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Page 1
1
FOUNDATION COURSE
MOCK TEST PAPER
PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS
Time Allowed 2 Hours Maximum Marks: 100
QUESTIONS
PART A: BUSINESS MATHEMATICS AND LOGICAL REASONING
1. The ratio compounded of 2:3, 9:4, 5:6 and 8: 10 is
(a) 1: 1
(b) 1:5
(c) 3: 8
(d) none of these
2. The sub-triplicate ratio of 8: 27
(a) 27: 8
(b) 24: 81
(c) 2: 3
(d) none of these
3. If
p r p r
q s q s
?
??
?
, the process is called
(a) Subtrahendo
(b) Componendo
(c) Alternendo
(d) none of these
4. The value of
? ? ? ? ? ?
2 2 2 2 2 2
a ab b b bc c c ca a
a b c
b c a
x x x
x x x
? ? ? ? ? ?
? ? ? ? ? ?
??
? ? ? ? ? ?
? ? ? ? ? ?
(a) 1
(b) 0
(c) -1
(d) none of these
5. If a =
12
log 24 , b =
36
log 24 , b =
48
log 36 then prove that 1 + abc =
(a) 2bc
(b) 2ca
(c) 2ba
(d) 3bc
6. If x = 5
1/3
+ 5
-1/3
, 5x
3
-15x is given by
(a) 25
© The Institute of Chartered Accountants of India
Page 2
1
FOUNDATION COURSE
MOCK TEST PAPER
PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS
Time Allowed 2 Hours Maximum Marks: 100
QUESTIONS
PART A: BUSINESS MATHEMATICS AND LOGICAL REASONING
1. The ratio compounded of 2:3, 9:4, 5:6 and 8: 10 is
(a) 1: 1
(b) 1:5
(c) 3: 8
(d) none of these
2. The sub-triplicate ratio of 8: 27
(a) 27: 8
(b) 24: 81
(c) 2: 3
(d) none of these
3. If
p r p r
q s q s
?
??
?
, the process is called
(a) Subtrahendo
(b) Componendo
(c) Alternendo
(d) none of these
4. The value of
? ? ? ? ? ?
2 2 2 2 2 2
a ab b b bc c c ca a
a b c
b c a
x x x
x x x
? ? ? ? ? ?
? ? ? ? ? ?
??
? ? ? ? ? ?
? ? ? ? ? ?
(a) 1
(b) 0
(c) -1
(d) none of these
5. If a =
12
log 24 , b =
36
log 24 , b =
48
log 36 then prove that 1 + abc =
(a) 2bc
(b) 2ca
(c) 2ba
(d) 3bc
6. If x = 5
1/3
+ 5
-1/3
, 5x
3
-15x is given by
(a) 25
© The Institute of Chartered Accountants of India
2
(b) 26
(c) 27
(d) 30
7. Ten years ago the age of a father was four times his son. Ten years hence the age of the father will be twice
that of his son. The present age of the father and the son are
(a) (50, 20)
(b) (60, 20)
(c) (55, 25)
(d) none of these
8. When two roots of quadratic equations are a and
1
?
then what will be quadratic equation.
(a) a x
2
-(a
2
+1) x + a = 0
(b) a x
2
- a
2
x + a = 0
(c) a x
2
+
(a
2
+1) x + a = 0
(d) none of these
(9) Let a and ß be the roots of equation x
2
+7 x + 12 = 0. Then the value of
22
aß
+
ßa
??
??
??
will be
(a)
49 144
144 49
+
??
??
??
(b)
7 12
12 7
+
??
??
??
(c)
91
12
??
?
??
??
(d) none of these
10. If A =
52
13
? ??
??
?
??
, then Adjoint of Matrix A
(a)
32
15
? ??
??
?
??
(b)
52
13
??
??
?
??
(c)
32
15
? ??
??
??
(d)
32
15
??
??
??
© The Institute of Chartered Accountants of India
Page 3
1
FOUNDATION COURSE
MOCK TEST PAPER
PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS
Time Allowed 2 Hours Maximum Marks: 100
QUESTIONS
PART A: BUSINESS MATHEMATICS AND LOGICAL REASONING
1. The ratio compounded of 2:3, 9:4, 5:6 and 8: 10 is
(a) 1: 1
(b) 1:5
(c) 3: 8
(d) none of these
2. The sub-triplicate ratio of 8: 27
(a) 27: 8
(b) 24: 81
(c) 2: 3
(d) none of these
3. If
p r p r
q s q s
?
??
?
, the process is called
(a) Subtrahendo
(b) Componendo
(c) Alternendo
(d) none of these
4. The value of
? ? ? ? ? ?
