Logical Reasoning
MCQs — 15 Questions
(+1)
1
number-series
easy
Find the missing number in the given number series.
360, 72, 18, 6, ?
Answer: B
360 ÷ 5 = 72, 72 ÷ 4 = 18, 18 ÷ 3 = 6, so the next step is 6 ÷ 2 = 3.
2
direction-sense
easy
Mohan is facing West. He walks 16 m, turns to his left and walks 12 m. He again turns to his left, walks 8 m and then turns to his right. In which direction is he facing now?
Answer: D
Facing West, a left turn makes him face South.
Another left turn makes him face East.
A right turn from East makes him face South.
3
venn-diagrams
easy
Which of the following Venn diagrams best represents the relationship amongst "Mothers, Doctors and Females"?
Answer: D
Every mother is a female, so the Mothers circle lies inside the Females circle.
Some doctors are females and some are mothers, but some doctors are male, so the Doctors circle overlaps both circles without lying inside them. That is diagram D.
4
blood-relations
medium
Pointing towards Shreya, a girl said, "She is the only daughter-in-law of the father of my mother's only son." How is Shreya related to that girl?
Answer: A
The girl's mother's only son is the girl's brother.
The father of her brother is the girl's father.
The only daughter-in-law of her father is her brother's wife, so Shreya is the girl's sister-in-law.
5
counting-figures
medium
Find the minimum number of straight lines required to make the given figure.
Answer: B
Horizontal lines: the top edge and the long middle line = 2.
The two short slanting sides at the top = 2, and the two long sides meeting at the bottom point = 2.
The 8 short lines in the top band, the 4 lines inside the bottom part going to the bottom point and the vertical line = 8 + 4 + 1 = 13.
Total = 2 + 2 + 2 + 13 = 19.
6
mirror-and-water-images
medium
Select the CORRECT mirror image of the given figure, if the mirror is placed along the line MN as shown.
Answer: C
A mirror on the right side swaps left and right but keeps top and bottom unchanged.
So the flat side and the grey square move to the right, the square stays at the top, the triangle stays at the bottom and now points left, and the dot and the cross also swap sides — figure C.
A is a water image, B is the figure turned upside down, and in D the dot and the cross have not been reflected.
7
mathematical-operations
easy
If 'F' means '+', 'S' means '×', 'T' means '÷' and 'U' means '−', then the value of 870 T 30 S 2 U 50 F 8 is ______.
Answer: B
The expression becomes 870 ÷ 30 × 2 − 50 + 8.
870 ÷ 30 = 29, 29 × 2 = 58, 58 − 50 + 8 = 16.
8
number-series
medium
How many odd numbers in the given number sequence are not prime numbers and are immediately followed by an even number?
1 4 2 6 9 2 8 3 1 7 8 5 7 1 9 6 5 2 6
Answer: A
The odd numbers that are not prime are 1 and 9.
The 1 followed by 4: yes. The 9 followed by 2: yes. The 1 followed by 7: no. The 1 followed by 9: no. The 9 followed by 6: yes.
So there are three such numbers.
9
counting-cubes
medium
Count the number of cubes in the given figure.
Answer: C
Count the cubes column by column (every cube that is not visible supports one above it).
Back row: 4 + 4 + 3 + 3 = 14. Middle row: 4 + 3 + 3 + 2 = 12. Front row: 3 + 3 + 2 + 1 = 9.
Total = 14 + 12 + 9 = 35.
10
paper-folding
medium
The given question consists of a set of three figures X, Y and Z which shows the sequence of folding of a piece of paper. Fig. Z shows the manner in which the folded paper has been cut. Select a figure from the options which would most closely resemble the unfolded form of Fig. Z.
Answer: C
The hexagon was folded along the horizontal line and then along the vertical line, so Z is one quarter of the sheet with four layers.
Each of the 2 small circles appears once in every quarter, giving 8 circles placed as mirror images across both fold lines.
The small triangle cut at the centre corner opens out into a diamond (a square standing on its corner) at the centre — figure C.
11
missing-figure
medium
Select a figure from the options which will complete the given figure matrix.
