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Logical Reasoning | |
Mathematical Reasoning | |
Everyday Mathematics | |
Achievers Section |
Note: The questions provided in this document are similar to the questions that were asked in the actual Olympiad exam. So, we recommend you study these for your Olympiad preparation
Q1: If ‘School’ is referred to as ‘Home’, ‘Home’ is referred to as ‘Office’, ‘Office’ is referred to as ‘Market’ and ‘Market’ is referred to as ‘Bus stop’, then we purchase vegetables from ________.
(a) Office
(b) Market
(c) Bus stop
(d) Home
Ans: (c)
Q2: Chetna ranked 19th from the bottom in a class of 25 students. What is her rank from the top in the class?
(a) 6th
(b) 7th
(c) 5th
(d) 8th
Ans: (b)
Q3: There is a specific connection between the terms on both sides of the ::. Determine the relationship of the left pair and identify the missing term.
SOF : UQH :: IMO : ?
(a) KQO
(b) JOQ
(c) KOQ
(d) GKM
Ans: (c)
Q4: Direction (4 & 5): Study the following information carefully and answer the questions.
L, M, N, O, P, Q and R are sitting in a row facing north.
L is sitting at the right end and R is sitting at the left end.
Q is the immediate right of P. N is 4th to the right of R.
N is the neighbour of M and O. O is third to the left of L.
Who is/are to the left of N?
(a) Only M
(b) R and M
(c) O, P, Q and L
(d) R, M an d O
Ans: (b)
R and M are to the left of N.
Q5: Which of the following statements is not true?
(a) L is at one of the ends.
(b) Q is sitting between P an d L
(c) P is to the immediate right of N
(d) R is at one of the ends.
Ans: (c)
Q6: How man y triangles are there in the following figures?
(a) 20
(b) 22
(c) 16
(d) 24
Ans: (b)
Smallest triangle - AEI, BIF, EKI, EGK, GKJ, IKJ, GJC, FLH, JLH, JLI, ILF, and JDH ie-12.
Contains two triangle - EIJ, EGJ, EGI, GIJ, IJH, EJH, IHF, FJH ie 8.
Contains 4 triangles - EJF and GIJ ie 2.
Total no. of triangle - 12 + 8 + 2 = 22
Q7: How many pairs of letters are there in the word "PREAMBLE" which have as many letters between them in the words as they have between them in the English alphabet?
(a) None
(b) One
(c) Two
(d) Three
Ans: (c)
Q8: D h as a sister A, whose moth er is P. D is the daughter of P. B is P's mother. In term of relationships what is A to B ?
(a) Daughter
(b) Sister
(c) Cousin
(d) Granddaughter
Ans: (d)
The relation diagram is as follows:
A is Granddaughter to B.
Q9: A house faces North. A man coming out from the house walked straight for 10 m, turned left and walked 25 m. He then turned right and walked 5 m and again turned right and walked 25 m. How far is he from his house ?
(a) 15 m
(b) 55 m
(c) 60 m
(d) 65 m
Ans: (a)
The direction diagram is as follows:
Required distance = AE = AB + BE
(Here, CD = BE = 5m) = 10m + 5m = 15 m
Q10: If in a code language KAMLESH is written as GUJLMCO. Then, how can NATURAL be written in that code?
(a) TCNUPCV
(b) TCOUPVC
(c) TCUOPVC
(d) TCOUVC
Ans: (a)
As,
Q11: Select the missing number from the given alternatives.
(a) 3
(b) 14
(c) 5
(d) 16
Ans: (c)
As, (2 + 3 + 4)2 = 81
(4 + 2 + 5)2 = 121
Similarly,
(1 + 5 + 7)2 = 169
Q12: 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner?
(a) 29
(b) 31
(c) 35
(d) 27
Ans: (a)
Clearly, every time except one ( i.e. the winner) must lose one game to decide the winner.
So, minimum number of matches to be played = 30 - 1 = 29.
Q13: Naman is ranked 14th from the top and Ricky is ranked 17th from the bottom in a class of 40 students. How many students are there between Naman and Ricky?
(a) 8
(b) 9
(c) 10
(d) 7
Ans: (b)
Number of students between Naman & Ricky.
Q14: If a person is walking towards North, what direction should he follow so that he is walking towards West?