2 2 2 2 2 2
a ab b b bc c c ca a
a b c
b c a
x x x
x x x
? ? ? ? ? ?
? ? ? ? ? ?
??
? ? ? ? ? ?
? ? ? ? ? ?
(a) 1
(b) 0
(c) -1
(d) none of these
5. If a =
12
log 24 , b =
36
log 24 , b =
48
log 36 then prove that 1 + abc =
(a) 2bc
(b) 2ca
(c) 2ba
(d) 3bc
6. If x = 5
1/3
+ 5
-1/3
, 5x
3
-15x is given by
(a) 25
© The Institute of Chartered Accountants of India
2
(b) 26
(c) 27
(d) 30
7. Ten years ago the age of a father was four times his son. Ten years hence the age of the father will be twice
that of his son. The present age of the father and the son are
(a) (50, 20)
(b) (60, 20)
(c) (55, 25)
(d) none of these
8. When two roots of quadratic equations are a and
1
?
then what will be quadratic equation.
(a) a x
2
-(a
2
+1) x + a = 0
(b) a x
2
- a
2
x + a = 0
(c) a x
2
+
(a
2
+1) x + a = 0
(d) none of these
(9) Let a and ß be the roots of equation x
2
+7 x + 12 = 0. Then the value of
22
aß
+
ßa
??
??
??
will be
(a)
49 144
144 49
+
??
??
??
(b)
7 12
12 7
+
??
??
??
(c)
91
12
??
?
??
??
(d) none of these
10. If A =
52
13
? ??
??
?
??
, then Adjoint of Matrix A
(a)
32
15
? ??
??
?
??
(b)
52
13
??
??
?
??
(c)
32
15
? ??
??
??
(d)
32
15
??
??
??
© The Institute of Chartered Accountants of India
3
11. If A =
5
0
x
y
??
??
??
and A = A
T
, then
(a) x = 0, y = 5
(b) x = y
(c) x + y = 5
(d) none of these
12. If A =
23
2
ii
ii
??
??
??
(here i
2
= -1) then A =
(a) 2
(b) 8
(c) 4
(d) 5
13. On solving the inequalities 5x + y =100, x + y = 60, x = 0 and y = 0, we get the following situation.
(a) (0, 0), (20, 0), (10, 50) and (0,60)
(b) (0, 0), (60, 0), (10, 50) and (0,60)
(c) (0, 0), (20, 0), (0, 100) and (10,50)
(d) none of these
14. A certain money doubles itself in 10 years when deposited on simple interest. It would triple itself in
(a) 30 years
(b) 20 years
(c) 25 years
(d) 15 years
15. A man deposited Rs. 8, 000 in a bank for 3 years at 5% per annum compound interest, after 3 years he will
get
(a) Rs. 9,000
(b) Rs.8, 800
(c) Rs. 9,200
(d) Rs. 9261
16. The effective rate of interest for one year corresponding to a nominal at 7% rate of interest per annum
convertible quarterly is
(a) Rs. 240
(b) Rs. 200
(c) Rs.220
(d) Rs.210
17. The value of furniture depreciates by 10% a year, if the present value of the furniture in an office is Rs. 21870,
calculate the value of furniture 3 years ago.
(a) Rs. 30,000
(b) Rs. 35,000
© The Institute of Chartered Accountants of India
Page 4
1
FOUNDATION COURSE
MOCK TEST PAPER
PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS
Time Allowed 2 Hours Maximum Marks: 100
QUESTIONS
PART A: BUSINESS MATHEMATICS AND LOGICAL REASONING
1. The ratio compounded of 2:3, 9:4, 5:6 and 8: 10 is
(a) 1: 1
(b) 1:5
(c) 3: 8
(d) none of these
2. The sub-triplicate ratio of 8: 27
(a) 27: 8
(b) 24: 81
(c) 2: 3
(d) none of these
3. If
p r p r
q s q s
?
??
?
, the process is called
(a) Subtrahendo
(b) Componendo
(c) Alternendo
(d) none of these
4. The value of
? ? ? ? ? ?
2 2 2 2 2 2
a ab b b bc c c ca a
a b c
b c a
x x x
x x x
? ? ? ? ? ?
? ? ? ? ? ?
??
? ? ? ? ? ?
? ? ? ? ? ?
