Logical Reasoning
MCQs — 15 Questions
(+1)
1
number-series
medium
How many such prime numbers are there in the given sequence, each of which is immediately preceded by an odd number but not immediately followed by an even number?
4 2 7 1 5 3 6 9 2 3 7 2 5 3 8 1 9 7 4
Answer: D
Check each prime with its neighbours:
1 5 3 — 5 is preceded by 1 (odd) and followed by 3 (odd) ✓
9 2 3 — 2 is preceded by 9 (odd) and followed by 3 (odd) ✓
7 2 5 — 2 is preceded by 7 (odd) and followed by 5 (odd) ✓
Every other prime is either preceded by an even number (2 7, 2 3, 2 5) or followed by an even number (5 3 6, 3 7 2, 5 3 8, 9 7 4).
So there are three such primes.
2
counting-cubes
medium
Count the number of unit cubes in the given figure.
Answer: A
Count the columns of cubes row by row (every cube is supported from below).
Back row: 4 + 4 + 4 + 4 = 16; second row: 4 + 4 + 3 + 3 = 14; third row: 3 + 3 + 3 + 2 = 11; front row: 3 + 3 + 2 + 2 = 10.
Total = 16 + 14 + 11 + 10 = 51.
3
mirror-and-water-images
medium
Select the correct water image of the given figure.
Answer: C
A water image flips the figure upside down, keeping left and right the same.
The circle moves from the top-left to the bottom-left, the grey triangle points upwards and the thick bar moves to the bottom-right — that is figure C.
A is a mirror image, B is the figure turned through 180°, and in D the circle has not been flipped.
4
alphanumeric-series
medium
Find the missing letter, if a certain rule is followed either row-wise or column-wise.
Answer: B
Use the positions of the letters in the alphabet.
Column 1: R + J + H = 18 + 10 + 8 = 36. Column 2: T + K + I = 20 + 11 + 9 = 40.
The column sums go up by 4, so column 3 must total 44: 22 (V) + ? + 13 (M) = 44, so ? = 9 = I.
5
venn-diagrams
easy
Which of the following Venn diagrams best represents the relationship amongst "Iron, Hydrogen and Metals"?
Answer: C
Iron is a metal, so the Iron circle lies inside the Metals circle.
Hydrogen is not a metal, so it is a separate circle. That is diagram C.
6
direction-sense
easy
Ankit is walking towards North. After walking 25 m, he takes two consecutive left turns, walking 30 m after each turn. Finally he turns 90° towards his right and walks 10 m. In which direction is he facing now?
Answer: A
North → left → West → left → South → right → West.
He is facing West.
7
blood-relations
medium
Neeta who is the sister-in-law of Anshu, is the daughter-in-law of Riya. Neeraj is the father of Abhishek, who is the only brother of Anshu. How is Neeta related to Abhishek, if Neeraj and Riya are a married couple?
Answer: C
Neeraj and Riya are the parents of Abhishek and Anshu.
Neeta is Riya's daughter-in-law and Anshu's sister-in-law, so she is married to Riya's son.
Abhishek is Anshu's only brother, so Neeta is Abhishek's wife.
8
calendar
medium
Riya visited India Gate on 3rd Wednesday of December 20XX. If first day of the next month is Tuesday, then on which date did she visit India Gate?
Answer: D
1st January is a Tuesday, so 31st December is a Monday.
The Wednesdays of December are then 26th, 19th, 12th and 5th.
The 3rd Wednesday is 19th December.
9
coding-decoding
medium
If in a certain code language, JUMP is written as 16132110 and BOAT is written as 201152, then how will SAIL be written in the same code language?
Answer: A
Each word is written backwards using alphabet positions: JUMP → P M U J → 16 13 21 10; BOAT → T A O B → 20 1 15 2.
SAIL → L I A S → 12 9 1 19 → 129119.
10
odd-one-out
medium
Select the odd one out.
Answer: D
In A, B and C one dot is in the region common to all three shapes, one is in the triangle and square only, and one is in the circle and square only.
In D there is no region common to all three shapes; it has a dot in the triangle and circle only instead. So D is the odd one out.
11
classification
medium
Group the given figures into three classes on the basis of their identical properties using each figure only once.
Answer: A
Figures 1, 3 and 5 are made of straight lines only.
Figures 2, 4 and 8 are made of both straight lines and curves.
Figures 6, 7 and 9 are made of curves only.
12
counting-figures
hard
Find the minimum number of straight lines required to draw the given figure.
Answer: C
The figure has three triangles (3 lines each) and two horizontal lines inside the upright triangle.
No two of these lines lie along the same straight line, so the minimum is 3 + 3 + 3 + 2 = 11.
