Mathematics Olympiad Model Test Paper - 1 PDF Download

 Page 1


1. Anuj starts walking towards East. After walking  
15 m, he turns towards North. After walking 17 m,  
he turns towards West and walks 10 m. He then turns 
towards South and walks 5 m. How far and in which 
direction is he now from his initial position?
 A. 13 m, North-East
 B. 15 m, South-West
 C. 13 m, North-West
 D. 15 m, South-East
2. Which of the following Venn diagrams best represents 
the relationship amongst, "India, Australia and Pakistan"?
 A.  B. 
 C.  D. 
3. A square transparent sheet with a pattern and a dotted 
line on it is given. Find the figure from the options as 
to how the pattern would appear when the transparent 
sheet is folded along the dotted line.
 A.  B. 
 C.  D. 
4. Which of the following figures completes the given 
figure matrix ?
?
 A. 
       
 B. 
 C.
 
 
D.
 
5. Find the water image of the given combination of 
letters and numbers.
A5MI16AN
 A. 
 B. 
 C. 
 D. 
6. Select the figure from the options which satisfies 
the same condition of placement of the dots as in  
Fig. (X).
 A.  B. 
 C.  D. 
7. Select a figure from the options which will replace 
the (?) to complete the given series.
 A.  B. 
 C.  D. 
LOGICAL  REASONING
Page 2


1. Anuj starts walking towards East. After walking  
15 m, he turns towards North. After walking 17 m,  
he turns towards West and walks 10 m. He then turns 
towards South and walks 5 m. How far and in which 
direction is he now from his initial position?
 A. 13 m, North-East
 B. 15 m, South-West
 C. 13 m, North-West
 D. 15 m, South-East
2. Which of the following Venn diagrams best represents 
the relationship amongst, "India, Australia and Pakistan"?
 A.  B. 
 C.  D. 
3. A square transparent sheet with a pattern and a dotted 
line on it is given. Find the figure from the options as 
to how the pattern would appear when the transparent 
sheet is folded along the dotted line.
 A.  B. 
 C.  D. 
4. Which of the following figures completes the given 
figure matrix ?
?
 A. 
       
 B. 
 C.
 
 
D.
 
5. Find the water image of the given combination of 
letters and numbers.
A5MI16AN
 A. 
 B. 
 C. 
 D. 
6. Select the figure from the options which satisfies 
the same condition of placement of the dots as in  
Fig. (X).
 A.  B. 
 C.  D. 
7. Select a figure from the options which will replace 
the (?) to complete the given series.
 A.  B. 
 C.  D. 
LOGICAL  REASONING
8. Find the missing number, if a certain rule is followed 
either row-wise or column-wise.
 A. 4                 
 B. 5
 C. 6
 D. 8
9. In a certain code language, if DREAM is coded as 
@+?*? and LAND is coded as %*$@, then MEADEN 
is coded as _______.
 A. $?@*??
 B. ?@*?@$
 C. @?*??$
 D. ??*@?$
10. Select a figure from the options, which will complete 
the pattern in given figure.
 A.  B. 
 C.  D. 
11. Find the number of squares formed in the given figure.
 A. 15
 B. 16
 C. 17
 D. 18
12. If the English alphabets are written in the reverse 
order, then which would be the 5
th
 letter to the right 
of the 18
th
 letter from the left end?
 A. G
 B. H
 C. I
 D. D
13. In which of the following figures, Fig. (X) is exactly 
embedded as one of its parts?
 A.  B. 
 C.  D. 
14. There is a certain relationship between figures (i) and 
(ii). Establish a similar relationship between figures 
(iii) and (iv) by selecting a suitable figure from the 
options that will replace the (?) in figure (iv).
 
 A.
 
 
B.
 
 
C.
 
 
D.
 
