Logical Reasoning
MCQs — 15 Questions
(+1)
1
paper-folding
medium
A rectangular transparent sheet with a pattern and a dotted line on it is given. Select a figure from the options as to how the pattern would appear when the transparent sheet is folded along the dotted line.
Answer: B
When the sheet is folded along the dotted line, the lower half turns over onto the upper half, so the lower part of the pattern is flipped top to bottom (its left–right positions stay the same). The upper part does not move.
The short line standing on the bottom edge now hangs from the top edge, and the slanting lines of the lower half now slope the other way. This matches B.
A just slides the lower half up without flipping it, C is reversed left to right, and D leaves out the short line from the lower half.
2
analogy
easy
There is a certain relationship between the pair of numbers on either side of ::. Identify the relationship and find the missing number.
87 : 56 :: 96 : ?
Answer: C
The second number is the product of the digits of the first: 8 × 7 = 56.
So 96 → 9 × 6 = 54.
3
ranking
easy
In a row of teachers, Nakul is 12th from the left end and 17th from the right end. How many teachers are there in the row?
Answer: A
Total = (position from left) + (position from right) − 1 = 12 + 17 − 1 = 28.
4
mirror-images
medium
Select the CORRECT mirror image of the given figure, if the mirror is placed vertically to the left.
Answer: D
A vertical mirror swaps left and right only; top and bottom stay where they are.
So the white triangle cell moves to the top-left and its triangle now points left, the shaded '5' moves to the top-right (reversed), the shaded '7' moves to the bottom-left (reversed) and the cell with the dots moves to the bottom-right with the black dot now on the right. This is D.
A and B are turned upside down, and in C the triangle still points right.
5
number-series
easy
Find the missing number in the given number series.
1024, 512, ?, 16, 1
Answer: C
The numbers are divided by 2, 4, 8, 16 in turn: 1024 ÷ 2 = 512, 512 ÷ 4 = 128, 128 ÷ 8 = 16, 16 ÷ 16 = 1.
The missing number is 128.
6
figure-counting
medium
Find the number of rectangles formed in the given figure.
Answer: C
Using the letters on the parts of the figure:
• Single parts: A, B, C, D, E, F, G → 7
• Two parts: BD, CE, GF → 3
• Three parts: ABD → 1
• Five parts: ABDGF → 1
• The whole figure → 1
Total = 7 + 3 + 1 + 1 + 1 = 13.
7
dot-situation
hard
Select a figure from the options which satisfies the same conditions of placement of dots as in the given figure.
Answer: A
In the given figure:
• one dot is in the region common to the triangle, the circle and the rectangle;
• one dot is in the triangle only;
• one dot is in the region common to the circle and the rectangle only (outside the triangle).
Only figure A has all three of these regions, so the dots can be placed the same way there.
In B no region is common to all three shapes, in C every part shared by the circle and the rectangle lies inside the triangle, and in D the circle and the rectangle do not overlap at all.
8
coding-decoding
hard
In a certain code language, if MEDIUM is written as GGNPWJ, then how will PLEASE be written in the same code language?
Answer: D
Split the word into two halves and reverse each half: MED IUM → DEM MUI.
Then shift the letters by +3, +2, +1 in each half: D+3 = G, E+2 = G, M+1 = N; M+3 = P, U+2 = W, I+1 = J → GGNPWJ.
PLEASE: PLE ASE → ELP ESA → E+3 = H, L+2 = N, P+1 = Q; E+3 = H, S+2 = U, A+1 = B → HNQHUB.
9
venn-diagrams
easy
Which of the following Venn diagrams best represents the relationship amongst "Brothers, Women and Fathers"?
Answer: B
Some brothers are fathers and some fathers are brothers, so these two circles overlap.
Women can be neither brothers nor fathers, so the circle for women is separate. This is B.
10
dice
medium
Three different positions of a dice are shown below. Which of the following numbers are not opposite to each other?
Answer: D
Numbers seen together on one dice are neighbours, never opposite.
• 4 is seen with 1, 2, 6 and 3, so 4 is opposite 5.
