Logical Reasoning
MCQs — 15 Questions
(+1)
1
alphanumeric-series
medium
How many such vowels are there in the given arrangement each of which is immediately preceded by an odd number and immediately followed by a prime number?
7 K 6 B 4 H 8 E O L 2 R 5 A 7 9 T 6 U 1 G 3 I 2
Answer: B
Look at each vowel with its neighbours:
E: 8 E O, so 8 is not odd. O: E O L, no numbers. A: 5 A 7, odd before and prime after ✓. U: 6 U 1, 6 is not odd. I: 3 I 2, odd before and prime after ✓.
So there are 2 such vowels.
2
counting-lines
hard
How many minimum number of straight lines are required to draw the given figure?
Answer: C
Horizontal lines: the bottom, the middle line and the shorter line below it = 3.
Vertical lines: the left side, the right side and the short line under the slanting top = 3.
The slanting top edge = 1.
The slanting lines inside: the two long diagonals that cross on the left, the long line from the short vertical down to the bottom-right corner, the line from the top-right corner, the steep line down to the bottom, and the two pieces on the right (they meet at an angle, so they are 2 lines) = 7.
Total = 3 + 3 + 1 + 7 = 14.
3
alphabet-series
easy
Find the missing alphabet in the given alphabet pattern.
Y, W, T, P, ?, E
Answer: A
Going back in the alphabet: Y −2 → W, W −3 → T, T −4 → P, P −5 → K, K −6 → E.
The missing letter is K.
4
odd-one-out
medium
Select the odd one out.
Answer: B
In each card, count the small circles and the sides of the shape inside.
A: triangle (3 sides), 4 circles. C: square (4 sides), 5 circles. D: hexagon (6 sides), 7 circles.
So the rule is circles = sides + 1.
B has a pentagon (5 sides) with 7 circles, which breaks the rule. B is the odd one out.
5
coding
easy
If "Train" is called "Bus", "Bus" is called "Aeroplane", "Aeroplane" is called "Ship" and "Ship" is called "Scooter", then ________ is an air transport.
Answer: B
An aeroplane is the air transport. In this code "Aeroplane" is called "Ship".
So the answer is Ship.
6
mirror-image
medium
Select the CORRECT mirror image of the given figure.
Answer: B
The mirror is on the right, so left and right swap. Top and bottom stay the same.
The shaded pieces move to the top-right and bottom-left. Each letter is also flipped: B comes out reversed on the left, and the reversed K and L come out as normal K and L.
Only option B has both the letters and the shading correct.
7
logical-reasoning
easy
Kanika's mother correctly remembers that Kanika's swimming competition will be after 10th June but before 15th June. Her brother correctly remembers that Kanika's swimming competition will be after 12th June but on an even date. On which date will Kanika's swimming competition be held?
Answer: D
Mother: 11, 12, 13 or 14 June.
Brother: after 12th, so 13 or 14 June, and it must be an even date.
So the competition is on 14th June.
8
directions
easy
Who is in the South-West of Riya?
Answer: C
North is at the top of the grid. South-West means down and to the left.
Monika is one step left and one step down from Riya, on the same diagonal.
So Monika is in the South-West of Riya.
9
blood-relations
easy
Shruti is the daughter of Anuj, who is the only son of Bhawna. If Deepika is the daughter-in-law of Bhawna, then how is Shruti related to Deepika?
Answer: C
Bhawna has only one son, Anuj, so her daughter-in-law Deepika is Anuj's wife.
Shruti is Anuj's daughter, so Shruti is Deepika's daughter.
10
dictionary-order
easy
Arrange the following words as they occur in a dictionary and select the CORRECT option.
1. Gentle 2. Galaxy 3. Genius 4. Gainer 5. Ginger
Answer: D
Gainer and Galaxy both start with Ga: Gai comes before Gal, so Gainer (4) comes before Galaxy (2).
