Question – 1

1. On day one, Smith ran to a shop and came back walking. He took 8 minutes to cover this trip. On the next day, he takes 6 minutes as he runs both ways.?

Column-A | Column-B |
---|---|

Time taken to complete his trip if he walks both ways | Time taken to complete his trip two times around if he runs both ways. |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:B
- Answer Explanation:Let his distance one way be k meters.Speed = distance/timeLet his speed while walking be x m/min and while running be y m/min.On day two, he runs both waysy = 2k/6=k/3k = 3yOn day one, he walks one way and runs the other wayk/x+k/y=8k(x+y)=8xyPutting k = 3y in this equation, we get3y(x+y)=8xy3x+3y=8x3y=8x-3x=5xy/x=5/3When he walks both waysTime taken = k/x+k/x= 3y/x+3y/x = 6y/x= 6(5/3) = 2*5=10 minsWhen he runs both waysTime taken for going two times around = 2*6mins =12 minsOption B is true.

Question – 2

2. A semi-circle is rolled and a cone is formed. The radius of the circle is 21cm.?

Column-A | Column-B |
---|---|

Lateral surface area of the cone | Total surface area of the semi-circle |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:C
- Answer Explanation:Since the semi-circle is turned into a cone, the surface area of the semi-circle becomes the lateral surface area of the cone. The two quantities are equal.Option C is correct.

Question – 3

3. A, B and C invest $80000 in a business. A invests the most and B and C invest equal amounts. The profit earned by each is proportional to his share of investment. A gets $4000 from the total profit.?

Column-A | Column-B |
---|---|

Investment of A | Total investment of B and C |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:D
- Answer Explanation:We know the total investment, but we do not know the ratio in which A, B and C invested. Hence, we cannot calculate the total investment of A, B and C.Option D is correct.

Question – 4

4. From a rectangular cardboard of length 25 cm and breadth 10 cm, Adam cuts a square whose diagonal is of length 4*sqrt(2) cm.?

Column-A | Column-B |
---|---|

Number of such squares | 30 |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:B
- Answer Explanation:Area of the cardboard = length*breath= 25*10 = 250 sq.cm.Diagonal of a square of side x cm is equal to x*sqrt(2) cm.Hence, side of square = 4 cmArea of square = side*side= 4*4 = 16 sq.cm.Number of squares that he can possibly cut = 250/16= 15.625Option B is correct.

Question – 5

5. A dishonest shopkeeper uses an 800 gm weight instead of a 1 kg weight. He claims to sell the items at their cost price.?

Column-A | Column-B |
---|---|

Profit | $50 |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:D
- Answer Explanation:We can only calculate the profit percent and we cannot calculate the profit earned by the shopkeeper since we do not have sufficient data.Option D is correct.

Question – 6

6. 585 has to be converted to a perfect square.?

Column-A | Column-B |
---|---|

The smallest number by which it should be multiplied | The smallest number by which it should be divided |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:C
- Answer Explanation:585=3*3*5*13The smallest number by which it should be multiplied is 5*13=65The smallest number by which it should be divided is 5*13=65Option C is correct.

Question – 7

7. Consider three numbers a<=b<=c.?

Column-A | Column-B |
---|---|

LCM of the three numbers | HCF of the three numbers |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:D
- Answer Explanation:The LCM of three numbers is always greater than the HCFWhen a=b=cLCM=a and HCF=aHence, the relationship cannot be established.Option D is correct.

Question – 8

8. log[(x+y)/3]=1/2(logx+logy).?

Column-A | Column-B |
---|---|

(x/y+y/x) | [(x+y)^2-2xy]/xy |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:C
- Answer Explanation:log[(x+y)/3]=1/2(logx+logy)log[(x+y)/3] = log[sqrt (xy)](x+y)/3 = sqrt(xy)Squaring both sides, we get(x^2+y^2+2xy)/9=xyx^2+y^2= 9xy-2xyx^2+y^2=7xyDividing by xy, we getx/y+y/x=7Also, (x^2+y^2)=7xy(x+y)^2-2xy=7xy[(x+y)^2-2xy]/xy=7Option C is true.[x^2=x*x]

Question – 9

9. x+1/x=3,?

Column-A | Column-B |
---|---|

x^2+1/x^2 | x^2+6/x-1/x^2 |

(Note: [x^2=x*x])

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:B
- Answer Explanation:x+1/x=3Squaring both sides, we getx^2+1/x^2+2*x*1/x=3^2x^2+1/x^2=9-2=7x^2+1/x^2=7x+1/x=3x=3-1/xSquaring both sides, we getx^2=9+1/x^2-6/xx^2-1/x^2+6/x=9Option B is correct.