(a) right, right, left
(b) left, left, right
(c) left, right, left
(d) left, left, left
Ans: (b)
The direction of a person is as follows:
Q15: Mohit correctly remember s that his father's birthday is not after eighteenth of April. His sister correctly remembers that their father's birthday is before twentieth but after seventeenth of April. On which day in April was definitely their father's birthday?
(a) Seventeenth
(b) Nineteenth
(c) Eighteenth
(d) Seventeenth or Eighteenth
Ans: (c)
According to Mohit:
April 18 or earlier ... (i)
According to his sister:
April 18 or 19 ... (ii)
From (i) and (ii), we get April 18
Q16: Which of the following options is organized in descending order?
(a) 5034; 7056; 80431; 10569
(b) 82540; 72042; 42035; 10568
(c) 6051; 10268; 24561; 54685
(d) 1029; 50552; 30251; 44162
Ans: (b)
Q17: How many packets of 750 g each can be obtained from a 30 kg sack of pulses?
(a) 36
(b) 40
(c) 55
(d) 60
Ans: (b)
Q18: The value of 78.80 + 19.45 – 17.20 is __________.
(a) 84.75
(b) 76.50
(c) 81.05
(d) 73.50
Ans: (c)
Q19: If P = CMXLIX and Q = CMLXVIII, which of the following statements is true?
(a) P > Q
(b) P < Q
(c) P = Q
(d) Cannot be determined
Ans: (b)
Q20: The total capacity of containers A and B is 30.32 L. If the capacity of containers A, B, and C altogether is 46.06 L, then the capacity of container C is:
(a) 15.74 L
(b) 12.58 L
(c) 19.36 L
(d) 16.49 L
Ans: (a)
Q21: Determine the largest 5-digit number that can be created using all unique digits with 4 positioned in the hundreds place.
(a) 98476
(b) 98765
(c) 98746
(d) None of these
Ans: (a)
Q22: 56 (4 + 2) = (56 × 4) + (56 × 2) is an example of the
(a) closure property of whole number
(b) commutative property of whole number
(c) associative property of whole number
(d) distributive property of whole number
Ans: (d)
Q23: The product of 1st natural, 1st whole and the 1st prime number is equal to
(a) 5
(b) 0
(c) 9
(d) 7
Ans: (b)
1st natural number = 1
1st whole number = 0
1st prime number = 2
Then, the product is 1 × 0 × 2 = 0
Q24: The sum of the prime numbers between 90 and 100 is
(a) 188
(b) 281
(c) 376
(d) 97
Ans: (d)
The only prime number between 90 and 100 is 97.
Q25: HCF and LCM of two numbers are 12 and 72 respectively. If the difference of the numbers is 60, then the larger number is:
(a) 12
(b) 60
(c) 24
(d) 72
Ans: (d)
Let the numbers be a and b.
∴ Product of numbers = LCM × HCF
ab = 72 × 12 ...(1)
and a – b = 60
a = 60 + b
Then, from (1), b (60 + b) = 12 × 72
⇒ b = 12
a = 60 + b = 72
Larger number is 72.
Q26: In which of the following prime factorisation is not completed?
(a) 70 = 2 × 5 × 7
(b) 28 = 2 × 2 × 7
(c) 48 = 2 × 2 × 2 × 2 × 3
(d) 108 = 2 × 2 × 27
Ans: (d)
Complete factorisation is 108 = 2 × 2 × 3 × 3 × 3
Q27: A quadrilateral is a rhombus but not a square if
(a) its diagonals do not bisect each other
(b) its diagonals are not perpendicular
(c) opposite angles are not equal
(d) the length of diagonals are not equal
Ans: (d)
Q28: In which of the following figures the adjacent sides are not necessarily be equal?
(a) Parallelogram
(b) Rhombus
(c) Equilateral Triangle
(d) Square
Ans: (a)
Q29: The number of line segments in the shown figure is
(a) 30
(b) 20
(c) 15
(d) 12
Ans: (c)
Q30: Number of lines passing through five points such that no three of them are collinear is
(a) 10
(b) 5
(c) 20
(d) 8
Ans: (a)
Q31: Which of the following statement (s) is/are true?
(a) In a trapezium the diagonals bisect each other
(b) In a rectangle diagonals intersect at right angles
(c) The diagonals of a rhombus are equal
(d) None of these
Ans: (d)
All the given statements are false.
