Special Quant Quiz (Miscellaneous) SSC CGL Tier-II 2016

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
(a) 2√3 ft
(b) 8√3 ft
(c) 6√3 ft
(d) 6√2 ft
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. 
(a) Rs. 1600
(b) Rs. 1400
(c) Rs. 1500
(d) Rs. 1800
S14. Ans.(d)
Sol. Suppose the total profit is Rs. 100. 
Then Rs. 10 goes to charity. 
Now, Rs. 90 is divided in the ratio 5 : 4. 
A’s share = 90/(5+4)×5=Rs.50
But we see that A’s actual share is Rs. 900. 
Actual total profit = 900 (100/50) = Rs. 1800
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.
(a) 88 kg     
(b) 98 kg 
(c) 68 kg   
(d) 63 kg
S15. Ans.(a)
Sol. Required answer =5×76-(71+72+74+75)=88 kg

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