Logical Reasoning
MCQs — 15 Questions
(+1)
1
symmetry
medium
How many of the following figures have more than one line of symmetry?
Answer: D
Count the lines of symmetry of each figure, from left to right:
Hourglass: 2 lines (vertical and horizontal).
Circle with one shaded sector: 1 line.
Square with two opposite quarters shaded: 2 lines (both diagonals).
Diamond with four shaded corners: 4 lines.
Triangle with a shaded top: 1 line.
Two circles with opposite halves shaded: 0 lines.
So 3 figures have more than one line of symmetry.
2
number-puzzle
easy
Find the missing number in the given grid.
Answer: A
Use the position of each letter in the alphabet and multiply.
F (6) × H (8) = 48 and I (9) × C (3) = 27.
So G (7) × D (4) = 28.
3
direction-sense
easy
Rohit walks 3 km towards North. Then he turns to his right and walks 6 km. Then he turns to his left and walks 3 km. In which direction is he now from his starting point?
Answer: B
He walks North, then turns right to face East, then turns left to face North again. In total he has gone 6 km North and 6 km East, so he is to the North-East of his starting point.
4
word-formation
easy
Some letters are numbered as given below. Select the combination of numbers so that the letters are arranged to form a meaningful English word.
C A R D E N
1 2 3 4 5 6
Answer: C
4 = D, 2 = A, 6 = N, 1 = C, 5 = E, 3 = R. So 4, 2, 6, 1, 5, 3 spells DANCER.
5
coding-decoding
easy
Each number in the table is written as a symbol. Using the table, how will 794615 be written?
Answer: B
7 = D, 9 = ©, 4 = ÷, 6 = K, 1 = $, 5 = #. So 794615 is written as D©÷K$#.
6
venn-diagram
easy
Which of the following Venn diagrams best represents the relationship amongst "Languages, English and Hindi"?
Answer: A
English and Hindi are both languages, so both circles go inside the big Languages circle. English and Hindi are different languages, so their circles do not overlap. This is diagram A.
7
calendar
easy
If Vani went for volleyball practice every day in January 20XX except the dates which are divisible by 5, then for how many days did she go for volleyball practice in that month?
Answer: D
January has 31 days. The dates divisible by 5 are 5, 10, 15, 20, 25 and 30, which is 6 days. So she practised on 31 − 6 = 25 days.
8
analytical-reasoning
medium
Aniket and Kabir like swimming and reading. Sonal and Monika like cooking and reading. Only Monika likes dancing. Who among them likes more than two activities?
Answer: D
Aniket and Kabir like 2 activities each (swimming, reading). Sonal likes 2 (cooking, reading). Monika likes cooking, reading and dancing, which is 3 activities.
9
pattern-completion
hard
Select a figure from the options which will complete the given figure pattern.
Answer: B
The figure is symmetrical about the vertical line, so the missing bottom-right quarter must be the mirror image of the bottom-left quarter. It needs an arrow pointing to the centre, the right half of the bar with its dot along the top, and the right half of the shaded triangle in the bottom corner next to the vertical line. Option A has no dot in the bar, so the answer is B.
10
odd-one-out
medium
Select the odd one out.
Answer: C
In FJH, RVT and TXV, the second letter is 4 places after the first and the third letter is 2 places before the second (F +4 → J −2 → H). In KPM, K +5 → P −3 → M, so KPM is the odd one out.
11
water-image
medium
Select the CORRECT water image of the given figure.
Answer: A
A water image flips the figure upside down. The small triangle with the dot moves to the top and the triangle with 8 moves to the bottom. The middle row keeps its order (5, E, T) but each character is turned upside down, so T becomes ⊥ and 5 is flipped. Only option A shows this.
12
ranking
medium
A man is standing in a queue of 28 people on a bus ticket counter. His position is 9th from the front. If 3 people behind him leave the queue, then what will be his new position from the end of the queue?
Answer: C
After 3 people leave, there are 28 − 3 = 25 people in the queue. He is still 9th from the front, so his position from the end is 25 − 9 + 1 = 17th.
13
time
medium
Shubham travels from Delhi to Bhopal via train as per the time shown in the clocks. For how long did he travel?
Answer: C
The train left Delhi at 3:45 in the morning and arrived at Bhopal at 12:20 in the afternoon.
3:45 to 11:45 is 8 hours, and 11:45 to 12:20 is 35 minutes. So he travelled for 8 hrs 35 mins.