13
mathematical-operations
easy
If '+' denotes '÷', '÷' denotes '−', '−' denotes '×' and '×' denotes '+', then find the value of 54 − 3 × 18 + 3 ÷ 24.
Answer: B
Replace the signs: 54 × 3 + 18 ÷ 3 − 24.
= 162 + 6 − 24 = 144.
14
pattern-completion
medium
Select a figure from the options which will complete the given figure matrix.
Answer: B
In the bottom row, the right figure is the mirror image (left–right) of the left figure.
So the missing figure is the mirror image of the top-left figure, which is B.
A is turned through 180°, C is flipped upside down and in D one line has changed.
15
transparent-sheet-folding
hard
A square 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
The bottom half folds up onto the top half, so its shapes are reflected in the dotted line.
The L-shape turns upside down and the small triangle at the bottom-left now points downwards at the top-left, while the shapes in the top half stay where they are.
A moves the bottom shapes up without flipping them, C does not flip the small triangle, and D has lost the triangle at the top-right. B is correct.
Mathematical Reasoning
MCQs — 20 Questions
(+1)
16
integers
easy
Which of the following statements represents a negative integer?
Answer: D
Diving 250 m below the surface is written as −250 m, a negative integer. The other three are positive.
17
fractions
easy
A square is divided into certain number of equal parts. If 22 such equal parts represent 1/15 of the square, then the total number of equal parts of the square is ______.
Answer: C
1/15 of the square = 22 parts, so the whole square = 22 × 15 = 330 parts.
18
angles
medium
How many right angles are required to be added to get (7/2 complete angles + 5/2 straight angles)?
Answer: A
A complete angle = 4 right angles, so 7/2 complete angles = 14 right angles.
A straight angle = 2 right angles, so 5/2 straight angles = 5 right angles.
Total = 14 + 5 = 19 right angles.
19
symmetry
medium
Which of the following figures has same number of line(s) of symmetry and order of rotational symmetry?
Answer: D
A (H): 2 lines of symmetry (vertical and horizontal) and order of rotational symmetry 2.
B (stack of ovals): 2 lines of symmetry and order 2.
C: the circles sit in a pinwheel pattern, so it has order 4 but no line of symmetry.
So both A and B.
20
place-value
easy
Which of the following has the least value?
Answer: C
A: 2000 + 100 = 2100. B: 2000 + 10 = 2010. C: 200 + 10 = 210. D: 2000 + 1000 = 3000.
The least is C (210).
21
graphs
medium
How many line segments are there in a complete graph with 5 vertices?
Answer: B
In a complete graph every pair of vertices is joined by one line segment.
Number of pairs = 5 × 4 ÷ 2 = 10.
22
data-handling
easy
The given pictograph shows the number of books of different subjects in a library. Study the given pictograph carefully and answer the question.
Which of the following subjects has 40 fewer books than Maths?
Answer: B
Maths = 5 × 20 = 100 books. 100 − 40 = 60 books = 3 symbols, which is History.
23
data-handling
easy
The given pictograph shows the number of books of different subjects in a library. If some computer books are added to the library and the total number of books becomes 360, then how many symbols would represent the number of computer books?
Answer: A
Books now = (4 + 3 + 5 + 2) × 20 = 280. Computer books = 360 − 280 = 80 = 80 ÷ 20 = 4 symbols.
24
number-properties
medium
Which of the following numbers has the same digit sum as 843, is greater than 500 and having digits arranged in decreasing order?
Answer: A
Digit sum of 843 = 15.
654: sum 15, more than 500, digits 6 > 5 > 4 ✓. 471 is less than 500; 645 and 582 are not in decreasing order.
25
divisibility
medium
Which of the following options shows the palindromic number greater than 500 that should replace xyz in 615xyz so that the resulting number is divisible by 8?
Answer: B
A number is divisible by 8 if its last three digits are divisible by 8.
The palindromes greater than 500 among the options: only 616, and 616 = 8 × 77 ✓. (232 and 404 are less than 500.)
26
rounding
medium
If P is the smallest 5-digit number formed by using the digits 7, 4, 3, 5, 6 (using each digit only once) and Q is obtained by rounding off P to nearest hundreds, then how much more is the value of Q than the number 31456?
Answer: B
P = 34567. Rounded to the nearest hundred, Q = 34600.
Q − 31456 = 3144.
27
lines
medium
The difference between the number of pairs of intersecting lines and the number of pairs of parallel lines in the given figure is ______.
Answer: C
There are 5 lines, giving 5 × 4 ÷ 2 = 10 pairs.
There are two pairs of parallel lines (the two lines slanting up to the right, and the two slanting down to the right).
The other 10 − 2 = 8 pairs intersect. Difference = 8 − 2 = 6.
28
quadrilaterals
easy
Which of the following describes the correct relationship between the diagonals of a square?