Answer: A
In each row, the outermost shape of the first figure becomes the innermost shape of the second figure, and the other two shapes move outwards.
Square ⊃ circle ⊃ triangle becomes circle ⊃ triangle ⊃ square.
So hexagon ⊃ diamond ⊃ triangle becomes diamond ⊃ triangle ⊃ hexagon — figure A.
12
embedded-figures
medium
Select the figure from the options in which the given figure is exactly embedded as one of its parts.
Answer: C
The given figure is a right-angled triangle with its right angle at the bottom-right and a short vertical line standing on its base.
In C, the bottom-left quarter has the bottom side, the vertical middle line and the diagonal forming this triangle, and the line x = 1 gives the short vertical line.
B has the triangle but no short vertical line, A has no vertical line at all, and in D the triangle faces the other way.
13
coding-decoding
hard
In a certain code language, if CARBON is written as SADMOA, then how will OXYGEN be written in the same code language?
Answer: D
Number the letters of CARBON 1 to 6.
Code letter 1 = letter 3 + 1 (R → S); code letter 2 = letter 2 (A); code letter 3 = letter 1 + 1 (C → D); code letter 4 = letter 6 − 1 (N → M); code letter 5 = letter 5 (O); code letter 6 = letter 4 − 1 (B → A).
For OXYGEN: Y + 1 = Z, X, O + 1 = P, N − 1 = M, E, G − 1 = F → ZXPMEF.
14
embedded-figures
medium
Which of the following options satisfies the same conditions of placement of dots as in the given figure?
Answer: B
In the given figure one dot is common to the triangle, the circle and the square, one dot is common to the triangle and the square only, and one dot is common to the circle and the square only.
Only figure B has all three of these regions.
In A the part shared by the triangle and the square lies inside the circle, C has no region common to all three shapes, and in D the part shared by the circle and the square lies inside the triangle.
15
lines-and-angles
easy
What will be the smallest angle between the hour and minute hands of a clock when the time is 4:20?
Answer: A
Minute hand at 20 minutes: 20 × 6° = 120°.
Hour hand at 4:20: 4 × 30° + 20 × 0.5° = 130°.
Angle = 130° − 120° = 10°.
Mathematical Reasoning
MCQs — 20 Questions
(+1)
16
integers
easy
What is the sum of the predecessor of the smallest positive integer and successor of the greatest negative integer?
Answer: B
The smallest positive integer is 1; its predecessor is 0.
The greatest negative integer is −1; its successor is 0.
Sum = 0 + 0 = 0.
17
lines-and-angles
easy
How many of the following letters have at least one pair of parallel lines?
Answer: D
Each outline letter is drawn with straight edges.
T: the top and bottom edges of the bar are parallel. R: the two sides of the upright stroke are parallel. E: all the horizontal edges are parallel. A: the edges of the crossbar and the top are parallel.
So all 5 letters T, R, E, A, T have at least one pair of parallel lines.
18
lines-and-angles
medium
How many acute angles are there inside the given figure?
Answer: D
Look at each corner from inside the figure.
Only the two corners on either side of the notch at the top-left (the top corner, about 77°, and the left corner, about 66°) are less than 90°.
The corner inside the notch is a reflex angle, the bottom-right corner is a right angle and the remaining corners are obtuse. So there are 2 acute angles.
19
factors-and-multiples
easy
The co-prime numbers from the following pairs, are ______.
Answer: B
Co-prime numbers have no common factor other than 1.
36 = 2 × 2 × 3 × 3 and 25 = 5 × 5 have no common factor, so they are co-prime.
7 and 63 share 7, 35 and 21 share 7, and 63 and 81 share 9.
20
symmetry
medium
Which of the following figures do not have any line of symmetry?
Answer: A
Figure A is a pinwheel: turning it gives the same figure, but folding it along any line does not make the halves match, so it has no line of symmetry.
Figures B, C and D each have lines of symmetry (vertical, horizontal and diagonal).
21
lines-and-angles
medium
How many pairs of intersecting lines are there in the given figure?