14
figure-analogy
hard
There is a certain relationship between the pair of figures on the either side of ::. Identify the relationship between the left pair and find the missing figure.
Answer: D
In the first pair, the outer square stays as the frame, the middle shape (square) becomes small in the centre, and the innermost shape (circle) is cut into two halves placed above and below it.
In the second figure the middle shape is a circle and the innermost shape is a diamond. So the answer has a small circle in the centre, with the diamond cut into two triangles above and below it. This is option D.
15
ranking
easy
In a group of 5 students P, Q, R, S and T; P scored more than S, Q scored less than T and S scored more than T. If R scored the least, then who amongst the following scored the highest?
Answer: A
P > S, S > T and T > Q, so P > S > T > Q. R scored the least, so the order is P > S > T > Q > R. P scored the highest.
Mathematical Reasoning
MCQs — 20 Questions
(+1)
16
angles
easy
Which of the following options shows an acute angle?
Answer: C
An acute angle is less than 90°. A is a right angle (90°), B and D are obtuse angles (more than 90°), and C is less than 90°.
17
multiples
easy
The difference between the 15th multiple of 20 and 9th multiple of 9 is ______.
Answer: B
15th multiple of 20 = 15 × 20 = 300. 9th multiple of 9 = 9 × 9 = 81. 300 − 81 = 219.
18
decimals
medium
The shaded decimal part for the given figure is ______.
Answer: C
The figure has 8 parts in the outer ring and 8 parts in the inner circle, so 16 equal parts in all. 5 outer parts and 5 inner parts are shaded, which is 10 parts.
10/16 = 5/8 = 0.625.
19
area
medium
Find the area of the shaded part in the given figure (not drawn to scale).
Answer: B
Area of the big rectangle = 22 × 8 = 176 sq. cm.
Area of the small square = 4 × 4 = 16 sq. cm. Area of the inner rectangle = 6 × 7 = 42 sq. cm.
Shaded area = 176 − 16 − 42 = 118 sq. cm.
20
expanded-form
easy
Select the CORRECT option.
Answer: B
72865 = 7 ten thousands + 2 thousands + 8 hundreds + 6 tens + 5 ones = 70000 + 2000 + 800 + 60 + 5.
A should have 5000, C should have 40000 and D should have 600.
21
symmetry
medium
How many line(s) of symmetry is/are there in the given figure?
Answer: C
Without the two slanting lines, the shaded pattern would have 4 lines of symmetry. The two slanting lines only match up when the figure is folded along the diagonal from the top-right corner to the bottom-left corner. So the figure has 1 line of symmetry.
22
money
medium
The given table shows the cost of shirt and pair of trousers at three different shops. Study it carefully and answer the question that follows.
If Ankur bought two pair of trousers and 1 shirt from shop B, then find the total amount spent by him.
Answer: A
At shop B, 2 pairs of trousers cost ₹1700. 3 shirts cost ₹2100, so 1 shirt costs ₹2100 ÷ 3 = ₹700.
Total = ₹1700 + ₹700 = ₹2400.
23
temperature
easy
Which of the following options represents the temperature shown on the given thermometer?
Answer: C
The thermometer shows 42°C.
A = 31°C, B = 41°C, C = 42°C and D = 51°C. So the answer is C.
24
rounding
easy
Which of the following options gives the GREATEST value when rounded off to the nearest thousands place?
Answer: B
69450 → 69000, 69857 → 70000, 68999 → 69000, 57293 → 57000. The greatest is 70000, from 69857.
25
addition-subtraction
medium
Compare the following and select the CORRECT option.
51780 + 29371 − 10258 ☐ 38542 + 52509 − 41002
Answer: A
Left: 51780 + 29371 = 81151, and 81151 − 10258 = 70893.
Right: 38542 + 52509 = 91051, and 91051 − 41002 = 50049.
70893 > 50049.
26
bar-graph
medium
Directions (Q26-27): The given bar graph shows the different activities liked by the students of a school. Study the given graph carefully and answer the following questions.
If 2/5 of the number of students who liked swimming are boys, then how many girls liked swimming?
Answer: A
225 students liked swimming. Girls are 1 − 2/5 = 3/5 of them. 3/5 × 225 = 135.
27
bar-graph
medium
Directions (Q26-27): The given bar graph shows the different activities liked by the students of a school. Study the given graph carefully and answer the following questions.
What fraction of the total students liked dancing and painting together?
Answer: B
Total = 275 + 175 + 225 + 250 = 925. Dancing and painting = 275 + 250 = 525.