Answer: A
The diagonals of a square are equal and are perpendicular bisectors of each other.
29
symmetry
hard
Which of the following square(s) must be shaded so that given figure is symmetric along both lines LM and AB?
Answer: C
Reflect each shaded square in both diagonals.
The shaded square next to Q in the top row reflects in AB onto Q, and the shaded square in the bottom row next to the corner reflects in AB onto P.
These two also reflect onto each other in LM, and every other shaded square already has its partners. So Q and P must be shaded.
30
word-problems
medium
Three water bottles X, Y and Z contain 920 mL of water altogether. Bottle X contains twice as much water as bottle Y. Bottle Z contains 20 mL less water than bottle X. How much quantity of water is there in bottle Z?
Answer: D
Let Y = y. Then X = 2y and Z = 2y − 20.
y + 2y + 2y − 20 = 920 → 5y = 940 → y = 188.
X = 376 mL, so Z = 376 − 20 = 356 mL.
31
perimeter-area
medium
The given figure (not drawn to scale) is made up of 10 squares of the same size. The perimeter of the figure is 80 cm. Find the area of the figure.
Answer: A
The boundary of the figure is made of 16 sides of the small squares.
Side of each square = 80 ÷ 16 = 5 cm, so each square has area 25 sq. cm.
Area = 10 × 25 = 250 sq. cm.
32
fractions
medium
Arrange the unshaded fractions of the following figures in descending order and select the CORRECT option.
Answer: C
P: 4 of 12 triangles unshaded = 1/3. Q: 16 of 20 squares unshaded = 4/5.
R: 4 of 8 parts unshaded = 1/2. S: 4 of 6 triangles unshaded = 2/3.
4/5 > 2/3 > 1/2 > 1/3, so the order is Q, S, R, P.
33
perimeter-area
medium
Which of the following figures have maximum area?
Answer: B
(i) 8 × 1 + 6 × 2 = 8 + 12 = 20 sq. m.
(ii) Top 10 × 2 = 20, left side 1 × 5 = 5, bottom 7 × 1 = 7 → 32 sq. m.
(iii) Top 10 × 1 = 10, right side 2 × 5 = 10 → 20 sq. m.
Figure (ii) has the maximum area.
34
angles
easy
Which of the following figures does not contain a reflex angle inside it?
Answer: B
A reflex angle (more than 180°) appears where a figure 'dents' inwards.
A, C and D all have such inward corners. The regular hexagon (B) has every angle equal to 120°, so it has no reflex angle.
35
place-value
hard
Which least number should be subtracted from 5476938 so that the place value of digit 1 in resulting numeral becomes 100000?
Answer: D
The place value of 1 is 100000 when 1 is in the lakhs place: the result must look like _1_____.
The largest such number less than 5476938 is 5199999, so the least number to subtract is 5476938 − 5199999 = 276939.
That is not among the options, so the answer is 'None of these'.
Everyday Mathematics
MCQs — 10 Questions
(+1)
36
integers
easy
Mr. Mehta has ₹ 42 in his metro card. At the time of exit, machine shows ₹ (−12) in the card. What was his journey cost?
Answer: A
Journey cost = 42 − (−12) = 42 + 12 = ₹ 54.
37
fractions
easy
A store sells pencils in packs of 12. If a customer buys 2/3 of the packs available in a box containing 24 packs, then how many pencils did the customer buy in total?
Answer: D
2/3 of 24 packs = 16 packs. 16 × 12 = 192 pencils.
38
perimeter-area
easy
A rectangular wall has a length of 20 m and a width of 6 m. How much paint is needed to paint the wall, if 1 litre of paint covers 6 sq. m area?
Answer: C
Area = 20 × 6 = 120 sq. m. Paint = 120 ÷ 6 = 20 litres.
39
number-properties
easy
A builder wants to construct houses in such a way that the number of houses on each street is a perfect number. If he has to build between 21 to 36 houses, then how many houses can be built on a street to match this plan?
Answer: A
A perfect number equals the sum of its factors other than itself.
28 = 1 + 2 + 4 + 7 + 14, and it is the only perfect number between 21 and 36.
40
word-problems
easy
The budget for the annual day function of a school was ₹ 60,000, out of which ₹ 14,500 was paid to the tent house; ₹ 10,400 to the band party and ₹ 5,000 for refreshments. How much money was left over after meeting the expenses?
Answer: C
Expenses = 14500 + 10400 + 5000 = ₹ 29,900.
Left over = 60000 − 29900 = ₹ 30,100.
41
estimation
easy
A chef is preparing 2 dishes. The first dish will take 18 minutes to cook, and the second dish will take 43 minutes. What is the estimated total cooking time, if we round off the minutes to the nearest tens?
Answer: C
18 → 20 and 43 → 40. Estimated total = 20 + 40 = 60 minutes.