• 3 is seen with 6, 4 and 2, and 5 is already opposite 4, so 3 is opposite 1.
• The remaining pair 2 and 6 are opposite.
6 and 4 appear together on the second dice, so they are not opposite.
11
blood-relations
medium
Read the given information carefully and select the CORRECT option.
N is the mother of R. R is the brother of A, who is daughter of G. S is the brother of G. How is S related to N?
Answer: C
R and A are children of N and G, so G is N's husband.
S is G's brother, i.e. the brother of N's husband, so S is N's brother-in-law.
12
direction-sense
easy
During a race, Nidhi ran 200 m towards East. She then turns right and runs 100 m and then turns right again and runs 400 m. Finally she turns right and runs 100 m to reach the finishing point. How far is she now from the starting point?
Answer: A
East 200 m, then right (South) 100 m, then right (West) 400 m, then right (North) 100 m.
The North and South runs cancel. She is 400 − 200 = 200 m West of the starting point.
13
pattern-completion
medium
Which of the following figures will complete the pattern in the given figure?
Answer: A
The right half of the pattern is the mirror image of the left half, and the bottom half is the mirror image of the top half.
So the missing bottom-right part is the top-left part flipped both left–right and top–bottom (turned half a turn). This is A.
14
mathematical-operations
medium
If 'J' means '−', 'K' means '+', 'L' means '×' and 'M' means '÷', then the value of 13 L 70 K 35 J 45 M 9 is ______.
Answer: D
13 L 70 K 35 J 45 M 9 = 13 × 70 + 35 − 45 ÷ 9 = 910 + 35 − 5 = 940.
15
calendar
easy
If the seventh day of July is Monday, then what day will be the fourth day after 26th July?
Answer: D
The fourth day after 26th July is 30th July.
7th is Monday, so 14th, 21st and 28th are also Mondays. 29th is Tuesday and 30th is Wednesday.
Mathematical Reasoning
MCQs — 20 Questions
(+1)
16
number-system
easy
Which of the following numbers is both a cube number and a power of 2?
Answer: A
64 = 4³ and 64 = 2⁶, so it is both.
125 = 5³ is not a power of 2; 32 = 2⁵ and 128 = 2⁷ are not cubes.
17
angles
medium
How much more is the value of 2⅓ right angles than the value of ¼ of a straight angle?
Answer: B
2⅓ right angles = 7/3 × 90° = 210°.
¼ of a straight angle = ¼ × 180° = 45°.
Difference = 210° − 45° = 165°.
18
fractions
medium
The value of 6⅕ − {4⅓ + (1¼ − 1⅙)} is
Answer: B
1¼ − 1⅙ = 1/4 − 1/6 = 1/12.
4⅓ + 1/12 = 4 + 4/12 + 1/12 = 4 5/12.
6⅕ − 4 5/12 = 2 + 12/60 − 25/60 = 1 47/60, which is less than 2 but more than 1.
19
multiples
easy
The sum of 5th multiple of 6 and 6th multiple of 12 is divisible by ______.
Answer: C
5th multiple of 6 = 30 and 6th multiple of 12 = 72. Sum = 102.
102 is even, so it is divisible by 2. It is not divisible by 8, 5 or 4.
20
data-handling
medium
The given bar graph shows the production of cupcakes in a bakery shop for the first 6 months.
In which month was the production of cupcakes ¾ of the production of cupcakes in June?
Answer: C
June = 600 cupcakes. ¾ × 600 = 450.
April shows 450 cupcakes.
21
data-handling
medium
Refer to the bar graph in the previous question (production of cupcakes in the first 6 months).
How many more cupcakes were produced in the months of March and May together than the number of cupcakes produced in the months of January and February together?
Answer: D
March + May = 750 + 350 = 1100.
January + February = 700 + 300 = 1000.
Difference = 1100 − 1000 = 100.
22
number-patterns
medium
If a number starts with 26, then which of the following numbers will not appear in the Collatz sequence?
Answer: C
Collatz rule: halve an even number; for an odd number n, take 3n + 1.
26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1.
21 does not appear.
