Mathematics Olympiad Model Test Paper - 3

``` Page 1

Logical Reasoning
1. Select the incorrect number in the given number pattern: 1 5 9 17 25 37 50 65.
Options:
A. 9
B. 17
C. 50
D. 65
Solution: The pattern increases by odd numbers incrementally (4, 4, 8, 8, 12, 12, 16).
37 + 12 = 49 (not 50).
2. How many such pairs of letters are there in the word DIGIT AL each of which
has as many letters between them in the word as in the English alphabets?
Options:
A. One
B. T wo
C. Three
D. Four
Solution : Pairs: (D, G), (I, L). In DIGIT AL, D and G have 2 letters between them in the
word as well as in the English alphabet. Similarly , I and L have 2 letters between them.
3. Study the following arrangement of digits, letters, and symbols carefully: F C 4
K B 5 9 # 3 R 2 @ 7 M G % 5 V T \$ 8 * 1 J A. How many such symbols are there in
the given arrangement each of which is immediately preceded and immediately
followed by a digit?
Options:
A. None
B. One
C. T wo
D. Three
Solution: There are two such symbols: 9#3 and 2@7.
4. In a certain code language, if ‘DET AIL ’ is coded as ‘EGUCJN’, then how will
‘HIGHER’ be coded in that language?
Options:
A. IKHJFT
B. IJHIFS
Page 2

Logical Reasoning
1. Select the incorrect number in the given number pattern: 1 5 9 17 25 37 50 65.
Options:
A. 9
B. 17
C. 50
D. 65
Solution: The pattern increases by odd numbers incrementally (4, 4, 8, 8, 12, 12, 16).
37 + 12 = 49 (not 50).
2. How many such pairs of letters are there in the word DIGIT AL each of which
has as many letters between them in the word as in the English alphabets?
Options:
A. One
B. T wo
C. Three
D. Four
Solution : Pairs: (D, G), (I, L). In DIGIT AL, D and G have 2 letters between them in the
word as well as in the English alphabet. Similarly , I and L have 2 letters between them.
3. Study the following arrangement of digits, letters, and symbols carefully: F C 4
K B 5 9 # 3 R 2 @ 7 M G % 5 V T \$ 8 * 1 J A. How many such symbols are there in
the given arrangement each of which is immediately preceded and immediately
followed by a digit?
Options:
A. None
B. One
C. T wo
D. Three
Solution: There are two such symbols: 9#3 and 2@7.
4. In a certain code language, if ‘DET AIL ’ is coded as ‘EGUCJN’, then how will
‘HIGHER’ be coded in that language?
Options:
A. IKHJFT
B. IJHIFS
C. JKIJGT
D. JKGIFS
Solution: The pattern in the coding: D -> E (Next letter), E -> G (Next consonant), T ->
U (Next letter), A -> C (Next consonant), I -> J (Next letter), L -> N (Next consonant).
Applying this pattern to HIGHER: H -> I, I -> J, G -> H, H -> I, E -> F , R -> S. Result:
IJHIFS.
5. Introducing a woman, Shashank said, “She is the mother of the only daughter
of my son.” How is the woman related to Shashank?
Options:
A. Daughter
B. Sister-in-law
C. Wife
D. Daughter-in-law
Solution: The woman is the mother of Shashank's granddaughter . Hence, she is the
daughter-in-law of Shashank.
6. If the English alphabets are written in the reverse order , then which would be
the 5th letter to the right of the 18th letter from the left end?
Options:
A. G
B. H
C. I
D. D
Solution: The 18th letter from the left end in the reverse order is I (since reverse
alphabet starting from A.. The 5th letter to the right of I is G.
7. Aman starts driving a car towards East and covers 4 km. Then he turns left and
covers 12 km, after that he takes a right turn and covers 10 km, then turns left and
covers 8 km. At the end, he takes a left turn again and covers 14 km. How much
total distance is covered by Aman?