Genius and Gentle both start with Gen: Geni comes before Gent, so Genius (3) comes before Gentle (1).
Ginger (5) comes last.
Order: 4, 2, 3, 1, 5.
11
pattern-completion
medium
Which of the following options will complete the given figure pattern?
Answer: B
Going clockwise, the design turns 90° at each step. The strip moves top → right → bottom → left, and it is striped, then green, then striped, so the next one is green.
The letters go M, O, Q, so the next letter is S.
The missing bottom-left quarter needs a green strip along its left side and the letter S. That is option B, the only piece shaped like a bottom-left quarter.
12
analogy
medium
There is a certain relationship between the pair of terms on the either side of : : . Establish the relationship on the left pair and find the missing term.
G9H : L14C : : K11Y : ?
Answer: D
G + 5 = L, 9 + 5 = 14, H − 5 = C.
So K + 5 = P, 11 + 5 = 16, Y − 5 = T.
The missing term is P16T.
13
symmetry
medium
Which of the following squares must be shaded so that the given figure has dotted line as a line of symmetry?
Answer: B
Compare each square with its mirror square across the dotted line.
Row 3: the second square from the left is shaded, but its mirror square R is white. To make the two sides match, R must be shaded.
All the other pairs already match.
14
combinations
easy
How many possible combinations of 1 wallet and 1 note each can be formed from the given wallets and notes?
Answer: C
There are 5 wallets and 7 notes.
Each wallet can be paired with any of the 7 notes: 5 × 7 = 35 combinations.
15
embedded-figure
medium
Select a figure from the options in which the given figure is exactly embedded as one of its parts.
Answer: B
The given figure has three parts: a short vertical line, a slanting line from its bottom going up to the right, and a curve from its top bending down to the right.
In option B, these are the vertical line between the curve and the base, the small slanting line on the right, and the right half of the curve.
In C the small slanting line goes to the left, and A and D have no curve.
Mathematical Reasoning
MCQs — 20 Questions
(+1)
16
large-numbers
easy
Difference between the greatest 8-digit number and smallest 7-digit number is ________.
Answer: C
Greatest 8-digit number = 99999999. Smallest 7-digit number = 1000000.
99999999 − 1000000 = 98999999.
17
roman-numerals
medium
Which of the following options shows the Roman numerals arranged in descending order?
Answer: C
MMMDCCXIX = 3719, MMMCCV = 3205, MMCMXCIX = 2999, MMDCCLXXV = 2775.
Descending: 3719, 3205, 2999, 2775. That is option C.
18
fractions
easy
What fraction of the given figure is shaded?
Answer: C
The figure is made of 8 squares, and each is cut into 2 equal triangles, so there are 16 equal parts.
10 of them are shaded.
Shaded fraction = 10/16 = 5/8.
19
parallel-perpendicular
medium
The difference between the number of pairs of parallel lines and the number of pairs of perpendicular lines in the given figure is ________.
Answer: B
Count the pairs within each shape.
Parallel pairs: the rectangle has 2 (left-right and top-bottom) and the small square has 2. Total 4.
The triangles have no parallel sides.
Perpendicular pairs: the rectangle has 4 corners where sides meet at right angles, and the square has 4. Total 8.
Difference = 8 − 4 = 4.
20
time
medium
The given clock shows the time in the morning. If the clock is 18 minutes fast, then what was the time 4 hours 15 minutes before the actual time?
Answer: C
The clock shows 7 : 05 a.m. It is 18 minutes fast, so the actual time is 7 : 05 − 0 : 18 = 6 : 47 a.m.
6 : 47 − 4 : 15 = 2 : 32 a.m.
21
symmetry
medium
How many lines of symmetry does the given figure have?
Answer: B
Fold along the diagonal running from bottom-left to top-right: the two halves match.
Fold along the other diagonal through the centre: the purple squares swap and the two yellow triangles swap, so this also works.
The figure has 2 lines of symmetry.