(a) 1
(b) 0
(c) -1
(d) none of these
5. If a =
12
log 24 , b =
36
log 24 , b =
48
log 36 then prove that 1 + abc =
(a) 2bc
(b) 2ca
(c) 2ba
(d) 3bc
6. If x = 5
1/3
+ 5
-1/3
, 5x
3
-15x is given by
(a) 25
© The Institute of Chartered Accountants of India
2
(b) 26
(c) 27
(d) 30
7. Ten years ago the age of a father was four times his son. Ten years hence the age of the father will be twice
that of his son. The present age of the father and the son are
(a) (50, 20)
(b) (60, 20)
(c) (55, 25)
(d) none of these
8. When two roots of quadratic equations are a and
1
?
then what will be quadratic equation.
(a) a x
2
-(a
2
+1) x + a = 0
(b) a x
2
- a
2
x + a = 0
(c) a x
2
+
(a
2
+1) x + a = 0
(d) none of these
(9) Let a and ß be the roots of equation x
2
+7 x + 12 = 0. Then the value of
22
aß
+
ßa
??
??
??
will be
(a)
49 144
144 49
+
??
??
??
(b)
7 12
12 7
+
??
??
??
(c)
91
12
??
?
??
??
(d) none of these
10. If A =
52
13
? ??
??
?
??
, then Adjoint of Matrix A
(a)
32
15
? ??
??
?
??
(b)
52
13
??
??
?
??
(c)
32
15
? ??
??
??
(d)
32
15
??
??
??
© The Institute of Chartered Accountants of India
3
11. If A =
5
0
x
y
??
??
??
and A = A
T
, then
(a) x = 0, y = 5
(b) x = y
(c) x + y = 5
(d) none of these
12. If A =
23
2
ii
ii
??
??
??
(here i
2
= -1) then A =
(a) 2
(b) 8
(c) 4
(d) 5
13. On solving the inequalities 5x + y =100, x + y = 60, x = 0 and y = 0, we get the following situation.
(a) (0, 0), (20, 0), (10, 50) and (0,60)
(b) (0, 0), (60, 0), (10, 50) and (0,60)
(c) (0, 0), (20, 0), (0, 100) and (10,50)
(d) none of these
14. A certain money doubles itself in 10 years when deposited on simple interest. It would triple itself in
(a) 30 years
(b) 20 years
(c) 25 years
(d) 15 years
15. A man deposited Rs. 8, 000 in a bank for 3 years at 5% per annum compound interest, after 3 years he will
get
(a) Rs. 9,000
(b) Rs.8, 800
(c) Rs. 9,200
(d) Rs. 9261
16. The effective rate of interest for one year corresponding to a nominal at 7% rate of interest per annum
convertible quarterly is
(a) Rs. 240
(b) Rs. 200
(c) Rs.220
(d) Rs.210
17. The value of furniture depreciates by 10% a year, if the present value of the furniture in an office is Rs. 21870,
calculate the value of furniture 3 years ago.
(a) Rs. 30,000
(b) Rs. 35,000
© The Institute of Chartered Accountants of India
4
(c) Rs. 40,000
(d) Rs. 45,000
18. The population of a town increases every year by 2 % of the population beginning of that year. The number
of years by which the total increase of population be 40% is
(a) 7 years
(b) 10 years
(c) 17 years (approximately)
(d) none of these
19. Find the future value of an annuity of Rs. 500 made annually for 7 years at interest rate of 14 % per annum
[Given that (1.14)
7
= 2.5023]
(a) Rs. 5365.35
(b) Rs. 5000
(c) Rs. 5325.65
(d) Rs.6000.35
20. Rs. 200 invested at the end of each month in an account paying interest 6% per year compounded monthly .
What is the future value of this annuity after 10
th
payment? [Given that (1.005)
10
= 1.0511]
(a) Rs. 2045
(b) Rs.5055
(c) Rs.2044
(d) Rs.2065
21. Suppose your father decides to gift you Rs. 10,000 every year starting from today for the next five years, you
deposit this amount in a bank as and when you receive and get 10% per annum interest rate compounded
annually. What is the present value of this annuity? ( P(4, 0.10) = 3.16987)
(a) Rs.41,698.70
(b) Rs.45,698.70
(c) Rs.42,698.70
(d) Rs.43,698.70
22. Nominal Rate of Return =
(a) Real Rate of Return – Inflation
(b) Real Rate of Return + Inflation
(c) Inflation -Real Rate of return
(d) None of the above
23. Net Present Value (NPV)
(a) Present value of net cash Inflow – Total net Investment
(b) Present value of net cash Inflow – Present value of cash outflow
(c) Total net Investment- Present value of net cash Inflow
(d) a or b
24. The annual birth rates per 1,000 are 39.4 and 19.4 respectively. The number of years which the population
will be doubled assuming there is no immigration or emigration is
(a) 35 years
© The Institute of Chartered Accountants of India
Page 5
1
FOUNDATION COURSE
MOCK TEST PAPER
PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS
Time Allowed 2 Hours Maximum Marks: 100
QUESTIONS
PART A: BUSINESS MATHEMATICS AND LOGICAL REASONING
1. The ratio compounded of 2:3, 9:4, 5:6 and 8: 10 is
(a) 1: 1
(b) 1:5
(c) 3: 8
(d) none of these
2. The sub-triplicate ratio of 8: 27
(a) 27: 8
(b) 24: 81
(c) 2: 3
(d) none of these
3. If
p r p r
q s q s
?