15. Pointing to a photograph of a man, Neha said,  
"His mother is the only daughter of my mother." 
How is the man in the photograph related to Neha?
 A. Brother-in-Law
 B. Grandson
 C. Nephew
 D. Son
Page 3


1. Anuj starts walking towards East. After walking  
15 m, he turns towards North. After walking 17 m,  
he turns towards West and walks 10 m. He then turns 
towards South and walks 5 m. How far and in which 
direction is he now from his initial position?
 A. 13 m, North-East
 B. 15 m, South-West
 C. 13 m, North-West
 D. 15 m, South-East
2. Which of the following Venn diagrams best represents 
the relationship amongst, "India, Australia and Pakistan"?
 A.  B. 
 C.  D. 
3. A square transparent sheet with a pattern and a dotted 
line on it is given. Find the figure from the options as 
to how the pattern would appear when the transparent 
sheet is folded along the dotted line.
 A.  B. 
 C.  D. 
4. Which of the following figures completes the given 
figure matrix ?
?
 A. 
       
 B. 
 C.
 
 
D.
 
5. Find the water image of the given combination of 
letters and numbers.
A5MI16AN
 A. 
 B. 
 C. 
 D. 
6. Select the figure from the options which satisfies 
the same condition of placement of the dots as in  
Fig. (X).
 A.  B. 
 C.  D. 
7. Select a figure from the options which will replace 
the (?) to complete the given series.
 A.  B. 
 C.  D. 
LOGICAL  REASONING
8. Find the missing number, if a certain rule is followed 
either row-wise or column-wise.
 A. 4                 
 B. 5
 C. 6
 D. 8
9. In a certain code language, if DREAM is coded as 
@+?*? and LAND is coded as %*$@, then MEADEN 
is coded as _______.
 A. $?@*??
 B. ?@*?@$
 C. @?*??$
 D. ??*@?$
10. Select a figure from the options, which will complete 
the pattern in given figure.
 A.  B. 
 C.  D. 
11. Find the number of squares formed in the given figure.
 A. 15
 B. 16
 C. 17
 D. 18
12. If the English alphabets are written in the reverse 
order, then which would be the 5
th
 letter to the right 
of the 18
th
 letter from the left end?
 A. G
 B. H
 C. I
 D. D
13. In which of the following figures, Fig. (X) is exactly 
embedded as one of its parts?
 A.  B. 
 C.  D. 
14. There is a certain relationship between figures (i) and 
(ii). Establish a similar relationship between figures 
(iii) and (iv) by selecting a suitable figure from the 
options that will replace the (?) in figure (iv).
 
 A.
 
 
B.
 
 
C.
 
 
D.
 
15. Pointing to a photograph of a man, Neha said,  
"His mother is the only daughter of my mother." 
How is the man in the photograph related to Neha?
 A. Brother-in-Law
 B. Grandson
 C. Nephew
 D. Son
16. In a triangle, if the sum of the least and the greatest 
angle is equal to twice of the third angle, then find 
the third angle.
 A. 30°
 B. 120°
 C. 60°
 D. 90°
17. In the given figure (not drawn to scale), if AB || CD, 
then find the value of x – y.
 A. 8°
 B. 9°
 C. 12°
 D. 3°
18. Find the value of x. 
6(3x + 2) – 5(6x – 1) = 6 (x – 3) – 5(7x – 6) + 12x
 A. 2
 B. –1
 C. 1
 D. 0
19. Aparna saves ` 500 less than Sumit every month.  
How long will it take Aparna and Sumit to save ` 6600 and  
` 9600 respectively?
 A. 7 months
 B. 6 months
 C. 4 months
 D. 8 months
20. If
  
ab c
89 6
== , then 
 
abc
c
++
 
is equal to _______ . 
 A. 7
 
B.
 
2
1
2
 
C.
 
3
5
6
 
D.
 
3
1
6
21. The given bar graph shows the number of toy bikes 
sold by Robin in 5 days.
If the cost of 1 toy bike is ` 33.60, then how much 
did he earn in 5 days?
 A. ` 9408
 B. ` 9240
 C. ` 8400
 D. ` 8408
22.  Sanjay and Manoj  lent ` 30000 each at 6% per annum 
for a period of 6 years and 10 years respectively. Find 
the difference in interest paid by them.
 A. ` 1080
 B. ` 3600
 C. ` 7200
 D. ` 1800
23. The runs scored by a cricket player in 20 matches 
are given below.
32, 17, 0, 61, 17, 32, 17, 5, 61, 70, 5, 32, 17, 61, 5, 
17, 70, 32, 17, 32
Find the average score of the player.
 A. 45
 B. 30
 C. 35
 D. 40
24. If 3
2x–3
 × 5
4x–1
 = 5
2x+1
 × 3
4x–5
, then x =
 A. – 1
 B. 2
 C. 1
 D. – 2
MATHEMATICAL REASONING
Page 4