22
area
medium
The area of the given figure (not drawn to scale) is ________.
Answer: C
Cut the figure into rectangles from top to bottom:
8 × 2 = 16, 2 × 2 = 4, (2 + 12) × 2 = 28, (14 − 4) × 4 = 40, (10 − 6) × 4 = 16.
Total area = 16 + 4 + 28 + 40 + 16 = 104 sq. cm.
23
angles
medium
How many more right angles than acute angles are there inside the given figure?
Answer: D
Right angles (marked): the top-left corner, the top-right corner, the corner of the step, and the bottom-left corner. That makes 4.
Acute angles: only the bottom-right corner. That makes 1.
The inner corner where the slanting side starts is more than 180°, so it is not acute.
4 − 1 = 3.
24
multiplication
easy
The product of 214 and a number is X. Taking 49 away from X gives 1449. Find the number.
Answer: A
X − 49 = 1449, so X = 1498.
214 × number = 1498, so the number = 1498 ÷ 214 = 7.
25
algebra-pictures
medium
Use the given information to find the value of one bottle + one lunch box.
Answer: B
2 bottles + 1 lunch box = ₹ 1480, and bottle − lunch box = ₹ 110.
Add the two: 3 bottles = 1480 + 110 = ₹ 1590, so 1 bottle = ₹ 530.
Lunch box = 530 − 110 = ₹ 420.
Bottle + lunch box = 530 + 420 = ₹ 950.
26
bar-graph
easy
DIRECTIONS (26-27): The given bar graph shows the number of books five students have. Study the graph carefully and answer the following question.
Who has 1 1/3 times the number of books Vidhi has?
Answer: B
Vidhi has 18 books. 1 1/3 × 18 = 4/3 × 18 = 24.
Ravi has 24 books.
27
bar-graph
easy
DIRECTIONS (26-27): The given bar graph shows the number of books five students have. Study the graph carefully and answer the following question.
How many students have less than 20 books?
Answer: B
Ravi 24, Kirti 26, Vidhi 18, Jai 14, Vipin 4.
Vidhi, Jai and Vipin have less than 20 books, so 3 students.
28
symmetry
easy
The sum of lines of symmetry of the given figures is ________.
Answer: C
(i) A regular pentagon has 5 lines of symmetry.
(ii) The arrow has 1, the horizontal line through its middle.
(iii) The four-pointed star has 4: two through opposite points and two between them.
Sum = 5 + 1 + 4 = 10.
29
place-value
medium
The number name of the number shown on the given abacus in International system of numeration is ________.
Answer: C
Bead counts: L = 8, TTh = 3, Th = 0, H = 5, T = 1, O = 8. The number is 830518 = 830,518.
In the International system this is eight hundred thirty thousand five hundred eighteen.
30
fractions
medium
In which of the following figures does the unshaded part represents 2/3?
Answer: D
A: 5 of 8 parts are unshaded = 5/8.
B: 6 of 12 squares are unshaded = 1/2.
C: 4 of 10 half-petals are unshaded = 2/5.
D: 6 of 9 small triangles are unshaded = 6/9 = 2/3.
31
perimeter
hard
The given figure (not drawn to scale) is made up of three identical equilateral triangles and one big equilateral triangle. Find the perimeter of the given figure.
Answer: A
The big triangle has sides of 30 cm. Each small triangle sits on half a side, so its sides are 15 cm.
For each side of the big triangle, the outline uses the free half (15 cm) plus the two outer sides of the small triangle (15 + 15 cm).
That is 45 cm per side, so the perimeter = 3 × 45 = 135 cm.
32
weights
medium
Find the weight of 3 cans + 1 book, using the weights shown on the scales.
Answer: A
4 cans weigh 400 g, so 1 can = 100 g.
5 books weigh 600 g, so 1 book = 120 g.
3 cans + 1 book = 300 + 120 = 420 g.
