**Directions (1-4): Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and**

**Give answer:**

**(a) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the questions.**

**(b) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.**

**(c) If the data in statement I alone or in statement II alone are not sufficient to answer the question.**

**(d) If the data in both the statements I and II are not sufficient to answer the question.**

**(e) If the data in both the statements I and II together are necessary to answer the question.**

**Q1. In how many days will five women complete a work?**

I. Two women, five boys and three men together complete the work in six days.

II. Eight women complete the same work in twelve days.

**Q2. What will be Shyam’s age after 6 years?**

I. The ratio between Ram’s and Shyam’s present age is 4 : 3 respectively.

II. Ram is seven years older than Shyam.

**Q3. What is the average speed of a car?**

I. The average speed of the car is five times the average speed of a truck whereas the average speed of a bus is 45 km/hr.

II. The average speed of the truck is half the average speed of a train whereas the average speed of a jeep is 40 km/hr.

**Q4. By selling a product at 20% profit, how much profit was earned?**

I. The difference between cost and selling price is Rs. 40/-

II. The selling price is 120% of the cost price.

**Q5. A bag contains 7 blue balls and 5 yellow balls. If two balls are selected at random, what is the probability that none is yellow?**

(a) 5/35

(b) 5/22

(c) 7/22

(d) 7/33

(e) 7/66

**Q6. A dice is thrown twice. What is the probability of getting a sum 7 from both the throws?**

(a) 5/18

(b) 1/18

(c) 1/9

(d) 1/6

(e) 5/36

**Directions (7-10): Study the information carefully to answer the following questions.**

**An orgnisation consists of 1500 employees. The ratio of males to females in 17 : 13. All the employees work at five different levels named I, II, III, IV and V. 28% of females are at level I. 18% of the males work at level II. One-fifth of the males work at level V. The ratio of females to males at level II is 2 : 3. 25% of the total number of employees are at level III. Females working at level V are 60% of the males working at the same level. 18% of the females are at level IV. The remaining females are at level III. 16% of the males work at level I and the remaining males are working at level IV.**

**Q7. What is the number of males working at level III?**

(a) 136

(b) 228

(c) 253

(d) 163

(e) 270

**Q8. Number of males working at level IV forms what percent of the number of females working at the same level? (rounded off to two digits after decimal)**

(a) 145.52%

(b) 169.12%

(c) 123.42%

(d) 150.62%

(e) 139.32%

**Q9. What is the number of females working at level V?**

(a) 147

(b) 182

(c) 117

(d) 102

(e) None of these

**Q10. Number of males working at level I forms approximately what per cent of total number of the employees in the organisation?**

(a) 9%

(b) 13%

(c) 18%

(d) 22%

(e) 28%

**Directions (11-15): In the following questions two equations numbered I and II are given. You have to solve both the equations and**

**Give answer:**

**(a) If x>y**

**(b) If x≥y**

**(c) If x<y**

**(d) If x≤y**

**(e) If x=y or the relationship cannot be established**

Q11.

I. x

^{2}+x-20=0
II. y

^{2}-y-30=0
Q12.

I. 225x

^{2}-4=0
II. √225 y+2=0

Q13.

I. 4/√x + 7/√x = √x

II. y

^{2}-(11)^{5/2}/√y=0
Q14.

I. x

^{2}-10x+24=0
II. y

^{2}-9y+20=0
Q15.

I. (x)

^{2}=961
II. y=√961

**Solutions**

**S1. Ans.(b)**

Sol. Let 5 women will complete the work in x days

Using Statement II

M1D1 = M2D2

5*x = 8*12

X = 19(1/5) days

**S2. Ans.(e)**

Sol. Using Statement I

Let the present ages of Ram and Shyam be 4x and 3x respectively.

Using Statement II

4x = 3x + 7

X = 7

Therefore, Shyam’s age after 6 years = 3x + 6 = 21 + 6 = 27 years

**S3. Ans.(d)**

Sol. The data in both the statements I and II are not sufficient to answer the question

**S4. Ans.(a)**

Sol. Using Statement I:

Profit = SP – CP = 40

**S5. Ans.(c)**

Sol. Required Probability = 7C2/12C2 = (7×6)/(12×11)=7/22

**S6. Ans.(d)**

Sol. Event (when sum is 7) = (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)

Required probability = 6/36=1/6

(7-10)

Level |
Male (850) |
Female (650) |

I |
136 |
182 |

II |
153 |
102 |

III |
228 |
147 |

IV |
163 |
117 |

V |
170 |
102 |

**S7. Ans.(b)**

Sol. The number of males working at level III = 228

**S8. Ans.(e)**

Sol. Required Probability = 163/117*100=139.32%

**S9. Ans.(d)**

Sol. The number of females working at level V = 102

**S10. Ans.(a)**

Sol. Required Probability = 136/1500*100=9.07%

**S11. Ans.(e)**

Sol. I. x^2+x-20=0

(x+5)(x-4)=0⇒x=-5,4

II. y^2-y-30=0

(y-6)(y+5)=0⇒y=6,-5

∴ No relation

**S12. Ans.(b)**

Sol. I. 225x^2-4=0

x^2=4/225⇒x=±2/15

II. √225 y+2=0

15y+2=0⇒y=(-2)/15

**S13. Ans.(e)**

Sol. I. 4/√x+7/√x=√x

4+7=x ⇒x=11

II. y^2-(11)^(5/2)/√y=0

y^(5/2)-(11)^(5/2)=0

y=11

∴x=y

**S14. Ans.(e)**

Sol. I. x^2-10x+24=0

(x-4)(x-6)=0

x=4 or x=6

II. y^2-9y+20=0

(y-4)(y-5)=0

y=4 or y=5

No Relation

**S15. Ans.(d)**

Sol. I. x^2=961

x=√961

x=±31

II. y=√961

y=31

So, x<=y

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