1. Anuj starts walking towards East. After walking  
15 m, he turns towards North. After walking 17 m,  
he turns towards West and walks 10 m. He then turns 
towards South and walks 5 m. How far and in which 
direction is he now from his initial position?
 A. 13 m, North-East
 B. 15 m, South-West
 C. 13 m, North-West
 D. 15 m, South-East
2. Which of the following Venn diagrams best represents 
the relationship amongst, "India, Australia and Pakistan"?
 A.  B. 
 C.  D. 
3. A square transparent sheet with a pattern and a dotted 
line on it is given. Find the figure from the options as 
to how the pattern would appear when the transparent 
sheet is folded along the dotted line.
 A.  B. 
 C.  D. 
4. Which of the following figures completes the given 
figure matrix ?
?
 A. 
       
 B. 
 C.
 
 
D.
 
5. Find the water image of the given combination of 
letters and numbers.
A5MI16AN
 A. 
 B. 
 C. 
 D. 
6. Select the figure from the options which satisfies 
the same condition of placement of the dots as in  
Fig. (X).
 A.  B. 
 C.  D. 
7. Select a figure from the options which will replace 
the (?) to complete the given series.
 A.  B. 
 C.  D. 
LOGICAL  REASONING
8. Find the missing number, if a certain rule is followed 
either row-wise or column-wise.
 A. 4                 
 B. 5
 C. 6
 D. 8
9. In a certain code language, if DREAM is coded as 
@+?*? and LAND is coded as %*$@, then MEADEN 
is coded as _______.
 A. $?@*??
 B. ?@*?@$
 C. @?*??$
 D. ??*@?$
10. Select a figure from the options, which will complete 
the pattern in given figure.
 A.  B. 
 C.  D. 
11. Find the number of squares formed in the given figure.
 A. 15
 B. 16
 C. 17
 D. 18
12. If the English alphabets are written in the reverse 
order, then which would be the 5
th
 letter to the right 
of the 18
th
 letter from the left end?
 A. G
 B. H
 C. I
 D. D
13. In which of the following figures, Fig. (X) is exactly 
embedded as one of its parts?
 A.  B. 
 C.  D. 
14. There is a certain relationship between figures (i) and 
(ii). Establish a similar relationship between figures 
(iii) and (iv) by selecting a suitable figure from the 
options that will replace the (?) in figure (iv).
 
 A.
 
 
B.
 
 
C.
 
 
D.
 
15. Pointing to a photograph of a man, Neha said,  
"His mother is the only daughter of my mother." 
How is the man in the photograph related to Neha?
 A. Brother-in-Law
 B. Grandson
 C. Nephew
 D. Son
16. In a triangle, if the sum of the least and the greatest 
angle is equal to twice of the third angle, then find 
the third angle.
 A. 30°
 B. 120°
 C. 60°
 D. 90°
17. In the given figure (not drawn to scale), if AB || CD, 
then find the value of x – y.
 A. 8°
 B. 9°
 C. 12°
 D. 3°
18. Find the value of x. 
6(3x + 2) – 5(6x – 1) = 6 (x – 3) – 5(7x – 6) + 12x
 A. 2
 B. –1
 C. 1
 D. 0
19. Aparna saves ` 500 less than Sumit every month.  
How long will it take Aparna and Sumit to save ` 6600 and  
` 9600 respectively?
 A. 7 months
 B. 6 months
 C. 4 months
 D. 8 months
20. If
  
ab c
89 6
== , then 
 
abc
c
++
 
is equal to _______ . 
 A. 7
 
B.
 
2
1
2
 
C.
 
3
5
6
 
D.
 