33
decimals
easy
The value of 88.64 − 43.21 + 63.51 is ________.
Answer: A
88.64 − 43.21 = 45.43.
45.43 + 63.51 = 108.94.
34
hcf
easy
The highest common factor of 72 and 168 is
Answer: C
72 = 2 × 2 × 2 × 3 × 3 and 168 = 2 × 2 × 2 × 3 × 7.
Common factors: 2 × 2 × 2 × 3 = 24.
35
angles
medium
Which of the following options has LEAST number of obtuse angles inside the given figures?
Answer: A
Count the obtuse angles (marked) inside each figure. Angles bigger than 180° are reflex angles and do not count.
A: 1, B: 4, C: 2, D: 3.
Option A has the least.
Everyday Mathematics
MCQs — 10 Questions
(+1)
36
area
easy
A rectangular garden has length 24 m and breadth 15 m. Find the cost of manuring the garden at ₹ 8 per sq. m.
Answer: C
Area = 24 × 15 = 360 sq. m.
Cost = 360 × 8 = ₹ 2880.
37
fractions
medium
Aditya spent 3/8 of his summer vacation at relative's home, 1/10 at hill station and rest at his home. If the summer vacation was of 40 days, then how many days did Aditya spend at his home?
Answer: B
Relative's home: 3/8 × 40 = 15 days. Hill station: 1/10 × 40 = 4 days.
Home: 40 − 15 − 4 = 21 days.
38
roman-numerals
medium
Ajay learns a total of MCCLXXXVIII words in the months of June, July and August. If he learnt equal number of words daily, then how many words did he learn daily?
Answer: A
MCCLXXXVIII = 1000 + 200 + 80 + 8 = 1288.
June + July + August = 30 + 31 + 31 = 92 days.
1288 ÷ 92 = 14 words a day.
39
place-value
medium
Arjun shows a number on the abacus. His sister removes 2 beads from ten thousands place and 1 bead from tens place. Which of the following number does the abacus show thereafter?
Answer: B
The abacus shows L = 5, TTh = 3, Th = 3, H = 4, T = 6, O = 4, that is 5,33,464.
Removing 2 beads from TTh leaves 1, and removing 1 bead from T leaves 5.
The new number is 5,13,454.
40
money
medium
Prisha wants to purchase a gift costing ₹ 1000. She has saved the amounts ₹ 235.45, ₹ 258.67, and ₹ 196.48 from her pocket money in three months respectively. How much more money does she need to buy the gift?
Answer: D
Savings = 235.45 + 258.67 + 196.48 = ₹ 690.60.
Money still needed = 1000.00 − 690.60 = ₹ 309.40.
41
perimeter
medium
Ananya walks around a rectangular park of length 220 m and breadth 190 m while Nitya walks around a triangular park each of side 190 m. If Ananya takes 7 rounds and Nitya takes 10 rounds, then who walks more distance and by how much?
Answer: C
Ananya: perimeter = 2 × (220 + 190) = 820 m, so 7 rounds = 5740 m.
Nitya: perimeter = 3 × 190 = 570 m, so 10 rounds = 5700 m.
Ananya walks 5740 − 5700 = 40 m more.
42
multiplication
medium
A boy was asked to multiply 54 and 861 but instead he multiplied 54 and 681. Find the difference between the actual answer and the answer obtained.
Answer: D
54 × 861 − 54 × 681 = 54 × (861 − 681) = 54 × 180 = 9720.
43
age
medium
Arpit's sister is 5 years 7 months younger than him. If age of Arpit, 5 years hence is 13 years, then his sister's age after 3 years from now will be
Answer: D
Arpit's age now = 13 − 5 = 8 years.
Sister's age now = 8 years − 5 years 7 months = 2 years 5 months.
After 3 years she will be 5 years 5 months.
44
calendar
medium
A trade fair is being organised in two cities P and Q. The starting and ending date is shown below.
In which city, trade fair is organised for more number of days?
