Table of contents | |
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: Which of the following Venn diagrams best represents the relationship amongst, 'Indian Navy, Indian Army, Indian Air Force?
(a)
(b)
(c)
(d)
Ans: (b)
Q2: If 'P' represents 'multiplication', 'Q' represents 'division', 'R' represents 'addition', and 'S' represents 'subtraction', what is the result of 152Q19P10R7S31?
(a) 73
(b) 45
(c) 39
(d) 56
Ans: (d)
Thus, the final answer is 56.
Q3: In search of fodder four buffaloes and three cows stand in a queue. What is the probability that they will be in alternate positions?
(a) 4/35
(b) 3/35
(c) 2/35
(d) 1/35
Ans: (d)
Total number of ways of arranging 4 buffaloes and 3 cows,
i.e., 7 animals in a queue (row) = n(S) = 7!
Let A: Event in which the 4 buffaloes and 3 cows occupy alternate position.
This is possible when the 4 buffaloes occupy the 4 odd places standing form position 1 and the cows fill in the three even places between
4 buffaloes can be arranged in a queue in 4! ways
3 cows can fill the gaps in the queue in 3! ways.
n(A) = 4! × 3!
Q4: Pointing to a woman in the picture, Shilpa remarked, "She is the mother of my brother's sole son." What is Shilpa's relationship to the woman in the picture?
(a) Sister
(b) Aunt
(c) Sister-in-law
(d) Mother-in-law
Ans: (c)
Q5: Find the number of straight lines and triangles in the given figure.
(a) 14 and 18
(b) 16 and 20
(c) 16 and 24
(d) 14 and 24
Ans: (d)
Number of straight lines = 14
Number of triangles = 24
Q6: Three of the following are alike in a certain way based on the given arrangement and hence form a group. Which one does not belong to the group?
(a) KN97
(b) *3ST
(c)
(d) 3S*U
View AnswerAns: (d)
Except option D, in all other options, there is a gap of 4 elements between any two consecutive elements.
Q7: Select the correct mirror image of the given figure, if mirror is placed vertically to the right.
(a)
(b)
(c)
(d)
Ans: (c)
Q8: Himani goes 14 m towards West, then she turns right and walks 10 m, again she turns right and walks 6 m. Then finally she turns left and walks 5 m. How far and in which direction is she now from her starting point?
(a) 17 m, North-West
(b) 11 m, South-East
(c) 17 m, North-East
(d) 11 m, South-West
Ans: (a)
Required distance (AB)
∴ Himani is 17 m in North-West direction from her starting point.
Q9: Group the given figures into three classes on the basis of their identical properties using each figure only once.
(a) 1, 5, 8; 2, 4, 7; 3, 6, 9
(b) 6, 5, 8; 1, 3, 7; 2, 4, 9
(c) 1, 3, 6; 4, 5, 9; 2, 7, 8
(d) 1, 3, 6; 2, 5, 7; 4, 8, 9
Ans: (a)
1, 5, 8; all are simple 2-D figures.
2, 4, 7; all having two figures, one inside the other.
3, 6, 9; all having two figures, one inside the other.
Q10: If each consonant in the following words is replaced with the letter before it, and each vowel is replaced with the letter after it in the English alphabet, how many of the resulting words contain no vowels?
RAG, FIN, PUT, LOW, SUE
(a) Two
(b) One
(c) Three
(d) More than three
Ans: (c)
Q11: Three figures P, Q, R shows a sequence of folding of a sheet of paper. Figure (R) shows the manner in which the folded paper has been cut. Select a figure from the options which represents the unfolded form of figure (R).
(a)
(b)
(c)
(d)
Ans: (d)
Q12: What will come in place of (?) to continue the given series?
7E19, 11J16, 15O13, 19T10, ?
(a) 22W6
(b) 23Y7
(c) 21U5
(d) 19V6
Ans: (b)
Q13: Select a figure from the options which satisfies the same conditions of placement of the dots as in the given figure.
