Quantitative Aptitude Mains Level || 05 – 12 – 2018

Mentor for Bank Exams

Dear Aspirants,
Welcome to Mentor for Bank Exams. Here is the Quantitative Aptitude Quiz to help you practice with the best of latest pattern questions for the upcoming IBPS PO, IBPS Clerk and other bank and Insurance Exams.

Directions (1 – 5): Answer the following questions based on below data,
Annual exams marks secured by seven students of class IX are given below:
Student
Mathematics (150)
Science (150)
English (100)
Computer (80)
Humanities (100)
Aditya
68
79
56
35
45
Brijesh
100
39
42
70
68
Chandan
59
75
46
45
69
Dinesh
60
60
89
32
89
Eashan
112
42
32
35
78
Faran
135
140
75
35
55
Govind
87
75
38
61
71
With the above information following is also known:
• Students are promoted to class tenth, if they score 40% or more marks in each subject separately and also 50% marks overall.
• There is a provision of passing a student with grace if he scores more than 50% marks overall but less than 40% and more than 35% marks in only one subject.
• Also there is a provision of supplementary exam for students failing not more than 2 subjects and acquiring more than 40% marks overall.
• For rest all the cases, a student is considered as fail.
1. What is the difference between the total marks obtained by students receiving grace and students receiving supplementary?
            a)        15
            b)        2
            c)         78
            d)        9
            e)        None of these
2. How many marks are allotted as grace marks taken together for students getting grace?
            a)        3
            b)        1
            c)         2
            d)        No one gets grace
            e)        None of these
3. Student receiving second highest marks is approximately what percent more than the student receiving third lowest marks, irrespective of grace and supplementary received?
            a)        19%
            b)        14%
            c)         21%
            d)        11%
            e)        None of these
4. How many students failed?
            a)        1
            b)        2
            c)         3
            d)        None
            e)        None of these
5. If students receiving supplementary are promoted to next year (until supplementary exam are conducted) and are not considered as fail and the class has only those students, then what is the pass percentage of the class?
            a)        100%
            b)        75.78%
            c)         87.51%
            d)        56.72%
            e)        85.71%
(1 – 5): Common Explanation:
Following table shows the marks obtained in various subjects and respective percentage of the subjects:
Student
Mathematics (150)
Science (150)
English (100)
Computer (80)
Humanities (100)
Total (580)
ADITYA
68(45.33%)
79(52.67%)
56(56%)
35(43.75%)
45(45%)
283(48.79%)
BRIJESH
100(66.67%)
39(26%)
42(42%)
70(87.5%)
68(68%)
319(55.00%)
CHANDAN
59(39.34%)
75(50%)
46(46%)
45(56.25%)
69(69%)
294(50.68%)
DINESH
60(40.00%)
60(40%)
89(89%)
32(40%)
89(89%)
330(56.89%)
ESHAN
112(74.67%)
42(28%)
32(32%)
35(43.75%)
78(78%)
299(51.55%)
FARAN
135(90%)
140(93.34%)
75(75%)
35(43.75%)
55(55%)
440(75.86%)
GOVIND
87(58%)
75(50%)
38(38%)
61(76.25%)
71(71%)
332(57.24%)
1. Answer: E)
Explanation:
From the given information, we get that chandan and Govind get grace marks and Brijesh and Eashan get supplementary. Total marks obtained by them are
Chandan: 59+75+46+45+69=294
Govind: 87+75+38+61+71=332
294+332=626
Brijesh: 100+39+42+70+68=319
Eashan: 112+42+32+35+78=299
319+299=618
Difference between the total marks obtained by students receiving grace and students receiving supplementary is
=626-618 =8.
2. Answer: A)
Explanation:
As we know chandan and Govind get grace in mathematics and English respectively,
40% is passing marks for any subject
Passing marks for maths = (40X150) /100=60
chandan gets 59 marks in maths and gets 1 mark grace to pass
Similarly
Passing marks for english = (40X100) /100=40
Govind gets 38 marks in English and gets 2 mark grace to pass
Total marks allotted for grace are 1+2=3.
3. Answer: D)
Explanation:
Student receiving second highest marks is Govind his total is=332
Student receiving third lowest marks is Eashan his total is=299 =332-299 =33
Required percentage =(33/299) X100=11.03% ≈11%
4. Answer: A)
Explanation:
With the help of above table, we can know that, Only Aditya is failing as his overall percentage of marks is less than 50%
5. Answer: E)
Explanation:
Pass percentage= Number of students passed/Total number of students*100
passed student with grace and supplementary exam = 6
so, pass percentage= (6/7) X100=85.71%
Directions (6 – 10): Each of the question 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?
6. What is the age of Radha?
(I) Radha is 5 years younger than Radhe. The product of the age of Radhe 8 years ago (In years) and his age 10 years ago (In years) is 120.