Options:
A. 18 km
B. 42 km
C. 20 km
D. 48 km
Solution: T otal distance covered = 4 + 12 + 10 + 8 + 14 = 48 km.
Page 3

Logical Reasoning
1. Select the incorrect number in the given number pattern: 1 5 9 17 25 37 50 65.
Options:
A. 9
B. 17
C. 50
D. 65
Solution: The pattern increases by odd numbers incrementally (4, 4, 8, 8, 12, 12, 16).
37 + 12 = 49 (not 50).
2. How many such pairs of letters are there in the word DIGIT AL each of which
has as many letters between them in the word as in the English alphabets?
Options:
A. One
B. T wo
C. Three
D. Four
Solution : Pairs: (D, G), (I, L). In DIGIT AL, D and G have 2 letters between them in the
word as well as in the English alphabet. Similarly , I and L have 2 letters between them.
3. Study the following arrangement of digits, letters, and symbols carefully: F C 4
K B 5 9 # 3 R 2 @ 7 M G % 5 V T \$ 8 * 1 J A. How many such symbols are there in
the given arrangement each of which is immediately preceded and immediately
followed by a digit?
Options:
A. None
B. One
C. T wo
D. Three
Solution: There are two such symbols: 9#3 and 2@7.
4. In a certain code language, if ‘DET AIL ’ is coded as ‘EGUCJN’, then how will
‘HIGHER’ be coded in that language?
Options:
A. IKHJFT
B. IJHIFS
C. JKIJGT
D. JKGIFS
Solution: The pattern in the coding: D -> E (Next letter), E -> G (Next consonant), T ->
U (Next letter), A -> C (Next consonant), I -> J (Next letter), L -> N (Next consonant).
Applying this pattern to HIGHER: H -> I, I -> J, G -> H, H -> I, E -> F , R -> S. Result:
IJHIFS.
5. Introducing a woman, Shashank said, “She is the mother of the only daughter
of my son.” How is the woman related to Shashank?
Options:
A. Daughter
B. Sister-in-law
C. Wife
D. Daughter-in-law
Solution: The woman is the mother of Shashank's granddaughter . Hence, she is the
daughter-in-law of Shashank.
6. If the English alphabets are written in the reverse order , then which would be
the 5th letter to the right of the 18th letter from the left end?
Options:
A. G
B. H
C. I
D. D
Solution: The 18th letter from the left end in the reverse order is I (since reverse
alphabet starting from A.. The 5th letter to the right of I is G.
7. Aman starts driving a car towards East and covers 4 km. Then he turns left and
covers 12 km, after that he takes a right turn and covers 10 km, then turns left and
covers 8 km. At the end, he takes a left turn again and covers 14 km. How much
total distance is covered by Aman?
Options:
A. 18 km
B. 42 km
C. 20 km
D. 48 km
Solution: T otal distance covered = 4 + 12 + 10 + 8 + 14 = 48 km.
8. If in a certain code language, FEMALE is coded as HODPHI, then how will
F ACING be coded in that language?
Options:
A. IPDLHQ
B. JPLFEJ
C. JQLEEI
D. JQLFDI
Solution: Following the coding pattern, F ACING is coded as JQLFDI.
9. Rectangle : Square :: Ellipse : ?
Options:
A. Centre
B. Diameter
C. Circle
10. In the given figure, the triangle represents girls, the square represents
sportspersons, and the circle represents coaches. Which portion of the figure
represents girls who are sportspersons but not coaches?
Options:
A. A
B. B
C. C
D. D
1 1. Five boys A, B, C, D, and E are standing in a row . A is between C and D, and B
is between D and E. Which of the following pairs represents the boys standing at
both ends?
Options:
A. C, B
B. E, C
C. E, A
D. A, C
12. Which will come next in the series? az, by , cx, ?
Options:
A. ef
Page 4

Logical Reasoning
1. Select the incorrect number in the given number pattern: 1 5 9 17 25 37 50 65.
Options:
A. 9
B. 17
C. 50
D. 65
Solution: The pattern increases by odd numbers incrementally (4, 4, 8, 8, 12, 12, 16).