525/925 = 21/37 (dividing both by 25).
28
decimals
medium
I am a decimal number. My decimal part is [1/4 of 32] and my whole part is 2 more than (2/5 of 20). Who am I?
Answer: A
Decimal part = 1/4 of 32 = 8. Whole part = 2/5 of 20 + 2 = 8 + 2 = 10. So the number is 10.8.
29
fractions
hard
Select the CORRECT option.
Answer: D
A: 195 ÷ 5 × 3 = 117. True.
B: 5 3/9 − 2 1/7 = 3 + (1/3 − 1/7) = 3 + (7 − 3)/21 = 3 4/21. True.
C: 5 × 3/15 = 1, and 1 + 1 1/8 = 2 1/8, not 3 1/8. False.
So both A and B are correct.
30
perimeter
hard
Find the perimeter of the SHADED part of the given figure (not drawn to scale).
Answer: C
Each small square has side 4.5 m. Count the sides of small squares that lie on the boundary of the shaded part: there are 24.
Perimeter = 24 × 4.5 = 108 m.
31
symmetry
medium
Which of the following figures does NOT have any line of symmetry?
Answer: A
B and C are symmetrical about a horizontal line and D is symmetrical about a vertical line. In A the shading on the left and right sides does not match, so it has no line of symmetry.
32
angles
medium
How many angles are MORE than 90° inside the given figures?
Answer: B
In the arrow, the two corners where the tail meets the head are reflex angles (270°). The other corners are 90° or less.
In the U shape, the two inner bottom corners are reflex angles (270°) and the rest are right angles.
Total = 2 + 2 = 4.
33
length
easy
If the height of pole X is 17 m 58 cm and the height of pole Y is 3 m 11 cm less than that of pole X, then find the total height of both the poles.
Answer: D
Height of Y = 17 m 58 cm − 3 m 11 cm = 14 m 47 cm.
Total = 17 m 58 cm + 14 m 47 cm = 31 m 105 cm = 32 m 5 cm.
34
roman-numerals
easy
The Roman numeral for 3539 is ______.
Answer: B
3539 = 3000 + 500 + 30 + 9 = MMM + D + XXX + IX = MMMDXXXIX.
35
abacus
medium
The number 7581 more than the number shown on the given abacus is ______.
Answer: A
The abacus shows L = 5, TTh = 3, Th = 6, H = 2, T = 0, O = 3, which is 536203.
536203 + 7581 = 543784.
Everyday Mathematics
MCQs — 10 Questions
(+1)
36
roman-numerals
easy
The number of students enrolled for a scholarship exam is 2783. Which of the following Roman numerals represents the number of students enrolled?
Answer: B
2783 = 2000 + 700 + 80 + 3 = MM + DCC + LXXX + III = MMDCCLXXXIII.
37
weight
medium
The weight of Aarav is 42.675 kg. His friend Sumit is 3.25 kg heavier than him. If Kartik's weight is 1 kg 90 g less than Sumit, then find the weight of Kartik.
Answer: D
Sumit = 42.675 + 3.25 = 45.925 kg. 1 kg 90 g = 1.090 kg.
Kartik = 45.925 − 1.090 = 44.835 kg.
38
perimeter
medium
A farmer has to wire around his rectangular field 5 times. How much wire is required, if the length of the field is 175 m and the breadth of the field is 85 m?
Answer: D
Perimeter of the field = 2 × (175 + 85) = 2 × 260 = 520 m.
Wire for 5 rounds = 5 × 520 = 2600 m.
39
addition
easy
In a particular branch of XYZ bank, the number of new savings accounts opened in the years 2022 and 2023 were 35780 and 27189 respectively. How many total savings accounts were opened in both the years?
Answer: A
35780 + 27189 = 62969.
40
temperature
easy
Pooja went for holiday in Himachal Pradesh. She recorded the temperature in the afternoon as 25°C and it got reduced by 11°C in the night. Find the temperature of that place in the night.
Answer: B
25°C − 11°C = 14°C.
41
fractions
medium
In a certain year, the number of tourists who visited Varanasi was 7500. If 2/5 of them were from America, 1/10 of remaining were from Canada and rest were from other countries, then how many tourists visited from the other countries?
Answer: D
From America = 2/5 × 7500 = 3000. Remaining = 7500 − 3000 = 4500.
From Canada = 1/10 × 4500 = 450. Other countries = 4500 − 450 = 4050.