(a)
(b)
(c)
(d)
Ans: (c)
Q14: A word arrangement machine takes an input line of words and rearranges them according to specific rules in each step. The following is an example of an input line of words and the steps of rearrangement.
Input: gone are take enough brought station
Step I: take gone are enough brought station
Step II: take are gone enough brought station
Step III: take are station gone enough brought
Step IV: take are station brought gone enough.
Step IV is the final step for this input.
Based on the rules applied in the above steps, answer the following question. If step IV of an input line of words is 'violet for sour height journey medium', which of the following is definitely the input?
(a) violet for journey height sour medium
(b) violet for sour journey height medium
(c) violet journey height for sour medium
(d) can't be determined
Ans: (d)
Q15: Find the missing number, if same rule is followed in all three figures.
(a) 148
(b) 336
(c) 225
(d) 369
Ans: (d)
The rule followed is:
(92 + 112) = 202;
(62 + 72) = 85
So, (152 + 122) = 369
Q16: Ten different slips with the numbers 1 through 10 are kept in a box and thoroughly mixed. Without looking at the slips, one gets picked out of the box. what is the probability of getting number 6
(a) 1/6
(b) 1/10
(c) 9/10
(d) 10/9
Ans: (b)
Sample space = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} → n(S) = 10
Let A be the event of getting 6 from the sample space.
A= {6} → n(A) = 1
Probability of getting number 6 = n(A)/n(S) = 1/10
Q17: From a group of 3 men and 2 women, two people are selected at random. Find the probability that at least one woman is selected:
(a) 1/5
(b) 7/10
(c) 2/5
(d) 5/6
Ans: (b)
Q18: The dimensions of a cuboidal container are 12 cm x 10 cm x 8 cm. How many bottles of syrup can be poured into the container if each bottle contains 20 cm3 of syrup?
(a) 46
(b) 54
(c) 48
(d) 58
Ans: (c)
Q19: A, B and C can complete a piece of work in 25, 30 and 50 days, respectively. They started the work together but A and C left 2 days before the completion of the work. In how many days will the work be completed?
(a) 14
(b) 12
(c) 18
(d) 10
Ans: (b)
Q20: In a three-digit number, the digit in the ones place is three times the digit in the hundreds place. The total of the digits in the ones and tens places equals the smallest two-digit number. What is the product of the three digits of the number if all the digits are even
(a) 42
(b) 24
(c) 27
(d) 48
Ans: (d)
Q21: Which of the following solids has twice the number of edges than faces?
(a) Triangular Prism
(b) Rectangular Pyramid
(c) Rectangular Prism
(d) Square Pyramid
Ans: (c)
Q22: If both (x - 2) and (x - (1/2)) are factors of px2 + 5x + r, then:
(a) p = r
(b) p + r = 0
(c) 2p + r = 0
(d) p + 2r = 0
Ans: (a)
Q23: In a survey, among all students, 53% responded with 'No', 20% replied 'Yes', and the rest indicated 'They could not decide'. If a student is selected randomly, what is the probability that the student did not say 'No'?
(a) 15/100
(b) 43/100
(c) 47/100
(d) 57/100
Ans: (c)
Q24: Which of the following options represents the ordinate of all points on the x-axis?
(a) 0
(b) 1
(c) 2
(d) -1
Ans: (a)
Q25: Determine the value of (t + 9/-2)-1, given that 4(t + 3) - 2(t - 1) = 3(t + 1).
(a) -5/7
(b) -1/10
(c) -2/11
(d) 3/10
Ans: (b)
Q26: The average of the first 10 prime numbers is:
(a) 10.9
(b) 10.5
(c) 12.9
(d) 9.7
Ans: (c)
Q27: What least number must be subtracted from 1294 so that the remainder when divided by 9, 11, 13 will leave in each case the same remainder 6?
