groups)

 ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ Average number of girls each state = 2693375 / 6 = 448895​​ 

  • Ans:​​ (a) 3306625

Sol:​​ there is no shortcut for these calculations, you will need to calculate number of boys in each state and add the numbers to get the total.

  • Ans:​​ (c) Delhi and Gujarat in age between 11-16

Sol:​​ From table calculations we can see a lot of similar numbers but options are confusing so make sure you check​​ all the options​​ before marking the answer.

  • Ans:​​ (c) Delhi

Sol:​​ From the table compare the options.​​ 

  • Ans:​​ (a) Assam

Sol:​​ As the number of children has been given for​​ age<10 and​​ age​​ 11-16, for number of boys between the age of​​ 10-11 we will need to​​ subtract no. of boys under age<10 from​​ the no. of boys between age​​ 11-16.​​ From the table below we can see Assam has the highest number of boys between​​ the​​ age​​ of​​ 10-11.​​ 

States

M

M

Difference

Delhi

168750

260000

91250

Karnataka

93750

328125

234375

Assam

168750

433125

264375

Gujrat

265625

400000

134375

Jharkhand

218750

327250

108500

UP

345000

297500

-47500

​​ 

  • Ans:​​ (a) Delhi and Assam

Sol:​​ Table observation.​​ 

  • Ans: (d) 400 cm2

Sol: ​​ Given, Length = 4* breadth (let length be l and breadth be b)

 ​​ Area of rectangle = l*b = 256​​ 

  ​​ ​​ ​​ ​​​​ => 4*b2​​ = 256

    ​​ ​​ ​​ ​​​​ b = 8 cm hence l = 8*4 = 32cm

Side of square = Average of l and b = 8+32/2 = 20cm

Area of square = 20*20 =400cm2

  • Ans: (a) 314 cm2

Sol:​​ Circle has to be made under square while touching all the sides; hence radius will be half of the side of square, i.e., 10cm

Area of circle = (pi) r2​​ = 3.14 *10*10 = 314 cm2

  • Ans:​​ (b) 1000

Sol:​​ C.I – S.I = 70.875​​ 

P [ (1 + r/100)^t -1 ] – P*r*t /100 = 70.875​​ 

R =15%, t = 3 years, putting the values in above equation gives P = 1000​​ 

Note:​​ In such questions one should start with the options available as it is easier to rule out options then dealing with complicated calculations.

  • Ans:​​ (d) 31

Sol:​​ Difference between SI and CI = P [ (1 + r/100)^t -1 ] – P*r*t /100

In last question P = 1000, here r = 10% and t = 3

Hence difference between CI and SI after putting in the values would be 31

  • Ans:​​ (b) 1103

Sol:​​ C.I for P = 1000, r = 10% and t = 3 = P[(1+r)^t – 1]

C.I = 331

S.I. = P*r*t / 100 (as S.I. has to be equal to C.I)

331 = P* 10*3/100

P = 1103.333

  • Ans:​​ (d) 126

Sol:​​ Profit % = 12.5 %

Let S be the selling Price and C be cost price,

(S-C)*100 / C = Profit %

S-C / C = 12.5 /100 = 0.125

S = 1.125 C

If S is increased by adding 28 then,

(S+28) –C /C = 37.5% = 0.375

C replaced by S​​ 

S + 28 =1.375 *C = 1.375*S/1.125

S = 126

  • Ans:​​ (c) 112

Sol:​​ Cost Price C​​ = S/1.125 = 126/1.125 = 112​​ ( from previous question)

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