Logical Reasoning
MCQs — 15 Questions
(+1)
1
seating-arrangement
medium
O, P, Q, R and S are sitting in a row facing North. Q is sitting third to the right of P, who is an immediate neighbour of S. Neither Q nor S is sitting at any of the ends. Who is sitting at the extreme right end of the row?
Answer: D
Q is third to the right of P, so P is in seat 1 or 2. S is not at an end and sits next to P.
If P were in seat 2, Q would be in seat 5, an end seat — not allowed. So P is in seat 1, S in seat 2 and Q in seat 4.
O and R take seats 3 and 5 in either order, so the extreme right end is either O or R.
2
number-puzzles
medium
Find the missing number, if same rule is followed in all the three figures.
Answer: B
Rule: multiply the three outer numbers and divide by 10.
15 × 8 × 4 = 480 → 48; 17 × 4 × 5 = 340 → 34.
So the missing number = 16 × 5 × 2 ÷ 10 = 160 ÷ 10 = 16.
3
embedded-figures
medium
Select a figure from the options which is exactly embedded in the given figure as one of its parts (without rotating it).
Answer: C
Inside the octagon, just above the horizontal line, there is a zig-zag of three equal slanting lines going down, up and down — exactly figure C.
The figure has no zig-zag of four such lines (A), no step made of horizontal and vertical pieces of equal length (B) and no steep zig-zag (D).
4
blood-relations
medium
Pointing towards a woman, a man said, "She is the only daughter-in-law of my father's only son-in-law's mother." How is that woman's daughter related to the man?
Answer: A
The man's father's only son-in-law is the husband of the man's sister.
The only daughter-in-law of that husband's mother is the husband's wife — the man's sister.
So the woman is the man's sister, and her daughter is the man's niece.
5
cube-and-dice
medium
The given net is folded to form a cube. Select the pair of symbols from the options, which are NOT opposite to each other.
Answer: C
In a row of four squares, the 1st and 3rd faces are opposite, and so are the 2nd and 4th: % is opposite #, © is opposite @.
The square above the row ($) and the square below it (*) are opposite each other.
So * and # are NOT opposite.
6
mirror-and-water-images
medium
Select the correct water image of the given combination of letters and numbers.
Answer: C
A water image is a reflection in a horizontal line: every character is turned upside down but the order from left to right stays the same.
A is a mirror image and B is the figure turned through 180°. In D, the letter N has not been turned upside down. C is correct.
7
counting-figures
medium
Find the number of squares formed in the given figure.
Answer: A
The figure is made of two 2 × 2 grids that overlap in one small square, and two more single squares.
Small squares: 4 + 4 − 1 (the shared one) + 2 = 9.
Big 2 × 2 squares: 2.
Total = 9 + 2 = 11.
8
mathematical-operations
easy
If '×' denotes '+', '+' denotes '−', '−' denotes '÷' and '÷' denotes '×', then what is the value of 150 ÷ 3 + 25 × 25 − 25?
Answer: C
Replace the signs: 150 × 3 − 25 + 25 ÷ 25.
= 450 − 25 + 1 = 426.
9
paper-folding-cutting
medium
A set of three figures X, Y and Z showing a sequence of folding of a piece of paper is given. Fig. Z shows the manner in which the folded paper has been cut. Select a figure from the options which shows the unfolded form of fig. Z.
Answer: B
The paper is folded in half twice, so each hole appears 4 times when it is opened: 2 holes × 4 = 8 small circles.
The corner that was cut is at the centre of the sheet, so it opens into one big diamond in the middle.
A has only 6 circles, C has a square in the middle and D has square holes. B is correct.
10
venn-diagrams
easy
In the given Venn diagram, triangle represents Olympic athletes, square represents hockey players and circle represents Asian players. Which of the following number represents Asian Olympic athletes who are not hockey players?
Answer: C
Asian Olympic athletes are in both the circle and the triangle: regions 2 and 3.
Region 3 is also inside the square (hockey players), so the answer is region 2.