(II) The present age of Radha is the average of the present ages of Riya and Rima. The ratio of the present ages of Riya and Rima is 8:7 and the product of Riya's age 4 years ago (In years) and Rima's age 9 years ago (In years) is 60.
            a)        The data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.
            b)        The data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.
            c)         The data either in Statement I alone or in Statement II alone is sufficient to answer the question.
            d)        The data in both the Statements I and II together are not sufficient to answer the question.
            e)        The data in both the Statements I and II together are necessary to answer the question.
7. What is the length of the train?
(I) The ratio of the time taken by the train to cross a pole to the time taken by the train to cross a bridge of length 30 m with the same speed is 9:10.
(II) Train A having length 140 m less than the length of the given train travels with the speed of 10 m/s less than the speed of the given train. The ratio of time taken by the given train to cross train A by moving in the same direction of train A to the time taken by the given train to cross train A by moving in the opposite direction of train A is 2:1.
            a)        The data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.
            b)        The data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.
            c)         The data either in Statement I alone or in Statement II alone is sufficient to answer the question.
            d)        The data in both the Statements I and II together are not sufficient to answer the question.
            e)        The data in both the Statements I and II together are necessary to answer the question.
8. In how many days will Umesh, Shiva, Kamlesh and Nagesh completes a task working together? (1 day = 12 hours).
(I) Shiva and Kamlesh together complete the task in 6 days 8 hours. Efficiency of Umesh is 50% more than the efficiency of Kamlesh and efficiency of Nagesh is 25% less than the efficiency of Shiva.
(II) Efficiency of Shiva is 25% more than the efficiency of Kamlesh. Number of hours taken by Nagesh alone to complete the task is 72 more than the number of hours taken by Umesh alone to complete the task.
            a)        The data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.
            b)        The data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.
            c)         The data either in Statement I alone or in Statement II alone is sufficient to answer the question.
            d)        The data in both the Statements I and II together are not sufficient to answer the question.
            e)        The data in both the Statements I and II together are necessary to answer the question.
9. What is the initial quantity of pure milk in a 40 litres solution of milk and water?
(I) If 4 litres of solution is removed and 9 litres of milk is added followed by 5 litres of the solution removed and 10 litres of milk is added, then volume of the milk becomes 84% of the volume of the solution.
(II) If 4 litres of the solution is replaced by water, then quantity of the milk left in the solution was 750 ml more than the quantity of milk left in the solution after replacing 5 litres of solution by water.
            a)        The data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.
            b)        The data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.
            c)         The data either in Statement I alone or in Statement II alone is sufficient to answer the question.
            d)        The data in both the Statements I and II together are not sufficient to answer the question.
            e)        The data in both the Statements I and II together are necessary to answer the question.
10. What is the total amount with Nikita?
(I) Nikita invested 60% of the total amount with her at the rate of 12% per annum simple interest and remaining at the rate of 20% per annum compound interest compounded annually for 2 years each. Total interested earned by Nikita was equal to the total interest earned in 2 years on Rs.10000 at the rate of 16% per annum.
(II) Nikita invested some of her amount at the rate of 14% per annum simple interest and remaining at the rate of 18% per annum simple interest. The effective rate of interest of Nikita on total amount is 16.8% per annum.
            a)        The data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.
            b)        The data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.
            c)         The data either in Statement I alone or in Statement II alone is sufficient to answer the question.
            d)        The data in both the Statements I and II together are not sufficient to answer the question.
            e)        The data in both the Statements I and II together are necessary to answer the question.
(6 – 10): Answers with Explanations:
6. Answer: C)
Explanation:
From statement I:
Let Radhe's present age be 'A' years
Age of Radhe 8 years ago = A-8
Age of Radhe 10 years ago = A-10
As per the given statement,
(A-8) x (A-10) = 120
A2 -10A -8A +80 =120
A2 -18A -40 = 0
A2 - 20A +2A -40 = 0
A(A-20) + 2(A-20) =0
A = 20 or A = -2
As age is always positive. So, A =20 years.
Age of Radhe is 20 years.
So, age of Radha = Radhe - 5 = 20 - 5 = 15 years.
Hence the data in statement I alone is sufficient to answer the question.
From statement II:
Let the present ages of Riya and Rima are 8A and 7A respectively.
As product of Riya's age 4 years ago (In years) and Rima's age 9 years ago (In years) is 60.
(8A -4) x (7A-9) =60
56A2 - 72A -28A +36 =60
56A2 - 100A - 24 = 0
14A2 -25A -6 =0
14A2 -28A +3A -6 = 0
A = 2 or A = - 3/14
As age is always positive, So A =2.
So, age of Radha = (16 +14)/2 = 15 years.
So, data in statement II alone is sufficient to answer the question.
7. Answer: A)
Explanation:
From statement I:
Let the length of train be L m and the speed of train be S m/s.
Time taken by the train to cross a pole = (L/S)
Time taken by the train to cross a bridge of length 30 m
= (L +30)/S
Ratio of time taken by the train to cross a pole to the time taken by the train to cross a bridge of length 30 m
= (L/S)/ ((L +30)/S) = (9/10)
10L = 9L +270
L = 270 m.