37 + 12 = 49 (not 50).
2. How many such pairs of letters are there in the word DIGIT AL each of which
has as many letters between them in the word as in the English alphabets?
Options:
A. One
B. T wo
C. Three
D. Four
Solution : Pairs: (D, G), (I, L). In DIGIT AL, D and G have 2 letters between them in the
word as well as in the English alphabet. Similarly , I and L have 2 letters between them.
3. Study the following arrangement of digits, letters, and symbols carefully: F C 4
K B 5 9 # 3 R 2 @ 7 M G % 5 V T \$ 8 * 1 J A. How many such symbols are there in
the given arrangement each of which is immediately preceded and immediately
followed by a digit?
Options:
A. None
B. One
C. T wo
D. Three
Solution: There are two such symbols: 9#3 and 2@7.
4. In a certain code language, if ‘DET AIL ’ is coded as ‘EGUCJN’, then how will
‘HIGHER’ be coded in that language?
Options:
A. IKHJFT
B. IJHIFS
C. JKIJGT
D. JKGIFS
Solution: The pattern in the coding: D -> E (Next letter), E -> G (Next consonant), T ->
U (Next letter), A -> C (Next consonant), I -> J (Next letter), L -> N (Next consonant).
Applying this pattern to HIGHER: H -> I, I -> J, G -> H, H -> I, E -> F , R -> S. Result:
IJHIFS.
5. Introducing a woman, Shashank said, “She is the mother of the only daughter
of my son.” How is the woman related to Shashank?
Options:
A. Daughter
B. Sister-in-law
C. Wife
D. Daughter-in-law
Solution: The woman is the mother of Shashank's granddaughter . Hence, she is the
daughter-in-law of Shashank.
6. If the English alphabets are written in the reverse order , then which would be
the 5th letter to the right of the 18th letter from the left end?
Options:
A. G
B. H
C. I
D. D
Solution: The 18th letter from the left end in the reverse order is I (since reverse
alphabet starting from A.. The 5th letter to the right of I is G.
7. Aman starts driving a car towards East and covers 4 km. Then he turns left and
covers 12 km, after that he takes a right turn and covers 10 km, then turns left and
covers 8 km. At the end, he takes a left turn again and covers 14 km. How much
total distance is covered by Aman?
Options:
A. 18 km
B. 42 km
C. 20 km
D. 48 km
Solution: T otal distance covered = 4 + 12 + 10 + 8 + 14 = 48 km.
8. If in a certain code language, FEMALE is coded as HODPHI, then how will
F ACING be coded in that language?
Options:
A. IPDLHQ
B. JPLFEJ
C. JQLEEI
D. JQLFDI
Solution: Following the coding pattern, F ACING is coded as JQLFDI.
9. Rectangle : Square :: Ellipse : ?
Options:
A. Centre
B. Diameter
C. Circle
10. In the given figure, the triangle represents girls, the square represents
sportspersons, and the circle represents coaches. Which portion of the figure
represents girls who are sportspersons but not coaches?
Options:
A. A
B. B
C. C
D. D
1 1. Five boys A, B, C, D, and E are standing in a row . A is between C and D, and B
is between D and E. Which of the following pairs represents the boys standing at
both ends?
Options:
A. C, B
B. E, C
C. E, A
D. A, C
12. Which will come next in the series? az, by , cx, ?
Options:
A. ef
B. gh
C. ij
D. dw
1 3 . S e l e c t a s u i t a b l e f i g u r e f r o m t h e A n s w e r F i g u r e s t h a t w o u l d r e p l a c e t h e q u e s t i o n m a r k
( ? ) .