11
analogy
medium
There is a certain relationship between the numbers on the either side of ::. Identify the relationship in the left pair and find the missing number.
45 : 405 :: ? : 301
Answer: B
Each number is multiplied by the sum of its digits: 45 × (4 + 5) = 45 × 9 = 405.
43 × (4 + 3) = 43 × 7 = 301, so the missing number is 43.
12
coding-decoding
easy
Some letters are coded as follows:
Letters: E, S, J, M, D, T, L, Y, N, K, I
Codes: $, @, ∀, >, ∧, <, π, ≈, ∞, =, ∅
What will be the code for DENSITY?
Answer: D
D → ∧, E → $, N → ∞, S → @, I → ∅, T → <, Y → ≈.
DENSITY → ∧$∞@∅<≈.
13
dot-situation
hard
Select a figure from the options which does NOT satisfy the same conditions of placement of the dots as in the given figure.
Answer: D
In the given figure the dots are placed in: (1) the triangle and circle only, (2) the triangle and rectangle only, (3) the circle and rectangle only.
Figures A, B and C all have these three regions.
In figure D the circle and the rectangle do not overlap, so the third dot cannot be placed.
14
direction-sense
medium
Mayank is facing towards South-West. He makes a 135° anti-clockwise turn, followed by 90° clockwise and 45° anti-clockwise turn. In the end, he turns 225° towards his right. In which direction is he facing now?
Answer: A
South-West → 135° anti-clockwise → East.
East → 90° clockwise → South.
South → 45° anti-clockwise → South-East.
South-East → 225° to the right (clockwise) → North.
He is facing North.
15
pattern-completion
medium
Select a figure from the options which will complete the given figure matrix.
Answer: B
Each row uses one outer shape, and the arrow inside turns 90° clockwise from one figure to the next: up, right, down.
The third row uses triangles, so the missing figure is a triangle with the arrow pointing down.
Mathematical Reasoning
MCQs — 20 Questions
(+1)
16
place-value
easy
On dividing the place value of 5 in 456397 by 1 less than the predecessor of 2002, we get
Answer: D
Place value of 5 in 456397 = 50000.
Predecessor of 2002 = 2001; 1 less than it = 2000.
50000 ÷ 2000 = 25.
17
angles
easy
If a bicycle wheel has 48 spokes, then the angle between a pair of two consecutive spokes is
Answer: B
The spokes divide the full turn of 360° into 48 equal angles.
360° ÷ 48 = 7.5° = (7½)°.
18
word-problems
easy
A question paper contains 30 questions. Questions from 1 to 17 are of 4 marks each and questions from 18 to 30 are of 5 marks each. Yash solves Q1, Q2, Q5, Q6, Q15, Q18, Q27 and Q30 correctly whereas Kunal solves all the questions correctly. Find the difference between the marks of Kunal and Yash.
Answer: B
Kunal: 17 × 4 + 13 × 5 = 68 + 65 = 133 marks.
Yash: 5 questions of 4 marks (Q1, Q2, Q5, Q6, Q15) + 3 questions of 5 marks (Q18, Q27, Q30) = 20 + 15 = 35 marks.
Difference = 133 − 35 = 98.
19
integers
easy
The given table shows the temperature of a city for 7 consecutive hours. Calculate the difference between the highest and the lowest temperature of the city over the 7-hour period.
Answer: B
Highest temperature = 23°C, lowest = −6°C.
Difference = 23 − (−6) = 29°C.
20
perimeter-area
medium
In the given figure, if the area of square A is 36 sq. cm and the perimeter of square C is 44 cm, then the area and perimeter of square B are respectively ___ and ___.
Answer: A
Side of A = 6 cm (6 × 6 = 36). Side of C = 44 ÷ 4 = 11 cm.
A and B together are as tall as C, so side of B = 11 − 6 = 5 cm.
Area of B = 25 sq. cm, perimeter of B = 20 cm.
21
numeration
medium
The sum of numbers shown on the given two abacuses in international system of numeration, is written as ______.