Answer: D
There are 5 lines p, o, l, m and n, which make 10 pairs.
Lines p and o are both vertical, so they are parallel and never meet.
Every other pair crosses, so there are 10 − 1 = 9 pairs of intersecting lines, which is more than 6.
22
fractions
medium
Which of the following is TRUE about the shaded fraction of the given figures?
Answer: A
Figure X has 16 equal triangles, of which 10 are shaded: 10/16 = 5/8.
Figure Y has 32 equal triangles, of which 18 are shaded: 18/32 = 9/16.
10/16 > 9/16, so X > Y.
23
large-numbers
easy
Which of the following options shows the number written in the International system of numeration?
Answer: B
In the International system commas are placed after every three digits from the right.
Only 98,520,003 follows this pattern; A and C use the Indian system and D is not correct in either.
24
integers
easy
If the room temperature is 11°C less than the temperature shown on the given thermometer, then the room temperature is ______.
Answer: C
The thermometer shows 33°C.
Room temperature = 33 − 11 = 22°C.
25
data-handling
easy
The given pictograph shows the favourite colour of school bag of students of a school.
Which colour bag was most liked by the students and how much?
Answer: A
Black has the most symbols: 12 whole bags and half a bag = 12½ symbols.
Each symbol stands for 80 students, so 12½ × 80 = 1000 students liked black.
26
data-handling
medium
The given pictograph shows the favourite colour of school bag of students of a school.
Find the fraction of number of students who liked pink colour bag to the number of students who liked red colour bag.
Answer: A
Pink = 5½ × 80 = 440 students. Red = 7½ × 80 = 600 students.
Fraction = 440/600 = 11/15.
27
area-and-perimeter
medium
Find the perimeter of the shaded part of the given figure.
Answer: C
Count the sides of small squares on the boundary of the shaded part (between a shaded square and a white square or the outside).
There are 26 such sides, each 3.5 cm long.
Perimeter = 26 × 3.5 = 91 cm.
28
decimals
easy
If X = 30.758 + 12.212 and Y = 45.375 − 15.225, then find the value of (X + Y)/5.
Answer: A
X = 30.758 + 12.212 = 42.970.
Y = 45.375 − 15.225 = 30.150.
(X + Y) ÷ 5 = 73.120 ÷ 5 = 14.624.
29
factors-and-multiples
easy
Which of the following is same as the difference between the 11th multiple of 25 and the greatest factor of 50?
Answer: B
11th multiple of 25 = 275. The greatest factor of 50 is 50.
Difference = 275 − 50 = 225 = 9 × 25, the 9th multiple of 25.
(7 × 15 = 105, 11 × 17 = 187, 15 × 13 = 195.)
30
area-and-perimeter
medium
The figure below shows 4 identical squares which lie within a big square. If the area of the big square is 576 cm², then find the shaded area of the given figure.
Answer: B
Side of the big square = 24 cm (24 × 24 = 576).
The 4 small squares are stacked one above the other along the full height, so each has side 24 ÷ 4 = 6 cm and area 36 cm².
Shaded area = 576 − 4 × 36 = 576 − 144 = 432 cm².
31
measurement
medium
The given clock shows the time at which Naksh left his home for office in the morning. After walking for 20 minutes, he boarded the metro and reached his office at 9:30 a.m. How much time did he travel by metro?
Answer: D
The clock shows 7:45 a.m.
He boarded the metro 20 minutes later, at 8:05 a.m.
From 8:05 a.m. to 9:30 a.m. is 1 hour 25 minutes, which is also 85 minutes. So both B and C are correct.
32
roman-numerals
medium
Compare the following and fill the box using '>', '<' or '='.
CMLXXVIII + MMCMXLIV ☐ MMMDCCL − CMLIX
Answer: A
CMLXXVIII = 978 and MMCMXLIV = 2944, so the left side is 3922.
MMMDCCL = 3750 and CMLIX = 959, so the right side is 2791.
3922 > 2791.
33
decimals
medium
Find the shaded decimal part of the given figure.
Answer: B
The figure has 25 equal small squares.
