Day 1: Numerical Ability Most Important practice Sets for IBPS Clerk Prelims 2018 :
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1. Three alcohols of concentrations 40%, 50% and 60% are mixed in the ratio 2 : 3 : 1. Find the approximate concentration of water in the final solution.
a)51.66%
b)48.33%
c)48.66%
d)51.33%
e)None of these
2. A dice is rolled. If the outcome is a prime number, what is the probability that it is greater than 3?
a)1/6
b)1/2
c)1/5
d)2/3
e)None of these
3. Aashu and Bunty together invested Rs. 7500 in a business. At the end of the year, out of a total profit of Rs. 1200, Aashu’s share was Rs. 700. What was the investment of Aashu?
a) Rs. 4375
b) Rs. 3125
c) Rs. 3500
d) Rs. 4500
e) None of the above
4. Rita invested 25% more than Sunil. Sunil invested 30% less than Abhinav who invested Rs. 6000. What is the respective ratio between the amount that Rita invested and the total amount invested by all of them together?
a)35 : 104
b)13 : 29
c)101 : 36
d)35 : 103
e)None of these
5. The total area of a circle and a rectangle is equal to 1166 sq.cm. The diameter of the circle is 28cm. What is the sum of the circumference of the circle and the perimeter of the rectangle if the length of the rectangle is 25 cm?
a)186 cm
b)182 cm
c)184 cm
d)176 cm
e)180 cm
6.Three unbiased coins are tossed simultaneously. What is the probability of obtaining at least two tails?
a)2/3
b)5/18
c)3/10
d)1/2
e)1/4
7. The mean temperature of Monday to Wednesday was 42°C and of Tuesday to Thursday was 39°C. If the temperature of Thursday was 4/5th that of Monday, find the temperature of Thursday.
a)45°C
b)36°C
c)40°C
d)Cannot be determined
e)None of these
8.A certain sum of money at simple interest amounted to Rs.575 at 5% in a time in which Rs.750 amounted to Rs.840 at 4%. Find the sum?
a)Rs.410
b)Rs.356
c)Rs.500
d)Rs.280
e)Rs.550
9. Two pipes A and B can fill a tank in 16 minutes and 24 minutes respectively. If both the pipes are opened simultaneously after how much time should pipe B be closed so that the tank can be full in 12 minutes?
a)8 min
b)6 min
c)10 min
d)5 min
e)None of these
10. After receiving 3 successive discounts of 10%, 20% and 25% on MP of furniture, Mohini purchased the furniture for Rs. 9720. Determine the MP of the furniture.
a)Rs. 15000
b)Rs. 12000
c)Rs. 20000
d)Rs. 18000
e)None of the above
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Answers:
1.Correct Choice :a
Solution :
The final concentration of alcohol = (40 x 2 + 50 x 3 + 60 x 1)/6 = 290/6 = 48.33%
So the concentration of water = 100 – 48.33 = 51.66%
2.Correct Choice :e
Solution :
Suppose A = Events of getting a prime number
B = Events of getting a prime number greater than 3
A = {2, 3, 5} B = {5}
Required probability = P(B)/P(A) = 1/3
3. Correct Choice :a
Solution :
Total investment of Aashu and Bunty = Rs. 7500
Total profit at the end of the year = Rs. 1200
Share of Aashu = Rs. 700
Share of Bunty = 1200 – 700 = Rs. 500
When the time period is same.
4. Correct Choice :d
Solution :
Sunil’s investment = 0.7 x 6000 = 4200
Rita’s investment = 1.25 x 4200 = 5250
Required ratio = 5250:(5250+4200+6000)
= 5250:15450 = 35:103
5.Correct Choice :b
Solution :
Area of circle = 22/7 x 14 x 14 = 616 sq cm
Hence area of rectangle = 1166-616 = 550 sq cm.
Breadth of rectangle = 550/25 = 22 cm
Circumference of the circle = 22/7 x 28 = 88 cm
Perimeter of the rectangle = 2(22+25) = 94 cm
Sum = 88+94 = 182 cm
6.Correct Choice :d
Solution :The total possible outcomes when three coins are tossed = 2 X 2 X 2 = 8
Let us denote head as 1 and tail as 0.
There are 4 possibilities of having at least two tails when all the three coins are tossed which are mentioned as follows:
{1, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 0, 0}
Probability of an event is defined by the formula, P(E) = n(E)/(n(s)) = 4/8= 1/2
7. Correct Choice :b
Solution :
Let the temperatures of Monday, Tuesday and Wednesday be p°C, q°C and r°C.
Temperature of Thursday= 4p/5
Now,
p + q + r = 42 x 3 .. (1)
q + r + 4p/5 = 39 x 3 .. (2)
(1) – (2) =>
p – 4p/5 =3 x 3
=> p/5 = 9
=> p = 45
Hence Thursday’s temperature was 45 x 4/5 =36°C.
8. Correct Choice : c
Solution : Interest = “Rs.840-Rs.750=Rs.90”
Simple interest = (principal X time X rate)/100
Time= (simple interest X 100)/(rate of interest X principal)= (90 X 100)/(750 X 4)=3 years
Using a direct formula that provides direct relation between principal and amount,
Sum= (100 X amount)/(100+(rate X time))= (100 X 575)/(100+(3 X 5))=Rs.500
9. Correct Choice : b
Solution :In 1 min, the pipes can fill = 1/16 +1/24 =5/48 portion
Let the pipe B be closed after N min.
Then,
Portion filled by (A + B) in N min + portion filled by A in (12-N) min = 1
=> N x 5/48 + (12-N) x 1/16 = 1
=> 5N + 36 – 3N = 48
=> N = 6
10. Let their ages be 4n and 5n respectively.
(4n+6):(5n+6) = 6:7
=> 28n+42 = 30n+36
=> 2n = 6
=> n = 3
Difference in their ages = 15 – 12 = 3 years