Answer: B
First abacus: 5 lakhs, 4 ten thousands, 6 thousands, 4 hundreds, 0 tens, 1 one → 546401.
Second abacus: 735263.
Sum = 546401 + 735263 = 1281664 = 1,281,664.
In the international system: One million two hundred eighty one thousand six hundred sixty four. (Option A is the Indian system.)
22
quadrilaterals
easy
A figure bounded by four sides is called rectangle, if
Answer: C
A rectangle has its opposite sides equal and every angle equal to 90°.
23
co-primes
easy
Which of the following pairs of numbers are NOT co-prime?
Answer: B
289 = 17 × 17, so 17 and 289 have the common factor 17 — they are not co-prime.
The other pairs have no common factor other than 1.
24
lines
medium
How many pairs of intersecting lines are there in the given figure?
Answer: A
There are 6 lines, giving 6 × 5 ÷ 2 = 15 pairs.
Lines l, m and n are parallel, which removes 3 pairs (l–m, m–n, l–n).
All other pairs meet: 15 − 3 = 12.
25
symmetry
hard
Find the minimum number of squares that must be added so that the line PQ becomes a line of symmetry.
Answer: D
Reflect every shaded square in PQ. Each reflection that is not already shaded must be added.
Counting row pairs (rows next to PQ first): 2 + 2 + 3 + 2 = 9 squares must be added.
9 is not among 5, 3 and 4, so the answer is 'None of these'.
26
fractions
medium
Arrange the shaded fractions of the given figures in ascending order and select the CORRECT option.
Answer: C
L: 6 of 9 equal triangles = 2/3.
M: 1 of 4 equal triangles = 1/4.
N: 2 of 9 squares = 2/9.
O: 20 of 36 squares = 5/9.
2/9 < 1/4 < 5/9 < 2/3, so the order is N, M, O, L.
27
integers
easy
Which of the following statements is CORRECT?
Answer: B
The additive inverse of −a is a, which is positive. So B is correct.
A is false (−2 + −3 = −5 is less than both), C is false (it is −6) and D is false (a − (−a) = 2a is always even).
28
decimals
hard
If 48.6305 = 4A + 8/B + 6C + 3/D + 5E, then what is the value of 6A + 3B + 4C + 2D + 3E?
Answer: C
48.6305 = 4 × 10 + 8/1 + 6 × 0.1 + 3/100 + 5 × 0.0001.
So A = 10, B = 1, C = 0.1, D = 100, E = 0.0001.
6A + 3B + 4C + 2D + 3E = 60 + 3 + 0.4 + 200 + 0.0003 = 263.4003.
29
divisibility
medium
Find the smallest values of y and z respectively such that 3725yz is divisible by both 5 and 8.
Answer: A
Divisible by 5 and by 8 (an even number) means the last digit z = 0.
For 8, the last three digits 5y0 must be divisible by 8: 500 no, 510 no, 520 = 8 × 65 yes.
So y = 2 and z = 0.
30
data-handling
easy
The given bar graph shows the quantity (in kg) of fruits sold on different days of the week. Study the given graph carefully and answer the question.
On which two consecutive days was the highest combined sale recorded?
Answer: B
Mon + Tue = 50 + 80 = 130 kg; Tue + Wed = 80 + 60 = 140 kg; Wed + Thurs = 60 + 40 = 100 kg; Thurs + Fri = 40 + 70 = 110 kg.
The highest is Tuesday and Wednesday.
31
data-handling
easy
The given bar graph shows the quantity (in kg) of fruits sold on different days of the week. If the cost of 1 kg of fruits is ₹125, then find the shopkeeper's total earning for the given 5 days.
Answer: B
Total sold = 50 + 80 + 60 + 40 + 70 = 300 kg.
Earning = 300 × ₹125 = ₹37500.
32
palindromes
medium
Find the digit sum of the number obtained by subtracting the smallest 4-digit palindrome number from the largest 4-digit palindrome number.