3
1
6
21. The given bar graph shows the number of toy bikes 
sold by Robin in 5 days.
If the cost of 1 toy bike is ` 33.60, then how much 
did he earn in 5 days?
 A. ` 9408
 B. ` 9240
 C. ` 8400
 D. ` 8408
22.  Sanjay and Manoj  lent ` 30000 each at 6% per annum 
for a period of 6 years and 10 years respectively. Find 
the difference in interest paid by them.
 A. ` 1080
 B. ` 3600
 C. ` 7200
 D. ` 1800
23. The runs scored by a cricket player in 20 matches 
are given below.
32, 17, 0, 61, 17, 32, 17, 5, 61, 70, 5, 32, 17, 61, 5, 
17, 70, 32, 17, 32
Find the average score of the player.
 A. 45
 B. 30
 C. 35
 D. 40
24. If 3
2x–3
 × 5
4x–1
 = 5
2x+1
 × 3
4x–5
, then x =
 A. – 1
 B. 2
 C. 1
 D. – 2
MATHEMATICAL REASONING
25. Out of 100 beads, there are 43 red beads, 23 blue 
beads and the rest are yellow. Find the percentage 
of yellow beads.
 A. 33%
 B. 34%
 C 32%
 D. 35%
26. If 20% of x = y, then y% of 20 is same as ______. 
 
A.
 
x
25
 B.  x
 
C.
 
x
2
 D. None of these
27. In a 3 kg fruit cake, 750 gm of dry fruits was used. 
What is the percentage of the weight of dry fruits 
used in the cake?
 A. 75%
 B. 25%
 C. 37
1
2
%
 D. 30%
28. Simplify :
 
1
3
3
4
2
5
1
3
1
2
3
3
4
1
4
4
5
+-
?
?
?
?
?
?
-    of of
.
 
 
A. 
1
63
 
B. 
23
40
 
C.
 
23
55
 
D. 
23
63
29. The given figure is divided into equal squares. How 
many squares should be shaded to show 40% of the 
whole figure shaded?
 A. 3
 B. 7
 C. 14
 D. 5
30. Which of the following statement do not hold in the 
process of solving the equation 15 + 3x = 3?
 A. 3x = 3 – 15 
 B. 15 – 3 = – 3x
 
C.
 
15
3
3
3 +=
x
 
 
D.
 
15
3
3
3
3
3
+=
x
31. Which of the following is the top view of the given 
solid?
A.
 
B. 
 
C. 
 D.
 
32. Arrange the following numbers in the ascending order.
1
4
6
7
3
5
5
10
2
7
,, ,,
-- -
 A.  
-- - 5
10
2
7
3
5
1
4
6
7
,, ,,
 
 B. 
-- - 3
5
5
10
2
7
1
4
6
7
,, ,,
 C. 
1
4
6
7
5
10
2
7
3
5
,, ,,
-- -
 
 D. 
-- - 2
7
3
5
5
10
1
4
6
7
,, ,,
33. If lines AB, AC, AD and AE are parallel to a line l, 
then _____ .
 A. A, B, C, D and E are collinear points.
 B. A, B, C, D and E are non-collinear points.
 C. Lines AB and AC are parallel and lines AD and 
AE are perpendicular.
 D. None of these
Page 5


1. Anuj starts walking towards East. After walking  
15 m, he turns towards North. After walking 17 m,  
he turns towards West and walks 10 m. He then turns 
towards South and walks 5 m. How far and in which 
direction is he now from his initial position?
 A. 13 m, North-East
 B. 15 m, South-West
 C. 13 m, North-West
 D. 15 m, South-East
2. Which of the following Venn diagrams best represents 
the relationship amongst, "India, Australia and Pakistan"?
 A.  B. 
 C.  D. 
3. A square transparent sheet with a pattern and a dotted 
line on it is given. Find the figure from the options as 
to how the pattern would appear when the transparent 
sheet is folded along the dotted line.
 A.  B. 
 C.  D. 
4. Which of the following figures completes the given 
figure matrix ?
?
 A. 
       
 B. 
 C.
 
 
D.
 
