UPSC PRELIMS EXAMINATION 2021 CSAT PAPER -2 MATHS MENTAL ABILITY SOLVED QUESTIONS PART - 2 solved by Kumar B Bagival

UPSC PRELIMS EXAMINATION 2021 CSAT PAPER -2 

MATHS MENTAL ABILITY SOLVED QUESTIONS PART - 2

1.  Consider all 3-digit numbers(without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.

Which of the following is/are correct?

1. S is always divisible by 74.

2. S is always divisible by 9.

Select the correct answer using the code given below.

1. 1 only

2. 2 only

3. Both 1 & 2

4. Neither 1 nor 2

Solution:  S= 369+396+639+693+936+963

                    = 3996 

1. 3996 ÷ 74 = 54 that is S is divisible by 74.

2. 3996 ÷ 9   = 444 that is S is divisible by 9

so both 1 and 2 are correct 

Answer is 

(C) both 1 and 2

2. There are two classes A and B  having 25 and 30 students respectively. In class - A highest score is 21 and lowest score is 17.In class B highest score is 30 and lowest score is 22. Four students are shifted from class A to class B.

Consider the following statements :

1). The average score of class B will definitely decrease.

2).The average score of class A will definitely increase.

Which of the above statements is/are correct?

1. Only 1

2. Only 2

3. Both 1&2

4. Neither 1 nor 2

Solution : 

                  Highest score in class A is 21

                   Therefore highest avg is also 21

If four students are shifted from class -A to class- B the number of students in class B increases but the average must decrease.

So answer is

 (a) only 1

 

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3. Consider two statements and a question.

  Statement 1 : Priya is 4th ranks below Seema, and is        31st from bottom.

Statement 2 : Ena is 2nd ranks above Seema, and 37th from bottom.

Question : what is Seema's rank from the top in the class of 40 students?

Which one of the following is correct in respect of the statements and the question? 

1. Statement 1 alone is not   sufficient to answer the question.

2. Statement 2 alone is not sufficient to answer the question.

3. Either statement 1 alone or statement 2 alone is sufficient to answer the question.

4. Both the Statement 1 and statement 2 required to answer the question.

Solution : 1 , 2 , Ena , 4 , Seema , 6 , 7 , 8 , Priya , 10 , 11 , 12 , 13, 14 , 15 , 16 , 17 , 18 , 19 , 20 ,21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 34 , 35 , 36 , 37 , 38 , 39 , 40.

So either 1 or 2 is sufficient to answer the question 

Answer is 

(C) Either statement 1 or statement 2 alone is sufficient to answer the question.

4. Consider two statements and question

     

Statement 1: Each of A and D is  heavier than each of B, E and F but none of them is heaviest.

Statement 2 : A is heavier than D, but is lighter than C

Question : Who is the heaviest among A,B,C,D and E.?

Which one of the following is correct in respect of the statements and the question? 

1. Statement 1 alone is   sufficient to answer the question.

2. Statement 2 alone is   sufficient to answer the question.

3. Both the Statement 1 and statement 2 required to answer the question.

4. Neither statement 1 alone nor statement 2 alone is sufficient to answer the question.

Solution : C > A  > D > B , E , F.

Answer is 

1. Statement 1 alone is sufficient to answer the question.

         

5. In the English alphabet, the first 4 letters are written in opposite order, and the next 4 letters are written in opposite order,and so on. And at the end Hand Z are interchanged.

Which will be the 4th letter to the right of the 13th letter?

1. N

2. T

3. H

4. I

Solution : English alphabet

 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

According to problem

D C B A   H G F E  L K J I  P O N M  T S R Q  X W V U

Z Y

Answer is 

(b) T

  6. A boy plays with a ball and he drops it from a height of 1.5 m.Every time the ball hits the ground it bounces back to attain a height 4/5th of the previous height . The ball does not bounce further if the previous height is less than 50cm. What is the number of times the ball hits the ground before the ball stops  bouncing ?

1. 4

2. 5

3. 6

4. 7

Solution :  

  

            Height   1.5 m = 150 cm    

1st bounce  150 × 4/5 = 120 cm

2nd bounce 120 × 4/5 =  96 cm

3rd bounce 96 × 4/5 = 76.8 cm

4th bounce 76.8 × 4/5= 61.44 cm

5th bounce 61.44 ×4/5 = 49.152 cm

 

So four times it bounce

 Answer is

 (A) 4

7. Images of consonants of the English alphabet ( Capitals) are observed in  a mirror. What is the number of images of these which do not look  like their original shape ?

1. 13

2. 14

3. 15

4. 16

Solution : English alphabet

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z.

consonants  

B C D F G H J K L M N P Q R S T V W X Y Z

Letters whose image in mirror is as same as original are

H M T V W X Y 

Letters whose images in mirror are not like original are

B C D E F G J K L N P Q R S 

There are 14 letters

Hence the answer is 

(b) 14

8. A bank employee drives 10km towards south from her house and turns to her left and drives another 20km. She again turns left and drives 40km, then she turns to her right and drives another 5km. She again turns to her right and drives another 30km to reach her bank where she works. What is the shortest distance from her bank and to her house ?

1. 20 km

2. 25 km

3. 30 km

4. 35 km

Solution :  

                 10 km towards south

                 Turn left and drives 20 km

                Again turn left and drives 40 km

                Turn right and drives 5 km

                Turn right  and drives 30 km

So the answer is 

(B) 25 km.

      

9. Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10 ?

1. 6

2. 7

3. 8

4. 9

Solution : Integers between 700 to 1000 in which sum of their digits is 10 are

703, 712, 721,  730, 802, 811, 820, 901, 910

There are 9

Answer is 

(d) 9

10. A woman runs 12km towards her north, then 6km towards her south and 8 km towards her east.In which direction is  she from her starting point?

1. An angle less than 45° south of east.

2. An angle less than 45° north of east.

3. An angle more than 45° south north

4. An angle more than 45° north of east.

Solution :  Runs towards north 12 km,from the starting  point.

                   Then towards south 6 km,

                  Then towards east 8 km.

So the answer is

 (B) An angle less than 45° north of east.

Solved by : KUMAR B BAGIVAL