So, data in statement I alone is sufficient to answer the question.
From statement II:
Let length of the given train be L m.
Let speed of the given train be S m/s.
Time taken by the given train to cross train A by moving in the same direction of train A
= (2L -140)/(S-S+10) = ((2L-140)/10)
Time taken by the given train to cross train A by moving in the opposite direction of train A
= (2L -140)/(S+S-10) = ((2L-140)/(2S-10))
The ratio of time taken by the given train to cross train A by moving in the same direction of train A to the time taken by the given train to cross train A by moving in the opposite direction of train A.
((2L-140)/10)/ (((2L-140)/(2S-10))) = ((2S-10)/10) = 2/1
2S - 10 = 20
S =15 m/s
But we don't have the exact time, so the answer cannot be determined.
So, data in statement II alone is not sufficient to answer the question.
8. Answer: E)
Explanation:
From statement I:
Number of days taken by Shiva and Kamlesh together to complete the task
= 6(8/12) = 6(2/3)
We have efficiencies of Nagesh and Umesh with respective to the efficiencies of Shiva and Kamlesh respectively, but we don't know the exact efficiencies of Shiva and Kamlesh. So data in statement I alone is not sufficient to answer the question.
From statement II:
Let Umesh takes N days to complete the task.
Number of days taken by Nagesh to complete the task
= N + (72/12) = (N +6).
Efficiency of Shiva is 25% more than the efficiency of Kamlesh.
But still data in statement II alone is not sufficient to answer the question.
By combining data from statements I and II together:
Let number of days taken by Shiva to complete the task alone be N
As efficiency of Shiva is 25% more than efficiency of Kamlesh. Kamlesh takes 25% more time than Shiva to complete the task alone.
Task done by Kamlesh and Shiva together in 1 day.
(1/N) + (1/(1.25N)) = (3/20)
(1/N) + ((4/5) x (1/N)) = 0.15
(1.8/N) = 0.15
N = 180/15 = 12
Number of days taken by Kamlesh to complete the task = 1.25 x 12 =15 days.
Efficiency of Umesh is 50% more than the efficiency of Kamlesh
Task done by Umesh in 1 day = 1.5 x (1/15) = (1/10)
Efficiency of Nagesh is 25% less than the efficiency of Shiva
Task done by Nagesh in 1 day = 0.75 x (1/12) = (1/16)
Task done by all the 4 persons in 1 day working together
= (1/10) + (1/12) + (1/15) + (1/16)
So, we can determine the answer by combining data from statements I and II.
9. Answer: C)
Explanation:
From statement I:
Let the initial volume of the pure milk in the solution be V litres.
Water in solution = (40-V) litres.
Milk removed after removing 4 litres of solution
= (V/40) x 4 = (V/10) litres.
Milk left in the solution = V- (V/10) = (0.9V)
Quantity of the milk in the solution after adding 9 litres of the milk
= 9 +0.9V
Milk removed after removing 5 litres of the milk
= ((9 + 0.9V)/45) x 5
= 1 +0.1V
Milk left in the solution = (9 + 0.9V) - (1 +0.1V)
= 8 +0.8V
Final quantity of the milk in the solution = 8 +0.8V +10
18 + 0.8V = 0.84 x 50 = 42
0.8V = 42-18 = 24
V = 30
So, initial volume of the pure milk in the solution was 30 litres. So, data in statement I alone is sufficient to answer the question.
From statement II:
Let initial volume of milk in the solution be V litres.
Quantity of milk left after replacing 4 litres of solution by water
= V x (1- (4/40))
= V x (9/10) = 0.9V
Quantity of milk left after replacing 5 litres of solution by water
= V x (1- (5/40))
= V x (7/8) = 0.875V
As per given,
0.9V - 0.875V = (750/1000) =0.75
0.025V = 0.75
V = 30 litres.
So, data in statement II alone is sufficient to answer the question.
10. Answer: A)
Explanation:
From statement I:
Let the total amount with Nikita be P
60% of the amount invested at 12% per annum simple interest
Interest earned on 60% of the amount = 2 x 0.12 x 0.6P = 0.144P
Total interest earned on 40% of the amount
= (0.4P x (1 + (20/100))2) - 0.4P
= (0.4P) x ((36-25)/25)
= 0.176P
Total interest earned = 0.144P +0.176P = 0.32P
= 0.32P
Total interested earned on Rs. 10000 = 2 x (16/100) x 10000 = 3200
0.32P = 3200
P = Rs.10000.
Hence data in statement I alone is sufficient to answer the question.
From statement II:
According to Alligation rule,
14%                                        18%
16.8%
1.2%                                       2.8%
Hence, we get (12/28) = 3: 7
We got ratio of the amount in different plans, but total amount invested cannot be determined.
So, data in statement II alone is not sufficient to answer the question.