Answer: A
P: 18th to 31st January = 14 days, plus 1st to 22nd February = 22 days. Total 36 days.
Q: 27th and 28th February = 2 days (2025 is not a leap year), plus 1st to 29th March = 29 days. Total 31 days.
The fair in P lasts more days.
45
length
medium
A contractor got a contract for the construction of three roads. The length of the first road is 130 km 750 m, that of the second road is 98 km 411 m and of the third road is 203 km 42 m. Find the total length of the roads that he needs to construct.
Answer: C
Metres: 750 + 411 + 42 = 1203 m = 1 km 203 m.
Kilometres: 130 + 98 + 203 + 1 = 432 km.
Total = 432 km 203 m.
Achievers Section
MCQs — 5 Questions
(+3)
46
decimals-fractions
hard
Fill in the blanks and select the CORRECT option.
(i) The value of 18.007 + 3.472 − 6.45 = __P__.
(ii) The value of 6 tens 13 tenths + 5 tens 18 tenths + 87 thousandths is __Q__.
(iii) The unit fraction whose denominator is (26/34 ÷ 1/17) is __R__.
Answer: B
P = 18.007 + 3.472 − 6.45 = 21.479 − 6.45 = 15.029.
Q = 60 + 1.3 + 50 + 1.8 + 0.087 = 113.187.
26/34 ÷ 1/17 = 26/34 × 17 = 13, so R = 1/13.
47
numbers
hard
Which of the following options is INCORRECT?
Answer: A
A: The predecessor of 2584 is 2583 = MMDLXXXIII. MMDLXXXV is 2585, so A is incorrect.
B: The greatest number is 85420. The 5 is in the thousands place, so its place value is 5000. Correct.
C: 3 crore + 44 lakh + 5 thousand + 6 = 3,44,05,006. Correct.
Only A is incorrect.
48
algebra-pictures
hard
Use the given information about the prices of the balls to find the values of (i) and (ii).
Answer: B
3 footballs (black and white) = ₹ 1056, so 1 football = ₹ 352.
Basketball + rugby ball = 1142 − 352 = ₹ 790.
2 rugby balls + basketball = ₹ 1105, so 1 rugby ball = 1105 − 790 = ₹ 315, and the basketball = 790 − 315 = ₹ 475.
(i) Football + basketball = 352 + 475 = ₹ 827.
(ii) Basketball − rugby ball = 475 − 315 = ₹ 160.
49
roman-numerals
hard
Read the given statements carefully and select the CORRECT option.
Statement-I: The sum of DLXX and DCCCLVIII is less than the difference of MDCXXX and CLXXVIII.
Statement-II: If X is the greatest 6-digit number that can be formed by using the digits 3, 1, 0 and 7 (using each digit at least once) and Y is the smallest 4-digit number that can be formed by using the digits 3, 1 and 0 (using each digit at least once), then the difference of X and Y is 774310.
Answer: C
Statement-I: DLXX + DCCCLVIII = 570 + 858 = 1428, and MDCXXX − CLXXVIII = 1630 − 178 = 1452. Since 1428 < 1452, it is true.
Statement-II: X = 777310 (repeat 7 as often as possible, then 3, 1, 0), and Y = 1003. X − Y = 776307, not 774310. So it is false.
50
perimeter-area
hard
Solve the following and select the CORRECT option.
(i) The perimeter of the first figure (not drawn to scale) is ________.
(ii) The area of the shaded region in the second figure (not drawn to scale) is ________.
Answer: C
(i) Perimeter = 4 × 3.5 + 4 × 0.5 + 2 × 2 = 14 + 2 + 4 = 20 cm.
(ii) Shaded top-right square = 4 × 4 = 16 sq. cm.
Shaded bottom-left rectangle = (16 − 4) × (12 − 4) = 12 × 8 = 96 sq. cm.
Total = 16 + 96 = 112 sq. cm.