Shaded: 4 whole squares and 12 half squares = 4 + 6 = 10 squares.
Shaded part = 10/25 = 0.4.
34
lines-and-angles
medium
How many angles are formed above the line AB?
Answer: D
There are 6 rays from O above or along the line: OA, OF, OE, OD, OC and OB.
Any two of them form an angle, so the number of angles = 5 + 4 + 3 + 2 + 1 = 15, which is more than 7.
35
fractions
medium
Which of the following gives the LEAST value?
Answer: D
A = 16/80 + 10/80 + 5/80 = 31/80 ≈ 0.39.
B = 7 2/5 + 3/4 = 8 3/20 = 8.15. C = 7.2 + 3 2/7 − 1.5 ≈ 8.99.
D = −3/10 + 3/7 = (−21 + 30)/70 = 9/70 ≈ 0.13.
So D gives the least value.
Everyday Mathematics
MCQs — 10 Questions
(+1)
36
large-numbers
easy
For a competitive exam, the number of candidates applied in years 2021, 2022 and 2023 were 7,50,320; 4,23,190 and 5,80,121 respectively. How many more candidates applied in the years 2022 and 2023 together than in the year 2021?
Answer: C
2022 and 2023 together = 4,23,190 + 5,80,121 = 10,03,311.
Difference = 10,03,311 − 7,50,320 = 2,52,991.
37
integers
easy
A mountain peak has an elevation of 14,250 feet above sea level. A deep sea trench in an ocean has a depression of 12,351 feet below the sea level (in a straight line with mountain peak). Find the distance between these two points.
Answer: D
The peak is at +14,250 ft and the trench is at −12,351 ft.
Distance = 14,250 + 12,351 = 26,601 feet, which is not among A, B and C.
38
area-and-perimeter
easy
The wall of a room is in the form of a rectangle. Manisha wants to paint the wall with blue colour. The cost of painting the wall at the rate of ₹ 25 per square metre is ₹ 1050. If the length of wall is 7 m, then find its breadth.
Answer: C
Area = 1050 ÷ 25 = 42 m².
Breadth = 42 ÷ 7 = 6 m.
39
fractions
medium
Rajni spends 4/15 of her monthly income on her children's education, 1/5 on grocery, 1/2 on miscellaneous items and saves ₹ 1800 in the end. What was her monthly income?
Answer: A
Spent = 4/15 + 1/5 + 1/2 = 8/30 + 6/30 + 15/30 = 29/30.
Saved = 1/30 of the income = ₹ 1800.
Income = 1800 × 30 = ₹ 54,000.
40
factors-and-multiples
easy
Two athletes participates in a race. A touches the start point in every 24 seconds and B touches it in every 32 seconds. If they start together, then after how much time will they next touch the point together?
Answer: A
They meet again after the LCM of 24 and 32.
24 = 2³ × 3 and 32 = 2⁵, so LCM = 2⁵ × 3 = 96 seconds.
41
decimals
easy
A water tanker with a capacity of 5325.25 L was full of water. If out of this tanker, 987.75 L and 1075.10 L were delivered to two restaurants, then how much water is left in the tanker?
Answer: D
Delivered = 987.75 + 1075.10 = 2062.85 L.
Left = 5325.25 − 2062.85 = 3262.40 L.
42
decimals
easy
80 students of the same height, stand with both hands stretched all along the sides of a rectangular garden, each student covering a length of 1.75 m. Then the perimeter of the garden is ______.
Answer: B
Perimeter = 80 × 1.75 m = 140 m.
43
direction-sense
medium
Smriti is facing towards the North-West direction. She rotates 3/4 of a revolution towards her right and then turn 180° in anti-clockwise direction. Find the smallest angle between the initial position and the final position.
Answer: B
3/4 of a revolution to the right is 270° clockwise; then 180° anti-clockwise.
Net turn = 270° − 180° = 90° clockwise, so she now faces North-East.
The angle between North-West and North-East is 90°.
44
measurement
medium
Ruchi travelled 115 km 200 m distance by train, 2150 km 500 m distance by aeroplane and 75 km 350 m distance by car. How much less distance did she travel by train and car together than by aeroplane?
