Logical Reasoning
MCQs — 15 Questions
(+1)
1
counting-cubes
medium
Count the number of cubes in the given figure.
Answer: B
Count the cubes row by row from front to back (the figure is 5 cubes wide):
Front row: 2 + 1 + 1 + 1 + 1 = 6
Second row: 2 + 2 + 1 + 1 + 1 = 7
Third row: 2 + 2 + 2 + 2 + 2 = 10
Fourth row: 3 + 3 + 2 + 2 + 2 = 12
Back row: 4 + 4 + 4 + 4 + 3 = 19
Total = 6 + 7 + 10 + 12 + 19 = 54.
2
calendar
easy
If yesterday was Friday, then 15th day from today will be ______.
Answer: B
Yesterday was Friday, so today is Saturday. 15 days = 2 weeks + 1 day. After 2 weeks it is Saturday again, and 1 more day makes it Sunday.
3
number-puzzle
medium
Find the missing number, if same rule is followed in all the three figures.
Answer: C
The middle number is the square of the sum of the three corner numbers.
(2 + 3 + 5)² = 10² = 100 and (4 + 1 + 3)² = 8² = 64.
So (5 + 6 + 7)² = 18² = 324.
4
odd-one-out
easy
Select the odd one out.
Answer: D
T, H and Y are made only of straight lines. G has a curved line, so G is the odd one out.
5
word-formation
easy
Some letters are numbered 1, 2, 3, 4, 5 and 6 as given. Arrange the given letters to form a meaningful English word and select the CORRECT option.
T A N T N E
1 2 3 4 5 6
Answer: D
The word is TENANT: T = 4, E = 6, N = 5, A = 2, N = 3, T = 1. So the order is 4, 6, 5, 2, 3, 1.
6
coding-decoding
easy
In a certain code language, if PLENTY is written as ELNPTY, then how will SURETY be written in the same code language?
Answer: C
ELNPTY is the letters of PLENTY written in alphabetical order. The letters of SURETY in alphabetical order are E, R, S, T, U, Y, so SURETY is written as ERSTUY.
7
directions
easy
Sakshi is facing towards West direction. She turns 90° anti-clockwise and then 135° clockwise. In which direction is she facing now?
Answer: C
Turning 90° anti-clockwise from West, she faces South. Turning 135° clockwise from South takes her through South-West (45°) and West (90°) to North-West (135°).
8
combinations
easy
How many possible combinations of 1 sticky note and 1 board pin each can be formed from given sticky notes and board pins?
Answer: D
There are 6 sticky notes and 3 board pins. Each sticky note can go with any of the 3 pins, so there are 6 × 3 = 18 combinations.
9
mirror-image
easy
Select the CORRECT mirror image of the given figure, if the mirror is placed vertically to the left.
Answer: A
With a vertical mirror, the order of the letters reverses (E, D, I, R, P) and every letter is flipped left to right. Only option A flips all the letters correctly.
10
analogy
medium
There is a certain relationship between the pair of figures on either side of : :. Identify the relationship between the left pair and find the missing figure.
Answer: A
In the first pair, the outer shape (triangle) becomes small and moves to the top-right corner, the innermost shape (circle) becomes the outer shape, and the middle shape (rectangle) stays inside it.
In the second pair, the outer square moves to the top-right corner, the innermost triangle becomes the outer shape, and the house shape stays inside it. This is option A.
11
patterns
easy
Study the given patterns carefully. What will be the number of rings in Pattern 6?
Answer: B
The patterns have 4, 7 and 10 rings, so each pattern has 3 more rings than the one before.
Pattern 4 = 13, Pattern 5 = 16, Pattern 6 = 19.
12
calendar
medium
Divya starts doing yoga in morning from second Tuesday of September 20XX. How many days does she do yoga in that month, if she takes rest on every Saturday?
Answer: C
The Tuesdays are 4 and 11, so the second Tuesday is 11 September. From 11 to 30 September there are 30 − 11 + 1 = 20 days.
The Saturdays in this period are 15, 22 and 29, so she rests on 3 days.
Yoga days = 20 − 3 = 17.
13
alphabet
medium
If all the letters in the given arrangement are arranged in reverse alphabetical order, then which letter will be exactly lies in the middle?
B D K M G S Y W R V A T P J E
Answer: D
In reverse alphabetical order the 15 letters are: Y W V T S R P M K J G E D B A.
The middle letter is the 8th one, which is M.
14
embedded-figure
hard
Select a figure from the options which is exactly embedded in the given figure as one of its parts.
Answer: A
Start at the top-left point on the big circle. Follow the slanting line down to the top of the small circle, go down the short vertical line to the centre, then turn right along the horizontal line. These lines make figure A.
15
ranking
medium
Akhil is shorter than only Shivam. Sahil is taller than Rohit but shorter than Varun. If Varun is shorter than Shivam, then who is shortest among them?