??
?
, the process is called
(a) Subtrahendo
(b) Componendo
(c) Alternendo
(d) none of these
4. The value of
? ? ? ? ? ?
2 2 2 2 2 2
a ab b b bc c c ca a
a b c
b c a
x x x
x x x
? ? ? ? ? ?
? ? ? ? ? ?
??
? ? ? ? ? ?
? ? ? ? ? ?
(a) 1
(b) 0
(c) -1
(d) none of these
5. If a =
12
log 24 , b =
36
log 24 , b =
48
log 36 then prove that 1 + abc =
(a) 2bc
(b) 2ca
(c) 2ba
(d) 3bc
6. If x = 5
1/3
+ 5
-1/3
, 5x
3
-15x is given by
(a) 25
© The Institute of Chartered Accountants of India
2
(b) 26
(c) 27
(d) 30
7. Ten years ago the age of a father was four times his son. Ten years hence the age of the father will be twice
that of his son. The present age of the father and the son are
(a) (50, 20)
(b) (60, 20)
(c) (55, 25)
(d) none of these
8. When two roots of quadratic equations are a and
1
?
then what will be quadratic equation.
(a) a x
2
-(a
2
+1) x + a = 0
(b) a x
2
- a
2
x + a = 0
(c) a x
2
+
(a
2
+1) x + a = 0
(d) none of these
(9) Let a and ß be the roots of equation x
2
+7 x + 12 = 0. Then the value of
22
aß
+
ßa
??
??
??
will be
(a)
49 144
144 49
+
??
??
??
(b)
7 12
12 7
+
??
??
??
(c)
91
12
??
?
??
??
(d) none of these
10. If A =
52
13
? ??
??
?
??
, then Adjoint of Matrix A
(a)
32
15
? ??
??
?
??
(b)
52
13
??
??
?
??
(c)
32
15
? ??
??
??
(d)
32
15
??
??
??
© The Institute of Chartered Accountants of India
3
11. If A =
5
0
x
y
??
??
??
and A = A
T
, then
(a) x = 0, y = 5
(b) x = y
(c) x + y = 5
(d) none of these
12. If A =
23
2
ii
ii
??
??
??
(here i
2
= -1) then A =
(a) 2
(b) 8
(c) 4
(d) 5
13. On solving the inequalities 5x + y =100, x + y = 60, x = 0 and y = 0, we get the following situation.
(a) (0, 0), (20, 0), (10, 50) and (0,60)
(b) (0, 0), (60, 0), (10, 50) and (0,60)
(c) (0, 0), (20, 0), (0, 100) and (10,50)
(d) none of these
14. A certain money doubles itself in 10 years when deposited on simple interest. It would triple itself in
(a) 30 years
(b) 20 years
(c) 25 years
(d) 15 years
15. A man deposited Rs. 8, 000 in a bank for 3 years at 5% per annum compound interest, after 3 years he will
get
(a) Rs. 9,000
(b) Rs.8, 800
(c) Rs. 9,200
(d) Rs. 9261
16. The effective rate of interest for one year corresponding to a nominal at 7% rate of interest per annum
convertible quarterly is
(a) Rs. 240
(b) Rs. 200
(c) Rs.220
(d) Rs.210
17. The value of furniture depreciates by 10% a year, if the present value of the furniture in an office is Rs. 21870,
calculate the value of furniture 3 years ago.