5. Find the water image of the given combination of 
letters and numbers.
A5MI16AN
 A. 
 B. 
 C. 
 D. 
6. Select the figure from the options which satisfies 
the same condition of placement of the dots as in  
Fig. (X).
 A.  B. 
 C.  D. 
7. Select a figure from the options which will replace 
the (?) to complete the given series.
 A.  B. 
 C.  D. 
LOGICAL  REASONING
8. Find the missing number, if a certain rule is followed 
either row-wise or column-wise.
 A. 4                 
 B. 5
 C. 6
 D. 8
9. In a certain code language, if DREAM is coded as 
@+?*? and LAND is coded as %*$@, then MEADEN 
is coded as _______.
 A. $?@*??
 B. ?@*?@$
 C. @?*??$
 D. ??*@?$
10. Select a figure from the options, which will complete 
the pattern in given figure.
 A.  B. 
 C.  D. 
11. Find the number of squares formed in the given figure.
 A. 15
 B. 16
 C. 17
 D. 18
12. If the English alphabets are written in the reverse 
order, then which would be the 5
th
 letter to the right 
of the 18
th
 letter from the left end?
 A. G
 B. H
 C. I
 D. D
13. In which of the following figures, Fig. (X) is exactly 
embedded as one of its parts?
 A.  B. 
 C.  D. 
14. There is a certain relationship between figures (i) and 
(ii). Establish a similar relationship between figures 
(iii) and (iv) by selecting a suitable figure from the 
options that will replace the (?) in figure (iv).
 
 A.
 
 
B.
 
 
C.
 
 
D.
 
15. Pointing to a photograph of a man, Neha said,  
"His mother is the only daughter of my mother." 
How is the man in the photograph related to Neha?
 A. Brother-in-Law
 B. Grandson
 C. Nephew
 D. Son
16. In a triangle, if the sum of the least and the greatest 
angle is equal to twice of the third angle, then find 
the third angle.
 A. 30°
 B. 120°
 C. 60°
 D. 90°
17. In the given figure (not drawn to scale), if AB || CD, 
then find the value of x – y.
 A. 8°
 B. 9°
 C. 12°
 D. 3°
18. Find the value of x. 
6(3x + 2) – 5(6x – 1) = 6 (x – 3) – 5(7x – 6) + 12x
 A. 2
 B. –1
 C. 1
 D. 0
19. Aparna saves ` 500 less than Sumit every month.  
How long will it take Aparna and Sumit to save ` 6600 and  
` 9600 respectively?
 A. 7 months
 B. 6 months
 C. 4 months
 D. 8 months
20. If
  
ab c
89 6
== , then 
 
abc
c
++
 
is equal to _______ . 
 A. 7
 
B.
 
2
1
2
 
C.
 
3
5
6
 
D.
 
3
1
6
21. The given bar graph shows the number of toy bikes 
sold by Robin in 5 days.
If the cost of 1 toy bike is ` 33.60, then how much 
did he earn in 5 days?
 A. ` 9408
 B. ` 9240
 C. ` 8400
 D. ` 8408
22.  Sanjay and Manoj  lent ` 30000 each at 6% per annum 
for a period of 6 years and 10 years respectively. Find 
the difference in interest paid by them.
 A. ` 1080
 B. ` 3600
 C. ` 7200
 D. ` 1800
23. The runs scored by a cricket player in 20 matches 
are given below.
32, 17, 0, 61, 17, 32, 17, 5, 61, 70, 5, 32, 17, 61, 5, 
17, 70, 32, 17, 32
Find the average score of the player.
 A. 45
 B. 30
 C. 35
 D. 40
24. If 3
2x–3
 × 5
4x–1
 = 5
2x+1
 × 3
4x–5
, then x =
 A. – 1
 B. 2
 C. 1
 D. – 2
MATHEMATICAL REASONING
25. Out of 100 beads, there are 43 red beads, 23 blue 
beads and the rest are yellow. Find the percentage 
of yellow beads.
 A. 33%
 B. 34%
 C 32%
 D. 35%
26. If 20% of x = y, then y% of 20 is same as ______. 
 
A.
 
x
25
 B.  x
 
C.
 
x
2
 D. None of these
27. In a 3 kg fruit cake, 750 gm of dry fruits was used. 
What is the percentage of the weight of dry fruits 
used in the cake?
 A. 75%
 B. 25%
 C. 37
1
2
%
 D. 30%
28. Simplify :
 
1
3
3
4
2
5
1
3
1
2
3
3
4
1
4
4
5
+-
?
?
?
?
?
?
-    of of
.
 
