**Q1. What is the remainder obtained when (1421 × 1423 × 1425) is divided 12?**

(a) 3

(b) 11

(c) 8

(d) 6

**S1. Ans.(a)**

**Sol.** Remainder of 1421/12 = 5

Remainder of 1423/12 = 7

Remainder of 1425/12 = 9

Remainder (1421 × 1423 × 1425)/12 = Remainder (5 × 7 × 9)/12 = Remainder (5 × 63)12 = Remainder (5 × 3)/12 = 3.

**Q2. If the number 13915 can be factorized as xy^2 z, where x, y and z are prime numbers, then what is the value of x + y + z?**

(a) 28

(b) 39

(c) 49

(d) None of these

**S2. Ans.(b)**

**Sol. **Factor of 13915 = 5 × 11 × 11 × 23

xy^2 z=5×11^2×23

x = 5

y = 11

z = 23

So, x + y + z = 5 + 11 + 23

= 39

**Q3. I have to pack some apples into some boxes. If I pack 3 or 4 or 5 or 6 apples in a box, I am left with one apple in each of the cases. However, if I pack 7 apples in a box, I am left with none. What is the minimum number of apples that I have?**

(a) 301

(b) 604

(c) 61

(d) 436

**S3. Ans.(a)**

**Sol. **LCM of 3, 4, 5, 6 = 60.

So the number should be of the format 60 K + 1. 1st number of the format 60 K + 1 which is divisible by 7 = 301.

**Q4. Average score of Rahul Dravid after 25 innings is 46 runs per innings. If after the 26th inning his average runs increased by 2 runs, then what is his score in the 26th inning?**

(a) 98

(b) 102

(c) 96

(d) can’t be determined

**S4. Ans.(a)**

**Sol. **Total run of Rahul Dravid after 25 innings

= 25 × 46

= 1150

Total no. of run after 26 inning = 26 × 48

= 1248

Run scored in 26th inning = 1248 – 1150

= 98

**Q5. How many litres of fresh water should by mixed with 30 litres of 60% milk solution so that resultant solution is a 20% milk solution.**

(a) 30 litres

(b) 60 litres

(c) 15 litres

(d) 45 litres

**Q6. There is a sequence of 11 consecutive odd numbers. If the average of first 7 numbers is X, then find the average of all the 11 integers.**

(a) X + 3

(b) X + 4

(c) X + 5

(d) X + 7

**S6. Ans.(b)**

**Sol.** Average of first 7 consecutive odd number = 4th number

4th number = x

Average of 11 consecutive odd number = 6th number

6th number = 4th number + 2 × (difference between the two number)

= X + 2 × 2

= X + 4

**Q7. Two shopkeepers sell some article for Rs. 4000 each. A shopkeeper calculates his profit % on his CP and another calculates his profit % wrongly on SP. What is the difference in their actual profit if both claim to have a profit of 20%?**

(a) Rs. 132.33

(b) Rs. 136.33

(c) Rs. 133.33

(d) Rs. 130.33

** S7. Ans.(c)**

**Sol. **When 20% profit on C.P.

S.P. = 4000

C.P. = 4000/1.2

C.P. = 3333.33

Profit = 4000 – 3333.33 = 666.66

When 20% profit on S.P.

S.P. = 4000

Profit = 20/100×4000

= 800

Difference in profit = 800 – 666.66

= 133.33

**Q8. A reduction of 20% in the price of sugar enables a person to obtain 40 kg more for Rs. 210. What is the reduced price per kg?**

(a) Re. 1

(b) Rs. 1.10

(c) Rs. 1.150

(d) None of these

**S8. Ans.(d)**

**Sol.** Owing to the fall in price, there is a saving of 20% on Rs. 210, i.e., Rs. 42.

So, for Rs. 42, a person purchases 40 kg of sugar.

Hence, reduced price per kg = Rs. 42 ÷ 40 = Rs. 1.05

**Q9. A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 min for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower?**

(a) 5(√3 + 1)

(b) 6(√3 + √2)

(c) 7(√3 – 1)

(d) 8(√3 – 1)

** S10. Ans.(a)**

**Sol.** ∠BAC = ∠ACT + ∠ATC = 50 + 30 = 80°

And ∠ACT = ∠ABC (Angle in alternate segment)

So ∠ABC = 50°

∠BCA = 180 – (∠ABC + ∠BAC)

= 180 – (50 + 80) = 50°

Since ∠BOA = 2∠BCA = 2 × 50 = 100°

**Q13. A 6-ft-tall man finds that the angle of elevation of the top of a 24-ft-high tower and the angle of depression of its base are complementary angles. The distance of the man from the pillar is**

**Q14. A and B invested in the ratio 5 : 4 in a business. If 10% of the total profit goes to charity and A’s share is Rs. 900, find the total profit.**

**S14. Ans.(d)**

**Sol.**Suppose the total profit is Rs. 100.

**Q15. The weights of four rowers of a boat are respectively 71kg, 72 kg, 75 kg and 74 kg and the average weight of whole crew, including the coxswain is 76 kg. Find the weight of the coxswain.**

**S15. Ans.(a)**

**Sol.**Required answer =5×76-(71+72+74+75)=88 kg