Answer: C
Largest 4-digit palindrome = 9999, smallest = 1001.
9999 − 1001 = 8998. Digit sum = 8 + 9 + 9 + 8 = 34.
33
decimals
medium
What should be subtracted from the difference of 852.38 and 217.50 to get the sum of 375.21 and 199.53?
Answer: C
Difference = 852.38 − 217.50 = 634.88. Sum = 375.21 + 199.53 = 574.74.
634.88 − 574.74 = 60.14.
34
number-patterns
easy
The sum of two consecutive triangular numbers is ______.
Answer: B
1 + 3 = 4, 3 + 6 = 9, 6 + 10 = 16, 10 + 15 = 25 — the sums are square numbers.
35
symmetry
easy
Which of the following letters does NOT have rotational symmetry of order 2?
Answer: D
Turning I through half a turn (180°) gives the same letter, so it has rotational symmetry of order 2.
T and P look different after a half turn, so both A and C do not.
Everyday Mathematics
MCQs — 10 Questions
(+1)
36
time
easy
Kanika takes 3 minutes 20 seconds to finish reading of one page of a storybook. If the book has 42 pages, then how long will she take to finish reading it?
Answer: C
3 min 20 s = 200 seconds per page.
200 × 42 = 8400 seconds = 140 minutes = 2 hours 20 minutes.
37
factors
easy
Radhika plants flowers in rows. Each row has the same number of flowers. If there are 180 flowers, then which of the following numbers could NOT be the number of flowers in each row?
Answer: B
The number in each row must be a factor of 180.
180 ÷ 5 = 36, 180 ÷ 12 = 15, 180 ÷ 15 = 12, but 180 ÷ 8 = 22.5, so 8 is not possible.
38
perimeter-area
medium
A room is 11.5 m long and 6.3 m wide. Its floor is to be covered with rectangular tiles of size 23 cm by 9 cm. Find the total cost of tiling the floor at the rate of ₹4.25 per tile.
Answer: D
Floor area = 1150 cm × 630 cm = 724500 sq. cm. Tile area = 23 × 9 = 207 sq. cm.
Number of tiles = 724500 ÷ 207 = 3500.
Cost = 3500 × ₹4.25 = ₹14875.
39
integers
easy
An elevator starts from the ground floor, goes up 7 floors, then goes down 5 floors, and finally goes up 3 more floors. On which floor is elevator now?
Answer: A
0 + 7 − 5 + 3 = 5, so the elevator is on the 5th floor.
40
fractions
medium
A magician has 16⅓ m long rope. He divides it into 3 parts. If the top and the bottom part measures 4⅞ m each, then find the length of the middle part of the rope.
Answer: B
Top + bottom = 4⅞ + 4⅞ = 9¾ m.
Middle = 16⅓ − 9¾ = 49/3 − 39/4 = 196/12 − 117/12 = 79/12 = 6 7/12 m.
41
fractions
medium
Sneha was asked to find the total of 4⅖ and 1½, but she made a mistake and subtract 1½ from 4⅖. Find the difference between the correct answer and the result she obtained.
Answer: C
Correct answer = 4⅖ + 1½ = 5 9/10. Her answer = 4⅖ − 1½ = 2 9/10.
Difference = 5 9/10 − 2 9/10 = 3 (that is, twice 1½).
42
divisibility
easy
You come across a bridge, but it is blocked by divisibility traps. You need to cross, but the bridge will only open if you choose a 3-digit number less than 500 which is divisible by 2, 4 and 8. Which of the following could be that possible 3-digit number?
Answer: B
A number divisible by 8 is also divisible by 2 and 4.
288 = 8 × 36 ✓. 246 and 498 are not divisible by 4, and 512 is more than 500.
43
division
easy
A baker baked 18 cakes. Each cake was cut into 12 slices. If he sold 196 slices, then how many full cakes are left?
Answer: D
Total slices = 18 × 12 = 216. Slices left = 216 − 196 = 20.
20 slices make 1 full cake (12 slices) with 8 slices left over, so 1 full cake is left.