Answer: A
Train + car = 115 km 200 m + 75 km 350 m = 190 km 550 m.
Difference = 2150 km 500 m − 190 km 550 m = 1959 km 950 m.
45
large-numbers
easy
The population of two towns in a city are 75,391 and 97,815 respectively. Estimate the total population of both towns, when rounded off each number to nearest thousands place.
Answer: C
75,391 rounds to 75,000 and 97,815 rounds to 98,000.
Estimated total = 75,000 + 98,000 = 1,73,000.
Achievers Section
MCQs — 5 Questions
(+3)
46
divisibility
medium
Read the given statements carefully and select the CORRECT option.
Statement-I : The number 280192 is exactly divisible by 8.
Statement-II : The number 295720 is exactly divisible by 2, 4, 5 and 10.
Answer: A
Statement-I: the last three digits 192 = 8 × 24, so 280192 is divisible by 8. True.
Statement-II: 295720 ends in 0, so it is divisible by 2, 5 and 10, and its last two digits 20 are divisible by 4. True.
47
area-and-perimeter
hard
Solve the following and select the CORRECT option.
(i) Find the difference between the area of shaded and unshaded part of the given figure.
(ii) The breadth of a rectangle is 28 cm and the length is 2 1/2 times the breadth. If two squares of side 15 cm and 12 cm are cut from the rectangle, then find the area of remaining part of the rectangle.
Answer: D
(i) The figure is a 6 × 6 grid of 5 cm squares, so its area is 36 × 25 = 900 cm².
Shaded: 16 whole squares and 10 half squares = 21 squares = 525 cm². Unshaded = 900 − 525 = 375 cm².
Difference = 525 − 375 = 150 cm².
(ii) Length = 2 1/2 × 28 = 70 cm, area = 70 × 28 = 1960 cm².
Remaining = 1960 − 225 − 144 = 1591 cm².
48
lines-and-angles
hard
Read the given statements carefully and state T for true and F for false.
(i) The number of line segments in the below figure is 5.
(ii) The number of right angles formed when hour hand of a clock moves from 3 to 12, is 3.
(iii) The smaller angle between the hour hand and the minute hand of a clock at 7:10 is an obtuse angle.
Answer: B
(i) With 4 points P, R, S, Q on a line, the segments are PR, PS, PQ, RS, RQ and SQ = 6. False.
(ii) From 3 to 12 the hour hand turns through 270° = 3 right angles (3 → 6 → 9 → 12). True.
(iii) At 7:10 the hour hand is at 215° and the minute hand at 60°, so the smaller angle is 155°, which is obtuse. True.
49
fractions
hard
Fill in the blanks and select the CORRECT option.
(i) In the word CREATIVE, the fraction of alphabets that are made up of only curved lines is ______.
(ii) The value of [2 1/5 − {1 2/3 + (3/4 − 1/2)}] is ______.
(iii) The number of one-thirds that needs to be added to 3 1/3 to make 7 is ______.
Answer: C
(i) Of the 8 letters C, R, E, A, T, I, V, E only C is made of curved lines alone: 1/8.
(ii) 3/4 − 1/2 = 1/4; 1 2/3 + 1/4 = 5/3 + 1/4 = 23/12; 2 1/5 − 23/12 = 132/60 − 115/60 = 17/60.
(iii) 7 − 3 1/3 = 3 2/3 = 11/3, so 11 one-thirds are needed.
50
factors-and-multiples
hard
Fill in the blanks and select the CORRECT option.
(i) The greatest 4-digit number which is exactly divisible by 15 is ______.
(ii) The HCF of 36 and 84 is ______.
(iii) The number of prime numbers between 20 and 40 is ______.
Answer: B
(i) 9999 ÷ 15 leaves remainder 9, so the greatest 4-digit multiple of 15 is 9999 − 9 = 9990.
(ii) 36 = 2² × 3² and 84 = 2² × 3 × 7, so HCF = 2² × 3 = 12.
(iii) The primes between 20 and 40 are 23, 29, 31 and 37 — 4 primes.