(a) 0
(b) 1
(c) 2
(d) 3
Ans: (b)
Q28: Which of the following steps is incorrect in the construction of ΔXYZ in which base XY = 6 cm, XZ = 3.5 cm and length of median from Z is 3.7 cm.
Step-I: Draw the base XY = 6 cm and draw the perpendicular bisector of XY intersecting XY at M.
Step-II: Taking M as centre draw an arc of 3.5 cm.
Step-III: Taking X as centre draw an arc of 3.7 cm cutting the previous arc at Z.
Step-IV: Join XZ and YZ. Thus, DXYZ is the required triangle.
(a) Only Step-I
(b) Both Step-II and Step-III
(c) Both Step-III and Step-IV
(d) Only Step-II
Ans: (b)
Q29: If the difference between the compound interest and simple interest on a certain amount at 4% per annum for 2 years is ₹200, what is the total amount?
(a) ₹1,55,000
(b) ₹1,25,000
(c) ₹1,22,500
(d) ₹1,45,000
Ans: (b)
Q30: The difference between the outer and inner curved surface areas of a cylindrical metallic pipe 14 cm long is 44 cm2. If the pipe is constructed from 88 cm3 of metal, what are the outer and inner radii of the pipe?
(a) 2.35 cm, 1.25 cm
(b) 3.25 cm, 2.75 cm
(c) 2.25 cm, 1.75 cm
(d) 4.25 cm, 0.75 cm
Ans: (c)
Q31: A hemispherical balloon's radius rises from 6 cm to 12 cm as air is pumped into it. The ratio of the balloon's surface areas in the two cases is:
(a) 1 : 2
(b) 1 : 3
(c) 1 : 4
(d) 1 : 5
Ans: (c)
Q32: Which of the following statements is false?
(a) Mean is the mid-values of the classes.
(b) Median is the cumulative frequency.
(c) Mode is the minimum frequency.
(d) Mode is the maximum frequency.
Ans: (c)
Mode is not the minimum frequency.
Q33: If the difference between the mean and median of a data is D, then what will be the difference between the mean and mode of the data?
(a) D/2
(b) 3D
(c) 2D
(d) D/3
Ans: (b)
Mode = 3 median - 2 mean
Mode - mean = 3 median - 3 mean
Mode - Mean = 3(Median - mean)
Mode - mean = 3D (Since median - mean = D)
Q34: What is the result of the expression (x + y)3 - (x - y)3- 6y(x2 - y2)?
(a) y3
(b) 2y3
(c) 4y3
(d) 8y3
Ans: (d)
Q35: Find the sum of all the digits of the result of the subtraction 10099 - 999.
(a) 874
(b) 1874
(c) 1756
(d) 1755
Ans: (c)
10099 is 1 followed by 198 0’s.
On subtracting 999:
It will be 198-digit number with the last 3 digits 0,0,1.
Therefore, 195 9’s and 1 1’s.
195 x 9 + 1 = 1756
Q36: Water flows through a cylindrical pipe of diameter 10 mm at the rate of 10 m per minute and falls into a conical vessel having 50 cm as the diameter of its base and 30 cm as its height. How long will it take to fill the vessel?
(a) 28 mins
(b) 25 mins 10 secs
(c) 22 mins
(d) 25 mins
Ans: (d)
Q37: The price of a shirt is half that of a pair of jeans. If the jeans cost ₹ p and the shirt costs ₹ q, which linear equation in two variables represents this situation?
(a) p + 2q = 0
(b) p - 2q = 0
(c) 2p + q = 0
(d) 2p - q = 0
Ans: (b)
Q38: A and B are two alloys made from gold and copper, mixed in the ratios of 7:5 and 7:17, respectively. If equal amounts of these alloys are combined to create a third alloy, what is the ratio of gold to copper in the new alloy?