23
time
easy
A train leaves the station at 9 : 20 and takes 2 hours 25 minutes to reach its destination. Which of the following clocks shows the time it reaches the destination?
Answer: B
9 : 20 + 2 h 25 min = 11 : 45.
Clock B shows 11 : 45 (hour hand near 12, minute hand at 9).
24
number-system
medium
I am a 5-digit palindrome. I am an even number. My hundreds place digit is twice of units place digit. My thousands place digit is three less than the hundreds place digit. My tens place digit is greater than the units place digit. Identify the number.
Answer: D
45854 reads the same both ways and is even.
Units = 4, hundreds = 8 = 2 × 4, thousands = 5 = 8 − 3, tens = 5 > 4. All conditions hold.
(25852: hundreds 8 ≠ 2 × 2. 46864: thousands 6 ≠ 8 − 3. 43834: tens 3 < 4.)
25
measurement
medium
The given figure shows 4 bars of different lengths. What is the length of the longest bar?
Answer: B
Read both ends of each bar on the ruler:
P: 1.2 cm to 9.0 cm → 7.8 cm
Q: 0.4 cm to 8.6 cm → 8.2 cm
R: 1.1 cm to 8.8 cm → 7.7 cm
S: 0.6 cm to 8.2 cm → 7.6 cm
The longest bar is Q, 8.2 cm.
26
area
hard
In the figure given below, pieces of squared sheets are shown. Each small square is of 1 square unit.
Two of them can be joined together without overlapping to form a rectangle. The area of this rectangle (in square units) is ______.
Answer: A
Pieces (2) and (4) fit together: the steps of piece (4) fill the gaps under piece (2) exactly, making a rectangle 3 squares wide and 6 squares tall.
Piece (2) has 9 squares and piece (4) has 9 squares, so the area is 9 + 9 = 18 square units (= 3 × 6).
No other pair of pieces makes a rectangle.
27
number-patterns
easy
Observe the following pattern and find the sum of 1 + 3 + 5 + 7 + 9 + … + 19 + 21.
1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
Answer: A
The sum of the first n odd numbers is n².
1, 3, …, 21 are the first 11 odd numbers, so the sum is 11² = 121.
28
angles
medium
A man is standing facing South. In which direction will he face, if he turns
(a) 3 right angles clockwise
(b) ¼ of 360° anti-clockwise?
Answer: C
(a) 3 right angles = 270° clockwise: South → West → North → East.
(b) ¼ of 360° = 90° anti-clockwise: South → East.
So both answers are East.
29
figure-counting
hard
How many line segments are there in the given figure?
Answer: B
• The top line has 5 points A, B, I, G, H: it gives 5 × 4 ÷ 2 = 10 segments.
• Line I–P–F has 3 points: IP, PF, IF → 3.
• Line G–P–E has 3 points: GP, PE, GE → 3.
• BC, BE, CE and HF → 4.
Total = 10 + 3 + 3 + 4 = 20.
30
area
easy
Find the maximum number of squares, each with side of 6 cm, that can be cut from a rectangular sheet of paper measuring 24 cm by 18 cm.
Answer: D
Along 24 cm: 24 ÷ 6 = 4 squares. Along 18 cm: 18 ÷ 6 = 3 squares.
Total = 4 × 3 = 12.
31
symmetry
medium
Which of the following figures does not have any line of symmetry?
Answer: D
A, B and C each have a vertical line of symmetry (C also has a horizontal one).
In D the two circles are at opposite corners, so no fold line makes the halves match. D has no line of symmetry.
32
integers
medium
Find the sum of largest 5-digit even positive integer and the largest 5-digit odd negative integer.
Answer: A
Largest 5-digit even positive integer = 99998.
Largest 5-digit odd negative integer = −10001 (closest to zero).
99998 + (−10001) = 89997.
33
number-system
easy
The sum of predecessor and successor of the smallest five digit number formed from the digits 1, 4, 0, 2 and 5 (using each digit only once) is ______.
Answer: A
Smallest 5-digit number = 10245 (0 cannot be first).
Predecessor + successor = 10244 + 10246 = 20490.
34
number-system
easy
What must be added to 98999 to make half a million?