 
A. 
1
63
 
B. 
23
40
 
C.
 
23
55
 
D. 
23
63
29. The given figure is divided into equal squares. How 
many squares should be shaded to show 40% of the 
whole figure shaded?
 A. 3
 B. 7
 C. 14
 D. 5
30. Which of the following statement do not hold in the 
process of solving the equation 15 + 3x = 3?
 A. 3x = 3 – 15 
 B. 15 – 3 = – 3x
 
C.
 
15
3
3
3 +=
x
 
 
D.
 
15
3
3
3
3
3
+=
x
31. Which of the following is the top view of the given 
solid?
A.
 
B. 
 
C. 
 D.
 
32. Arrange the following numbers in the ascending order.
1
4
6
7
3
5
5
10
2
7
,, ,,
-- -
 A.  
-- - 5
10
2
7
3
5
1
4
6
7
,, ,,
 
 B. 
-- - 3
5
5
10
2
7
1
4
6
7
,, ,,
 C. 
1
4
6
7
5
10
2
7
3
5
,, ,,
-- -
 
 D. 
-- - 2
7
3
5
5
10
1
4
6
7
,, ,,
33. If lines AB, AC, AD and AE are parallel to a line l, 
then _____ .
 A. A, B, C, D and E are collinear points.
 B. A, B, C, D and E are non-collinear points.
 C. Lines AB and AC are parallel and lines AD and 
AE are perpendicular.
 D. None of these
34. In the given figure (not drawn to scale), if AB = AC, 
then find the value of x.
 A. 80° B. 70°
 C. 60° D. 110°
35. Select the correct option.
 Exponent Base Value
 A.  3
5
 3  87
 B.  2
4
 5  32
 C.  4
2
 4  16
 D.  5
2
 5  125
36. In an examination, Ramesh was asked to find
 
3
14
 
of a certain number. By mistake, he found
 
3
4
of that
 
number. His answer was 50 more than the correct 
answer. The number is ______.
 A. 93
1
3
 B. 93
1
7
 C. 
95
1
3
 D. 95
1
5
37. Anita runs around a circular field of radius 50 metres.   
How much distance did she cover in 3 complete 
rounds? [Use p = 3.14]
 A. 6600 m
 B. 942 m
 C. 150 m
 D. 1043 m
38. If 18 girls consume 5 kg of rice in a day, then how 
much quantity of rice will be consumed by 27 girls 
in a day?
 A. 8 kg
 B. 12 kg
 C. 5.9 kg
 D. 7.5 kg
39. A shopkeeper sells two televisions for ` 1955 each, 
gaining 15% on one and losing 15% on other. Find 
his gain or loss percent in the whole transaction.
 A. Profit, 2
1
4
% B. Profit, 3%
 C. Loss, 
2
1
4
%
 D. Loss, 3%
40. Salaries of Raman and Mayank are in the ratio  
2 : 3. If the salary of each is increased by ` 4000, 
then new ratio becomes 40 : 57. What is Mayank's 
present salary approximately?
 A. ` 17,000
 B. ` 20,000
 C. ` 25,500
 D. ` 38,000
41. Mrs Kirti bought 6 oranges at 3 for ` 1.00, 
1
2
kg of 
potatoes at ` 15.00 per kilogram and a fish weighs 
5
7
kg at  ` 7 per kilogram. How much amount would 
she receive, if she gave ` 50 to the cashier?
 A. ` 35.50
 B. ` 37.50
 C. ` 33.50
 D. ` 39.50
42. Priya invests 
1
3
 of her capital at 7% p.a., 
1
4
 at 8% p.a. 
and the remainder at 10% p.a. If her annual income 
is ` 561, then find the capital.
 A. ` 5400
 B. ` 6000
 C. ` 6600
 D. ` 7200
43. 270 students appeared for an examination, out of 
which 252 passed. What is the percentage of pass 
students?
 A. 80%
 
B.
 
83
1
2
%
 
C.
 
90
1
3
%
 
D.
 
93
1
3
%
EVERYDAY MATHEMATICS