42
number-patterns
medium
An exotic flower species grows petals in a circular pattern. Each next layer of petals follow Virahānka sequence in the petals. If first and second layer has 1 and 2 petals, then how many petals does the 9th layer have?
Answer: B
In the Virahānka (Fibonacci) sequence each term is the sum of the two before it: 1, 2, 3, 5, 8, 13, 21, 34, 55.
The 9th layer has 55 petals.
43
word-problems
medium
2500 metres of cotton cloth was made into 20 rolls of 30 m each and 25 rolls of 20 m each. Find the length of the remaining cloth in metres and how many rolls of 70 m can be made with the remaining cloth?
Answer: B
Used = 20 × 30 + 25 × 20 = 600 + 500 = 1100 m. Remaining = 2500 − 1100 = 1400 m.
1400 ÷ 70 = 20 rolls.
44
perimeter-area
medium
A square plot has an area 225 sq. m. If the plot has to be reshaped into rectangle by increasing the length by 10 m and decreasing the breadth by 5 m, then what would be the perimeter of new rectangular plot?
Answer: C
Side of the square = 15 m. New length = 25 m, new breadth = 10 m.
Perimeter = 2 × (25 + 10) = 70 m.
45
number-patterns
medium
A toy robot is programmed to perform the Kaprekar routine with any 4-digit number. What output will the robot give if the input is 9831?
Answer: D
Kaprekar routine: arrange the digits in descending order and subtract the number with the digits in ascending order.
9831 − 1389 = 8442, which is not among the options. (Repeating the routine leads to 6174, which is also not listed.)
Achievers Section
MCQs — 5 Questions
(+3)
46
prime-numbers
hard
Study the following statements carefully and select the CORRECT option.
Statement-I : The sum of all 2-digit prime numbers less than 60 whose both digits are also prime is again a prime number.
Statement-II : There are 5 pairs of twin prime between 1 and 50.
Answer: B
Statement-I: the 2-digit primes below 60 with both digits prime are 23, 37 and 53. 23 + 37 + 53 = 113, which is prime. True.
Statement-II: the twin primes up to 50 are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31) and (41, 43) — 6 pairs, not 5. False.
47
data-handling
hard
The given table shows the tally marks of the number of different books sold by 5 stores in a week. Observe the given table carefully and answer the following questions.
(i) If the number of books sold by a sixth store U is 3/5 of the total number of books sold by stores P and Q, then find the number of books sold by store U.
(ii) If the cost of each book is ₹ 132, then find the total amount earned by the given five stores.
Answer: C
From the tally marks: P = 27, Q = 18, R = 11, S = 34, T = 16.
(i) U = 3/5 × (27 + 18) = 3/5 × 45 = 27.
(ii) Total books = 27 + 18 + 11 + 34 + 16 = 106. Amount = 106 × 132 = ₹ 13992.
48
angles
hard
Read the given statements carefully and state 'T' for true and 'F' for false.
(i) The smaller angle formed on turning from West to South-East is an obtuse angle.
(ii) If a circle is divided into 9 equal parts then the angle each part makes at the centre is 40°.
(iii) Sum of two acute angles can never be an acute angle.
Answer: A
(i) West to South-East is 135°, which is obtuse. True.
(ii) 360° ÷ 9 = 40°. True.
(iii) 20° + 30° = 50° is acute, so the statement is false.
49
perimeter
hard
Select the INCORRECT match, if figures (not drawn to scale) are made up of identical squares and identical equilateral triangles of side 4 cm each.
(Each option shows a figure and its perimeter.)
Answer: D
Count the sides of length 4 cm on the boundary.
A: 3 (bottom) + 2 (ends) + 6 (triangles) = 11 sides → 44 cm ✓.
B: 10 sides → 40 cm ✓.
C: 2 (ends) + 10 (top triangles) + 6 (bottom triangles) + 2 (bare bottoms) = 20 sides → 80 cm ✓.
D: 11 sides → 44 cm, not 40 cm. So D is the incorrect match.
50
number-patterns
hard
Fill in the blanks and select the CORRECT option.
(i) The maximum number of supercells in any table of 13 values is (P).
(ii) The value of (the second largest 3-digit palindrome) − (the smallest 3-digit palindrome) is (Q).
(iii) If you start with number 21, then after 4th step of Collatz sequence, the number obtained is (R).
Answer: C
(i) A supercell is greater than its neighbours, so no two supercells can be next to each other. In 13 cells the most is cells 1, 3, 5, …, 13 = 7.
(ii) Second largest 3-digit palindrome = 989; smallest = 101. 989 − 101 = 888.
(iii) 21 → 64 → 32 → 16 → 8 (odd: ×3 + 1; even: ÷2). After the 4th step we get 8.