Question – 10

10. 2x+y=35 and 3x+4y=65.?

Column-A | Column-B |
---|---|

x/y. | y/x |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:A
- Answer Explanation:2x+y=35 ….(1)3x+4y=65..(2)Multiply (1) by 4 and subtracting (2) from it8x+4y-3x-4y = 140-655x=75x = 75/5=15Put x = 15 in (1)2*15+y=3530+y=35y= 35-30=5x/y=15/5=3y/x=5/15=1/3Option A is correct.

Question – 11

11.

Column-A | Column-B |
---|---|

The sum of the first 100 even natural numbers divisible by 5. | The sum of numbers between 35 and 95 divisible by 3 |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:A
- Answer Explanation:The even natural numbers divisible by 5 are 10, 20, 30,….These form an AP with the first term a = 10 and the common difference d = 20-10=10Sum of n terms of an AP is given bySn=n/2[2a+(n-1)d]=100/2[2*10+(100-1)*10]=50(20+990)=50*1010= 50500The numbers divisible by 3 and lying between 35 and 95 are 36, 39, 42,….These form an AP with the first term a = 36 and the common difference d = 3The last term is 93 and it is given by 93 = 36+(n-1)*3(93-36)/3=n-119=n-1n=19+1=20Sum of n terms of an AP is given bySn=n/2[2a+(n-1)d]=20/2[2*36+(20-1)*3]=10(72+57)=10*129= 1290Option A is correct.

Question – 12

12. Seven-letter words are formed by the letters of the word EQUATION.?

Column-A | Column-B |
---|---|

Number of words that end in a vowel | Number of words having a vowel in the third place |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:C
- Answer Explanation:There are 5 vowels and 3 consonants in the word EQUATION.The last letter of the 7 letter words can be filled in 5 waysThe remaining 6 places can be filled by remaining 7 letters in P(7,6) waysP(7,6) = 7!/(7-6)!= 7!/1!=7*6*5*4*3*2= 5040 waysTotal words = 5*5040 = 25200Similarly, the third place can be filled in 5 ways and the remaining places can be filled in P(7,6) ways.Option C is correct.

Question – 13

13. The parallel sides of a trapezium are 28m and 12m. The area of the trapezium is 180 sq.m.?

Column-A | Column-B |
---|---|

Distance between the parallel sides | 18 cm |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:A
- Answer Explanation:Area of trapezium= 1/2(sum of parallel sides)*distance between parallel sides180= 1/2*(28+12)*Distance180*2/40= DistanceDistance = 9 m9m>18cmOption A is correct.

Question – 14

14. The volume of a solid sphere A is 87.5% less than the volume of solid sphere B.?

Column-A | Column-B |
---|---|

Percent of surface area of A that the surface area of B is | Percent of radius of A that the radius of B is |

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:A
- Answer Explanation:Let r and R be the radii of sphere A and sphere B respectively.Volume of sphere A = 4/3*pi*r^3Volume of sphere B = 4/3*pi*R^3According to the conditions, we haveVolume of A = volume of B – 87.5% volume of B4/3*pi*r^3 = 4/3*pi*R^3 – 87.5/100*4/3*pi*R^3r^3=R^3-875/1000*R^3r^3=(1000-875)/1000*R^3r^3= 125/1000*R^3Taking cube root on both sides, we getr = 5/10*RR=2rPercentage of radius = R/r*100= 2r/r*100= 200%Percentage of surface area = Surface area of B/surface area of A *100= 4pi*R^2/(4pi*r^2)*100= R^2/r^2*100= (2r)^2/r^2*100= 4r^2/r^2*100= 400%Option A is correct.[r^3=r*r*r]

Question – 15

15.

Column-A | Column-B |
---|---|

The maximum possible value of x when 10^x divides 10*11*…*20 | The maximum possible value of x when 2^x divides 20*21*…*30 |

(Note: [10^x=10*10*10…x times])

- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:B
- Answer Explanation:Consider the product 10*11*…*20The number of zeros can be calculated by multiplying the digits in the unit’s place in the product10*12*15*20 = 10*180*20= 36000No other combination of numbers shall give a product ending in 0.The product is divisible by 10^3The maximum value of x is 3.20*21*22*…*30 = (2*2*5)*21*(2*11)*23*(2*2*2*3)*25*(2*13)*27*(2*2*7)*29*(2*15)2^10 can divide the product.Option B is correct.