42
multiplication
easy
A library has 30 racks. Each rack has 25 shelves and there are 50 books on each shelf. Find the total number of books in the library.
Answer: D
Shelves = 30 × 25 = 750. Books = 750 × 50 = 37500.
43
area
medium
Nitin walked along a square field and covered 812 m in 7 rounds. Find the area of the field.
Answer: C
One round = 812 ÷ 7 = 116 m, which is the perimeter. Side = 116 ÷ 4 = 29 m. Area = 29 × 29 = 841 sq. m.
44
place-value
easy
Vishal bought 5 caps having digits 5, 1, 9, 3 and 2 written on the caps. What is the greatest 5-digit number that can be formed from the digits written on the caps (using each digit exactly once)?
Answer: B
Write the digits from largest to smallest: 9, 5, 3, 2, 1. The greatest number is 95321.
45
length
medium
Priya travelled 212 km 380 m distance by train, 18 km 385 m distance by scooter, 120 km 280 m distance by car and 120 m distance by walk. How much total distance did she travel?
Answer: C
212.380 + 18.385 + 120.280 + 0.120 = 351.165 km.
Achievers Section
MCQs — 5 Questions
(+3)
46
number-sense
hard
Read the given statements carefully and state T for true and F for false.
(p) The Roman numeral MMCMXLVVI is meaningless.
(q) The place value and face value of the digit at thousands place in the number 750892 are same.
(r) The predecessor of the greatest 6-digit number is 1000000.
(s) 1 million is same as 100 lakhs.
Answer: B
(p) V is never repeated in Roman numerals, so MMCMXLVVI is meaningless. True.
(q) The thousands digit of 750892 is 0. Its place value and face value are both 0. True.
(r) The greatest 6-digit number is 999999 and its predecessor is 999998. False.
(s) 1 million = 10 lakhs, not 100 lakhs. False.
47
angles
hard
Fill in the blanks and select the CORRECT option.
(i) The angle whose measure is less than 360° but more than 180° is ______ angle.
(ii) The smaller angle between the hands of a clock at 6 : 15 is a/an ______ angle.
(iii) The number of acute angles inside the given figure is ______.
Answer: A
(i) An angle between 180° and 360° is a reflex angle.
(ii) At 6:15 the minute hand is at 3 and the hour hand is a quarter of the way from 6 to 7. The angle between them is 90° + 7.5° = 97.5°, which is obtuse.
(iii) The acute angles are at the top-left corner, the bottom-left corner and the pointed tip on the right of the upper part. That is 3.
48
symmetry
hard
The sum of number of lines of symmetry in the given figures is ______.
Answer: B
Left figure: the top and bottom triangles point outwards but the left and right triangles point inwards, and the two shaded centre squares are on one diagonal only. No fold makes the two halves match, so it has 0 lines.
Right figure: it matches when folded along the diagonal from the top-right corner to the bottom-left corner, so it has 1 line.
Sum = 0 + 1 = 1.
49
area
hard
The given figure is made up of four squares P, Q, R and S and a rectangle T. The area of rectangle is 3 1/5 times the area of square Q.
(p) Find the sum of areas of squares Q and S.
(q) Find the area of unshaded part in the given figure.
Answer: C
Area of Q = 80 ÷ 3 1/5 = 80 × 5/16 = 25 sq. cm, so the side of Q is 5 cm.
S has side 15 cm, so its area is 225 sq. cm.
(p) Q + S = 25 + 225 = 250 sq. cm.
R is as tall as S, so R is also 15 cm × 15 cm = 225 sq. cm. P fits inside R leaving a 5 cm gap, so the side of P is 15 − 5 = 10 cm and its area is 100 sq. cm.
(q) Whole figure = S + R + Q + T = 225 + 225 + 25 + 80 = 555 sq. cm. Unshaded = 555 − 100 = 455 sq. cm.
50
time
hard
The given two clocks show the time in the morning. Observe the given clocks carefully and select the INCORRECT option.
Answer: B
Clock P shows 7:15 and clock Q shows 8:30 (morning).
A: 7:15 + 1 hr 25 min = 8:40, which is 08 : 40. Correct.
B: 8:30 + 7 hr 20 min = 15:50, not 16 : 50. Incorrect.
C: Correct time of P = 8:40 and correct time of Q = 8:30 − 30 min = 8:00. Difference = 40 minutes. Correct.
D: 8:30 − 7:15 = 1 hr 15 min. Correct.
So the INCORRECT option is B.