Answer: D
Half a million = 500000.
500000 − 98999 = 401001.
35
circles
easy
To construct two concentric circles, you need to ensure that they:
Answer: C
Concentric circles share the same centre and have different radii.
Everyday Mathematics
MCQs — 10 Questions
(+1)
36
perimeter
easy
A thin wire is bent to form a regular octagon with each side measuring 10 cm. If it is reshaped into regular pentagon, then what is the length of each side of the pentagon?
Answer: B
Length of wire = 8 × 10 = 80 cm.
Pentagon side = 80 ÷ 5 = 16 cm.
37
fractions
medium
If one-eighth of a pencil is black, half of the remaining is yellow and the remaining 3½ cm is blue, then what is the total length of the pencil?
Answer: C
After the black part, 7/8 is left. Half of that is yellow, so blue = ½ × 7/8 = 7/16 of the pencil.
7/16 of the length = 3½ = 7/2 cm, so length = 7/2 × 16/7 = 8 cm.
38
multiplication
easy
Each floor of a building is fitted with 20 doors. There are 12 such floors in one building and there are 25 such buildings in a complex. Find the total number of doors fitted in the complex.
Answer: C
Doors = 20 × 12 × 25 = 240 × 25 = 6000.
39
time
medium
Mr. Kapoor left his office at 15:45 to attend a 3-hour seminar in Delhi. He took 2 hours 20 minutes to drive there but was 25 minutes late for the seminar. At what time did the seminar end?
Answer: D
He reached at 15:45 + 2 h 20 min = 18:05.
He was 25 minutes late, so the seminar started at 18:05 − 25 min = 17:40.
It ended 3 hours later at 20:40.
40
number-patterns
medium
Alisha is given two number sequence namely Triangular numbers and Virahānka numbers. She needs to identify among the following numbers which is both a Triangular number and Virahānka number. What could be her answer?
Answer: A
Triangular numbers: 1, 3, 6, 10, 15, 21, 28, …
Virahānka numbers: 1, 2, 3, 5, 8, 13, 21, 34, …
21 is in both lists. (28 and 15 are only triangular; 13 is only Virahānka.)
41
fractions
easy
In a survey, 80 students were asked to vote for their favourite subject from English, Science and Maths. ⅕ voted for English, ¼ voted for Science and the rest voted for Maths. How many more students voted for Maths than English?
Answer: C
English = ⅕ × 80 = 16. Science = ¼ × 80 = 20.
Maths = 80 − 16 − 20 = 44.
44 − 16 = 28 more students.
42
direction-sense
easy
From Library, Drishti need to take left turn and cover 93 steps to reach the community hall. One day, by mistake, she turns to right and after walking 53 steps, she realised that she is walking in the opposite direction. How many steps she has to walk back to reach the community hall?
Answer: A
She is 53 steps away from the library on the wrong side. She must walk 53 steps back to the library and then 93 more steps to the hall.
53 + 93 = 146 steps.
43
area
hard
Priya used four similar rectangular carpets and a square carpet for the flooring in her study room as shown below.
If it cost her ₹6 per square metre for the rectangular carpets and ₹8 per square metre for the square carpet, then how much did she pay in all?
Answer: D
Each rectangular carpet is 6 m long and 2 m wide, so its area is 12 m². Four of them: 48 m² × ₹6 = ₹288.
The square carpet in the middle has side 6 − 2 = 4 m, so its area is 16 m²: 16 × ₹8 = ₹128.
Total = ₹288 + ₹128 = ₹416.
44
prime-numbers
medium
A safe has digital lock with password which is the product of three distinct prime numbers. If the sum of these prime numbers is 15, then which of the following could be the password of safe?
Answer: A
Three distinct primes adding to 15: 3 + 5 + 7 = 15.
Product = 3 × 5 × 7 = 105.
(132 = 2 × 2 × 3 × 11, 175 = 5 × 5 × 7, 30 = 2 × 3 × 5 with sum 10.)
45
multiplication
easy
There are 26 rows of mango trees in a farm. Each row has 324 trees. Trees of 7 rows are cut down. The total number of remaining mango trees in the farm is ______.