44
estimation
medium
A bookstore sells novels for ₹275 each and magazines for ₹85 each. If a customer buys 4 novels and 6 magazines, then estimate the total cost nearest to the thousands place.
Answer: D
Total = 4 × 275 + 6 × 85 = 1100 + 510 = ₹1610.
Rounded to the nearest thousand: ₹2000.
45
perimeter-area
medium
A square plot of land has an area of 625 sq. m. A road of uniform width is constructed along the boundary of the plot, reducing the area of the plot to 400 sq. m. What is the width of the road?
Answer: A
Side of the plot = 25 m. Side of the remaining square = 20 m.
The road takes 25 − 20 = 5 m off the side, shared between two edges: width = 5 ÷ 2 = 2.5 m.
Achievers Section
MCQs — 5 Questions
(+3)
46
integers
hard
Solve the following and select the CORRECT option.
(i) Find the sum of smallest 3-digit odd positive integer and additive inverse of the smallest 2-digit prime number.
(ii) In a set of 3 numbers, the first number is −5, the second number is the additive inverse of the first number and the third number is the additive inverse of the second number. What is the sum of the three numbers?
Answer: A
(i) Smallest 3-digit odd number = 101; smallest 2-digit prime = 11, its additive inverse = −11. 101 + (−11) = 90.
(ii) The numbers are −5, 5 and −5. Sum = −5.
47
fractions
hard
Study the following statements carefully and select the CORRECT option.
Statement-I : In a group of 35 students, 3/5 of the students are wearing glasses. If 2/3 of those students are wearing glasses are boys and 1/2 of the boys wearing glasses are in grade 6, then 7 boys from grade 6 are wearing glasses.
Statement-II : If 5/8 of a certain number is 45 and 3/4 of that number is divided equally into 9 parts, then the value of each part is 8.
Answer: C
Statement-I: 3/5 of 35 = 21 wear glasses; 2/3 of 21 = 14 are boys; 1/2 of 14 = 7. True.
Statement-II: the number = 45 × 8/5 = 72; 3/4 of 72 = 54; 54 ÷ 9 = 6, not 8. False.
48
number-properties
hard
Read the given statements carefully and state 'T' for true and 'F' for false.
(i) All numbers that have 5 at the ones place are prime.
(ii) The largest number less than 299 that is divisible by 4 is 298.
(iii) The sum of the largest and the smallest 3-digit palindrome numbers that are divisible by 2 is 1100.
Answer: B
(i) False: 15 = 3 × 5 is not prime.
(ii) False: 298 is not divisible by 4; the answer is 296.
(iii) True: the even 3-digit palindromes run from 202 to 898, and 202 + 898 = 1100.
49
angles
hard
Fill in the blanks and select the CORRECT option.
(i) The number of right angles formed when an hour hand of a clock moves from 4 to 10 is (P).
(ii) The angle bisector of a right angle divides it into two angles of (Q) each.
(iii) The largest angle formed between the hands of a clock at 9 O' clock is (R).
Answer: A
(i) From 4 to 10 is 6 hour marks = 6 × 30° = 180° = 2 right angles.
(ii) 90° ÷ 2 = 45°.
(iii) At 9 o'clock the hands make 90°; the larger (reflex) angle is 360° − 90° = 270°.
50
symmetry
hard
Match the following and select the CORRECT option.
Column-I: figures P, Q and R.
Column-II:
(i) Order of rotational symmetry = 3, Angle of rotational symmetry = 120°
(ii) Number of lines of symmetry = 2, Order of rotational symmetry = 2
(iii) Order of rotational symmetry = 4, Angle of rotational symmetry = 90°
Answer: B
P (square, diamond and four rings at the corners) looks the same after every quarter turn: order 4, angle 90° → (iii).
Q (oval with two circles) has a horizontal and a vertical line of symmetry and looks the same after a half turn → (ii).
R (circle with a triangle and three spokes) looks the same after every 120° turn: order 3 → (i).