Q32: Where does the vertex of an angle lie?
(a) In its interior
(b) In its exterior
(c) On the angle
(d) None of these
Ans: (c)
The vertex lies on the angle.
Q33: The infinite number of lines that can pass through a given point are called.
(a) Concurrent lines
(b) Parallel lines
(c) Perpendicular lines
(d) None of these
Ans: (a)
Q34: If a quadrilateral with two pairs of adjacent sides equal but opposite sides are not equal then it is called
(a) parallelogram
(b) square
(c) rectangle
(d) kite
Ans: (d)
Q35: Which one of the following is a pair of supplementary angles?
(a) 30º, 180º
(b) 100º, 140º
(c) 105º, 75º
(d) All of these
Ans: (c)
Q36: A family consumes 1 9/20 L of oil each week. Calculate the total amount of oil the family will use in February of a regular year.
(a) 4 3/4 L
(b) 5 4/5 L
(c) 3 3/4 L
(d) 3 4/5 L
Ans: (b)
Q37: A tailor uses two different colored fabrics measuring 67.75 cm and 89.68 cm to create a dress. What is the total length of fabric used by the tailor for the dress?
(a) 136.43 cm
(b) 142.84 cm
(c) 152.84 cm
(d) 157.43 cm
Ans: (d)
Q38: The cost of fencing a rectangular garden at ₹15 per meter is ₹2100. If the breadth of the field is 20 m, then its length is ______.
(a) 50 m
(b) 40 m
(c) 70 m
(d) 30 m
Ans: (a)
Q39: In an electronic store, there are 450 electronic products. Among these, 5/18 are electric fans, while the remaining are other products. How many other products are available in the store?
(a) 185
(b) 325
(c) 275
(d) 260
Ans: (b)
Q40: An experienced stock broker invested ₹8,75,684; ₹8,75,713; ₹8,81,312, and ₹8,57,995 in four different shares P, Q, R, and S respectively. In which share did he invest the least amount?
(a) P
(b) Q
(c) R
(d) S
Ans: (d)
Q41: A university charges ₹5,658 per student for a specific course. If 45 students enrolled for the course, then find the total amount collected by the university for that particular course.
(a) ₹1,82,560
(b) ₹2,54,610
(c) ₹1,68,740
(d) ₹2,24,530
Ans: (b)
Q42: The weight of Akshara is 57.89 kg. If Sandeep weighs 16.47 kg more than Akshara, what is the combined weight of Akshara and Sandeep?
(a) 168.36 kg
(b) 89.93 kg
(c) 132.25 kg
(d) 74.36 kg
Ans: (c)
Q43: A company earned ₹5648000 in a year. If the total expenses were ₹474596, then how much money was saved?
(a) ₹234467
(b) ₹6137007
(c) ₹5234728
(d) ₹5173404
Ans: (d)
Q44: Mukul bought two T-shirts priced at ₹719 each and a cap costing ₹348. He paid the shopkeeper with a ₹2000 note. What will be the change Mukul receives from the shopkeeper?
(a) ₹306
(b) ₹186
(c) ₹214
(d) ₹197
Ans: (c)
Q45: How many numbers are there containing 2 digits?
(a) 90
(b) 99
(c) 100
(d) 89
Ans: (a)
(Greatest two digit number-smallest two digit number) = (99 – 10) + 1 = 89 + 1 = 90
Q46: Which digit in the number 568731 has a place value of thousands?
(a) 8
(b) 7
(c) 6
(d) 5
Ans: (a)
Place value of 8 is 8000.
Q47: Which one of the following numbers in Roman numerals is correct?
(a) CLDL
(b) VDC
(c) LDC
(d) CDLX
Ans: (d)
Q48: Which of the following is not defined?
(a) 5 + 0
(b) 5 – 0
(c) 5 × 0
(d) 5 ÷ 0
Ans: (d)
Q49: Whole numbers are not commutative under ________.
(a) Multiplication
(b) Subtraction
(c) Addition
(d) Both multiplication and addition
Ans: (b)
Q50: The difference of L.C.M. and H.C.F. of the numbers 40, 240 and 480 is equal to twice a number. Find the number.
(a) 340
(b) 440
(c) 220
(d) 880
Ans: (c)
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