Answer: C
Remaining rows = 26 − 7 = 19.
19 × 324 = 6156 trees.
Achievers Section
MCQs — 5 Questions
(+3)
46
angles
hard
Study the following statements about the given figure carefully and state 'T' for true and 'F' for false.
P. There are 6 reflex angles inside the figure.
Q. There are 5 pairs of perpendicular lines inside the figure.
R. There are 2 acute angles inside the figure.
Answer: A
Go round the 15 corners of the figure and look at each inside angle.
• Reflex angles (more than 180°): the 6 corners that point inwards → P is true.
• Pairs of perpendicular sides: 4 right-angled corners, plus the 2 inward corners of 270° where the sides are also perpendicular → 6 pairs, not 5 → Q is false.
• Acute angles: the 4 sharp points of the figure (two on the right, two on the left) → 4, not 2 → R is false.
Answer: T, F, F.
47
data-handling
hard
The given pictograph shows the sales of bicycles in various shops in a year. Study the given graph carefully and answer the following questions.
(i) The cost of a bicycle in shop R is ₹1250. If cost of a bicycle in shop P is ₹450 more than of shop R, then who among shop P and shop R had more earning and by how much?
(ii) Find the difference of earning of shop Q and shop S, if cost of each bicycle in shop Q and shop S are ₹1500 and ₹1750 respectively.
Answer: B
Bicycles sold: P = 4 × 40 = 160, Q = 3 × 40 = 120, R = 5 × 40 = 200, S = 2 × 40 = 80.
(i) R earns 200 × ₹1250 = ₹250000. P's price is ₹1250 + ₹450 = ₹1700, so P earns 160 × ₹1700 = ₹272000. P earns more, by ₹22000.
(ii) Q earns 120 × ₹1500 = ₹180000 and S earns 80 × ₹1750 = ₹140000. Difference = ₹40000.
48
integers
medium
Read the given statements carefully and select the CORRECT option.
Statement-1 : The sum of −5, 8, −11, 14 and 29 is 36 more than the largest negative integer.
Statement-2 : The sum of two integers is −108. If one of them is −74, then the additive inverse of other integer is −34.
Answer: A
Statement-1: −5 + 8 − 11 + 14 + 29 = 35. The largest negative integer is −1, and −1 + 36 = 35. True.
Statement-2: the other integer = −108 − (−74) = −34. Its additive inverse is 34, not −34. False.
49
fractions
hard
Match the following and select the CORRECT option.
Column-I
(i) The fraction of prime numbers from 1 to 30 is
(ii) If the product of a number and the sum of 2⅕ and 9/5 is 76, then the number is
(iii) The equivalent fraction of 13/15 is
(iv) If one-sixth of two-fifth of a number is 50, then 1/15 of the same number is
Column-II
(p) 19
(q) 50
(r) 1/3
(s) 52/60
Answer: C
(i) Primes from 1 to 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 → 10 of 30 = 1/3 → (r).
(ii) 2⅕ + 9/5 = 11/5 + 9/5 = 4. The number = 76 ÷ 4 = 19 → (p).
(iii) 13/15 = (13 × 4)/(15 × 4) = 52/60 → (s).
(iv) 1/6 × 2/5 = 1/15, so 1/15 of the number is 50 → (q).
50
perimeter-area
hard
Refer to the given figure (not drawn to scale), answer the following questions and select the CORRECT option.
(i) Find the perimeter of the figure.
(ii) Find the area of the figure.
Answer: C
The full width is 6 + 3 + 9 = 18 cm, and along the bottom 12 + 4 + 2 = 18 cm, so the gap at the bottom is 4 cm wide.
The gap is as deep as the 5 cm step on the left: the bottom of the 3 cm notch is 5 cm high (10 − 5), and the top of the gap is at the same height.
(i) Perimeter = 10 + 6 + 5 + 3 + 10 + 9 + 15 + 2 + 5 + 4 + 5 + 12 = 86 cm.
(ii) Area = left part 6 × 10 + middle strip 3 × 5 + right part (9 × 15 − 4 × 5) = 60 + 15 + 115 = 190 cm².