(a) 3 : 8
(b) 8 : 3
(c) 9 : 7
(d) 7 : 9
Ans: (d)
Q39: A swimming pool, 30 m long has a depth of water of 80 cm at one end and 2.4 m at the other end. Find the area of the each vertical cross-section of the pool along the length.
(a) 54 m2
(b) 48 m2
(c) 36 m2
(d) 42 m2
Ans: (b)
Q40: A shopkeeper purchased 30 kg of wheat for ₹ 45 per kg. He sold 40% of the total amount at ₹ 50 per kg. To achieve a 25% overall profit, what should be the selling price per kg for the remaining quantity?
(a) ₹ 60
(b) ₹ 50
(c) ₹ 54
(d) ₹ 52
Ans: (a)
Q41: A batsman in his 10th inning scores 48 runs, which raises his average score by 3. What is his average score after the 10th inning
(a) 21
(b) 20
(c) 22
(d) 19
Ans: (a)
Q42: A motorboat takes 3 hours to cover a distance of 12 km downstream. It takes 4 hours to cover the same distance upstream. Determine the speed of the motorboat in still water and the speed of the stream (in km/h), respectively.
(a) 3 km/h and 1 km/h
(b) 3.5 km/h and 0.5 km/h
(c) 0.5 km/h and 3.5 km/h
(d) 1 km/h and 3 km/h
Ans: (b)
Q43: If 5x - 5x-1 = 20, what is the value of (2x) x?
(a) 2
(b) 16
(c) 4
(d) 5
Ans: (b)
Q44: Along a path, 25 conical pillars are built. Each pillar has a radius of 15 cm and a height of 20 cm. Calculate the total expense for painting these pillars at the rate of ₹ 50 per cm². (Take π = 3.14)
(a) ₹ 2,01,752.50
(b) ₹ 20,52,325
(c) ₹ 32,14,325.50
(d) ₹ 14,71,875
Ans: (d)
Q45: The population of a town is 126,800. It increases by 15% in the first year and decreases by 20% in the second year. What is the population of the town at the end of 2 years?
(a) 174984
(b) 116656
(c) 135996
(d) 145820
Ans: (b)
Q46: If ay2 + 5y + c, is divisible by y - 2 and y - 1/2.
(a) a > c
(b) a = c
(c) a < c
(d) Both b and c
Ans: (b)
If y - 2 is a factor of ay2 + 5y + c,
4a + c + 10 = 0 ...... (1)
If y – 1/2 is a factor of ay2 + 5y + c,
By solving (1) and (2), we get
a = c = -2
Q47: Find a and b so that the polynomial x3 - 10x2 + ax + b is exactly divisible by the Polynomial (x - 1) and (x - 2).
(a) -23, -14
(b) 23, 14
(c) 23, -14
(d) -23,14
Ans: (c)
Q48: Read the following statements carefully and choose the correct option.
Statement I: In a cyclic quadrilateral ABCD, if ∠A – ∠C = 60°, then the smaller of the two is 60°.
Statement II: The angle subtended by an arc of a circle at the center is half the angle subtended by it at any point on the remaining part of the circle.
(a) Both Statement I and Statement II are true.
(b) Both Statement I and Statement II are false.
(c) Statement I is true but Statement II is false.
(d) Statement I is false but Statement II is true.
Ans: (c)
Q49: Louis is a farmer. A pile of wheat is in the shape of a cone with a 48-metre diameter and a 7-metre height. Find the area of the canvas needed if the heap needs to be covered to keep it dry in the rain.
(a) 1775.2 m2
(b) 1885.7 m2
(c) 1895.3 m2
(d) 1990.2 m2
Ans: (b)
Q50: Nike has marked four points on his plot where a fence will be built, and he wants to know the shape of the plot. The points A(1, 2), B(5, 4), C(3, 8) and D(- 1, 6) taken in order are the vertices of:
(a) A rectangle
(b) A rhombus
(c) A square
(d) A kite
Ans: (c)
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