(a) Rs. 30,000
(b) Rs. 35,000
© The Institute of Chartered Accountants of India
4
(c) Rs. 40,000
(d) Rs. 45,000
18. The population of a town increases every year by 2 % of the population beginning of that year. The number
of years by which the total increase of population be 40% is
(a) 7 years
(b) 10 years
(c) 17 years (approximately)
(d) none of these
19. Find the future value of an annuity of Rs. 500 made annually for 7 years at interest rate of 14 % per annum
[Given that (1.14)
7
= 2.5023]
(a) Rs. 5365.35
(b) Rs. 5000
(c) Rs. 5325.65
(d) Rs.6000.35
20. Rs. 200 invested at the end of each month in an account paying interest 6% per year compounded monthly .
What is the future value of this annuity after 10
th
payment? [Given that (1.005)
10
= 1.0511]
(a) Rs. 2045
(b) Rs.5055
(c) Rs.2044
(d) Rs.2065
21. Suppose your father decides to gift you Rs. 10,000 every year starting from today for the next five years, you
deposit this amount in a bank as and when you receive and get 10% per annum interest rate compounded
annually. What is the present value of this annuity? ( P(4, 0.10) = 3.16987)
(a) Rs.41,698.70
(b) Rs.45,698.70
(c) Rs.42,698.70
(d) Rs.43,698.70
22. Nominal Rate of Return =
(a) Real Rate of Return – Inflation
(b) Real Rate of Return + Inflation
(c) Inflation -Real Rate of return
(d) None of the above
23. Net Present Value (NPV)
(a) Present value of net cash Inflow – Total net Investment
(b) Present value of net cash Inflow – Present value of cash outflow
(c) Total net Investment- Present value of net cash Inflow
(d) a or b
24. The annual birth rates per 1,000 are 39.4 and 19.4 respectively. The number of years which the population
will be doubled assuming there is no immigration or emigration is
(a) 35 years
© The Institute of Chartered Accountants of India
5
(b) 30 years
(c) 25 years
(d) none of these
25. Y bought Motor Bike Costing 80,000 by making down payment of Rs. 30000 and agreeing to make annual
payment for four years. How much would be each payment if the interest on unpaid amount be 14%
compounded annually. [Given P (4, 0.14) = 2.91371]
(a) Rs. 17160.25
(b) Rs. 17600.25
(c) Rs.15600.25
(d) Rs. 16600.25
26. The value of K, for which the terms 7K +3, 4K-5, 2K+10 are in A.P., is
(a) 13
(b) - 23
(c) 13
(d) 23
27. If A = {1,2,3,4} and B = {1,4,9,16,25} is a function of f is defined set A to B where f(x) = x
2
then the range of f
is
(a) {1,2,3,4}
(b) {1,4,9,16}
(c) {1,4,9,16, 25}
(d) none of these
28. If
n
P r = 336 and
n
Cr = 56, then n and r will be
(a) (3,2)
(b) (8, 3)
(c) (7, 4)
(d) none of these
29. If A = {1,2,3,4,5,6,7} and B = {2,4,6} Cardinal number of AUB
(a) 3
(b) 16
(c) 5
(d) 7
30. In how many ways the letters of the word ‘ARRANGE’ be arranged?
(a) 1,200
(b) 1,250
(c) 1,260
(d) 1,300
31. The number of ways in which 8 examination papers be arranged so that the best and worst papers never
come together.
(a) 8! - 2× 7!
© The Institute of Chartered Accountants of India
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FAQs on Quantitative Aptitude Sample Paper Series - I - Mock Tests & Past Year Papers for CA Foundation
| 1. What is the CA Foundation exam and how can I apply for it? |  |
Ans. The CA Foundation exam is an entry-level exam for students who wish to pursue a career in Chartered Accountancy. To apply for the exam, candidates need to register with the Institute of Chartered Accountants of India (ICAI) by filling out the application form available on the ICAI website. The application process is online, and candidates need to submit the required documents along with the application fee to complete the registration process.
| 2. What is the syllabus for the CA Foundation exam? | |
Ans. The CA Foundation exam has four papers, namely Principles and Practice of Accounting, Business Laws and Business Correspondence and Reporting, Business Mathematics and Logical Reasoning & Statistics, and Business Economics and Business and Commercial Knowledge. The syllabus for each paper is available on the ICAI website, and candidates are advised to go through it thoroughly before starting their preparation.
| 3. What is the format of the CA Foundation exam? | |
Ans. The CA Foundation exam is conducted in online mode, and the duration of each paper is three hours. The exam consists of multiple-choice questions (MCQs) and subjective questions. Candidates need to answer all the questions within the stipulated time, and there is no negative marking for incorrect answers.
| 4. How should I prepare for the CA Foundation exam? | |
Ans. To prepare for the CA Foundation exam, candidates need to focus on understanding the concepts and practicing questions regularly. They can refer to the study material provided by ICAI and also use reference books and online resources for additional practice. It is also important to manage time effectively and revise the topics regularly.
| 5. What is the passing criteria for the CA Foundation exam? | |
Ans. To pass the CA Foundation exam, candidates need to score a minimum of 40% marks in each paper and 50% marks in aggregate of all papers. The result of the exam is declared within two months of the exam date, and candidates can check their result on the ICAI website.
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