P r o b l e m F i g u r e s :
A n s w e r F i g u r e s :
A . 1
B . 2
C . 3
D . 4
A n s w e r : C . 3
14. How many numbers in the series are preceded by a vowel?
Alphanumeric Series: W % ^ K V P 1 I 7 E 0 & 2 9 A F Z N 4 * @ U ? M
Options:
A. Four
B. None
C. T wo
D. One
Answer: C. T wo; 7 is preceded by I and 0 is preceded by E.
15. In a row of persons, the position of Sakshi from the left side of the row is 26th
and position of Sakshi from the right side of the row is 35th. Find the total
number of students in the row?
A. 67
B. 32
C. 46
Page 5

Logical Reasoning
1. Select the incorrect number in the given number pattern: 1 5 9 17 25 37 50 65.
Options:
A. 9
B. 17
C. 50
D. 65
Solution: The pattern increases by odd numbers incrementally (4, 4, 8, 8, 12, 12, 16).
37 + 12 = 49 (not 50).
2. How many such pairs of letters are there in the word DIGIT AL each of which
has as many letters between them in the word as in the English alphabets?
Options:
A. One
B. T wo
C. Three
D. Four
Solution : Pairs: (D, G), (I, L). In DIGIT AL, D and G have 2 letters between them in the
word as well as in the English alphabet. Similarly , I and L have 2 letters between them.
3. Study the following arrangement of digits, letters, and symbols carefully: F C 4
K B 5 9 # 3 R 2 @ 7 M G % 5 V T \$ 8 * 1 J A. How many such symbols are there in
the given arrangement each of which is immediately preceded and immediately
followed by a digit?
Options:
A. None
B. One
C. T wo
D. Three
Solution: There are two such symbols: 9#3 and 2@7.
4. In a certain code language, if ‘DET AIL ’ is coded as ‘EGUCJN’, then how will
‘HIGHER’ be coded in that language?
Options:
A. IKHJFT
B. IJHIFS
C. JKIJGT
D. JKGIFS
Solution: The pattern in the coding: D -> E (Next letter), E -> G (Next consonant), T ->
U (Next letter), A -> C (Next consonant), I -> J (Next letter), L -> N (Next consonant).
Applying this pattern to HIGHER: H -> I, I -> J, G -> H, H -> I, E -> F , R -> S. Result:
IJHIFS.
5. Introducing a woman, Shashank said, “She is the mother of the only daughter
of my son.” How is the woman related to Shashank?
Options:
A. Daughter
B. Sister-in-law
C. Wife
D. Daughter-in-law
Solution: The woman is the mother of Shashank's granddaughter . Hence, she is the
daughter-in-law of Shashank.
6. If the English alphabets are written in the reverse order , then which would be
the 5th letter to the right of the 18th letter from the left end?
Options:
A. G
B. H
C. I
D. D
Solution: The 18th letter from the left end in the reverse order is I (since reverse
alphabet starting from A.. The 5th letter to the right of I is G.
7. Aman starts driving a car towards East and covers 4 km. Then he turns left and
covers 12 km, after that he takes a right turn and covers 10 km, then turns left and
covers 8 km. At the end, he takes a left turn again and covers 14 km. How much
total distance is covered by Aman?
Options:
A. 18 km
B. 42 km
C. 20 km
D. 48 km
Solution: T otal distance covered = 4 + 12 + 10 + 8 + 14 = 48 km.
8. If in a certain code language, FEMALE is coded as HODPHI, then how will
F ACING be coded in that language?
Options:
A. IPDLHQ
B. JPLFEJ
C. JQLEEI
D. JQLFDI
Solution: Following the coding pattern, F ACING is coded as JQLFDI.
9. Rectangle : Square :: Ellipse : ?
Options:
A. Centre
B. Diameter
C. Circle
10. In the given figure, the triangle represents girls, the square represents
sportspersons, and the circle represents coaches. Which portion of the figure
represents girls who are sportspersons but not coaches?
Options:
A. A
B. B
C. C
D. D
1 1. Five boys A, B, C, D, and E are standing in a row . A is between C and D, and B
is between D and E. Which of the following pairs represents the boys standing at
both ends?
Options:
A. C, B
B. E, C
C. E, A
D. A, C
12. Which will come next in the series? az, by , cx, ?
Options:
A. ef
B. gh
C. ij
D. dw
1 3 . S e l e c t a s u i t a b l e f i g u r e f r o m t h e A n s w e r F i g u r e s t h a t w o u l d r e p l a c e t h e q u e s t i o n m a r k
( ? ) .
P r o b l e m F i g u r e s :
A n s w e r F i g u r e s :
A . 1
B . 2
C . 3
D . 4
A n s w e r : C . 3
14. How many numbers in the series are preceded by a vowel?
Alphanumeric Series: W % ^ K V P 1 I 7 E 0 & 2 9 A F Z N 4 * @ U ? M
Options:
A. Four
B. None
C. T wo
D. One
Answer: C. T wo; 7 is preceded by I and 0 is preceded by E.
15. In a row of persons, the position of Sakshi from the left side of the row is 26th
and position of Sakshi from the right side of the row is 35th. Find the total
number of students in the row?
A. 67
B. 32
C. 46
D. 60
Answer: (D. 60 ; {26+35-1 = 61-1 = 60}
Mathematical Reasoning
16. Which of the following is not a Pythagorean triplet?
Options:
A. 6, 8, 10
B. 9, 12, 15
C. 10, 24, 26
D. 12, 16, 21
17. Find the values of P and Q. (i) The sum of two integers is 45. If one of them is
-27, then the other integer is P . (ii) The product of an integer and Q is zero.
Options:
A. 72, 0
B. 58, 1
C. 72, 1
D. 72, 2
18. If 25, 100, x are in continued proportion, then find the value of x.
Options:
A. 400
B. 500
C. 625
D. 800
19. If x = -1, y = 4, and z = -3, then the value of the expression 3x^2 + 2y^2 + z^2 +
4xyz is ____.
Options:
A. 10
B. 25
C. 12
D. 30
20. Difference between the greatest and smallest 8-digit number that can be
formed using the digits 5, 7, 1, 3, 8, 2, 9, and 4 (each digit used exactly once) is:
```

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FAQs on Mathematics Olympiad Model Test Paper - 3 - Mathematics Olympiad Class 7

 1. How can I prepare effectively for a Mathematics Olympiad exam?
Ans. To prepare effectively for a Mathematics Olympiad exam, it is essential to practice regularly, solve previous year's question papers, and seek help from teachers or mentors for guidance. Additionally, focusing on understanding concepts rather than rote memorization can be beneficial.
 2. What are some common topics covered in Mathematics Olympiad exams?
Ans. Some common topics covered in Mathematics Olympiad exams include algebra, geometry, number theory, combinatorics, and probability. It is important to have a solid understanding of these topics and their applications in problem-solving.
 3. How can I improve my problem-solving skills for Mathematics Olympiad exams?
Ans. To improve problem-solving skills for Mathematics Olympiad exams, one can practice solving challenging mathematical problems regularly, participate in mock tests and competitions, and analyze solutions to understand different problem-solving techniques.
 4. Are there any recommended books or resources for preparing for Mathematics Olympiad exams?
Ans. Yes, there are several recommended books and resources for preparing for Mathematics Olympiad exams, such as "Math Olympiad Contest Problems" by Richard Kalman, "The Art of Problem Solving" series, and online platforms like Brilliant.org and AoPS (Art of Problem Solving).
 5. How can I manage my time effectively during a Mathematics Olympiad exam?
Ans. To manage time effectively during a Mathematics Olympiad exam, it is important to practice solving problems under timed conditions, prioritize questions based on difficulty level, and allocate sufficient time for each section of the exam. Additionally, staying calm and focused can help in maximizing time utilization.

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