Answer: B
Akhil is shorter than only Shivam, so Shivam is the tallest and Akhil is second.
Varun is taller than Sahil, and Sahil is taller than Rohit.
Order from tallest: Shivam, Akhil, Varun, Sahil, Rohit. So Rohit is the shortest.
Mathematical Reasoning
MCQs — 20 Questions
(+1)
16
decimals
easy
Which of the following options is CORRECT?
Answer: C
Compare the tenths first: 0.3__ is greater than 0.2__. Then 0.359 > 0.352 (9 thousandths > 2 thousandths) and 0.293 > 0.246.
So 0.359 > 0.352 > 0.293 > 0.246.
17
roman-numerals
easy
The sum of face value and place value of digit 8 in the number 31807 is represented by which Roman numeral?
Answer: C
In 31807, the face value of 8 is 8 and its place value is 800. Sum = 808.
808 = 500 + 300 + 8 = D + CCC + VIII = DCCCVIII.
18
prime-factors
medium
Which of the following has least number of distinct prime factors?
Answer: B
1750 = 2 × 5³ × 7 (3 distinct prime factors)
1280 = 2⁸ × 5 (2 distinct prime factors)
4410 = 2 × 3² × 5 × 7² (4 distinct prime factors)
900 = 2² × 3² × 5² (3 distinct prime factors)
So 1280 has the least.
19
angles
medium
The smaller angle made by the minute hand and hour hand of a clock when it is 12 : 20 a.m. is a/an ______.
Answer: B
At 12:20 the minute hand is at 4, which is 20 × 6° = 120° from 12. The hour hand has moved 20 × 0.5° = 10° past 12.
Angle = 120° − 10° = 110°, which is between 90° and 180°, so it is an obtuse angle.
20
perimeter
hard
Find the perimeter of the given figure (not drawn to scale).
Answer: D
Horizontal sides: the top edges (2 + 2 + 2 + 2 = 8 cm) and the bottom edges (3 + 1 + 2 + 1 + 1 = 8 cm), where the 1 cm edges are the tops of the two gaps. Total = 16 cm.
Vertical sides: the left steps (2 + 2 + 2 + 2 = 8 cm) and the right side (8 cm) = 16 cm. Each gap is as tall as the 2 cm block on the left, so its two sides add 2 + 2 = 4 cm. Two gaps add 8 cm.
Perimeter = 16 + 16 + 8 = 40 cm.
21
bar-graph
easy
Directions (Q21-22): The given bar graph shows the funds raised by different NGOs for child education. Study the given bar graph carefully and answer the following questions.
How many NGOs collected more than ₹15,000?
Answer: C
NGO I = ₹9,000, NGO II = ₹18,000, NGO III = ₹24,000, NGO IV = ₹15,000 and NGO V = ₹21,000.
More than ₹15,000: NGO II, NGO III and NGO V. NGO IV collected exactly ₹15,000, so it is not counted. Answer: 3.
22
bar-graph
easy
Directions (Q21-22): The given bar graph shows the funds raised by different NGOs for child education. Study the given bar graph carefully and answer the following questions.
Which NGO collected an amount equal to 3/4 of what NGO III collected?
Answer: A
NGO III collected ₹24,000. 3/4 of ₹24,000 = ₹18,000, which is what NGO II collected.
23
successor-predecessor
medium
Which of the following options is INCORRECT?
Answer: C
For a number n, the successor is n + 1 and the predecessor is n − 1.
A: (n + 1) + (n − 1) = 2n, which is true.
B: (n + 1) − (n − 1) = 2, which is true.
C: The successor is always greater than the number. It can never be equal, so C is incorrect.
24
fractions
medium
Find the product of shaded fraction of figure (i) and unshaded fraction of figure (ii).
Answer: B
Figure (i) has 9 equal triangles and 3 are shaded, so its shaded fraction is 3/9 = 1/3.
Figure (ii) has 6 equal squares. One full square and three half squares are shaded: 1 + 3/2 = 5/2 squares. Shaded fraction = (5/2) ÷ 6 = 5/12, so the unshaded fraction is 7/12.
Product = 1/3 × 7/12 = 7/36.
25
decimals
medium
If P = 200 + 50 + 7 + 1/100 + 2/1000 and Q = 500 + 10 + 7/10 + 2/100 + 3/1000, then the value of Q − P is ______.
Answer: A
P = 257.012 and Q = 510.723.
Q − P = 510.723 − 257.012 = 253.711.
26
area-perimeter
medium
The area of a square and rectangle are equal. If the side of square is 18 cm and length of rectangle is 27 cm, then which has more perimeter?
Answer: B
Area of square = 18 × 18 = 324 sq. cm. Breadth of rectangle = 324 ÷ 27 = 12 cm.
Perimeter of square = 4 × 18 = 72 cm. Perimeter of rectangle = 2 × (27 + 12) = 78 cm.
The rectangle has the greater perimeter.
27
symmetry
easy
Which of the following shapes has minimum 3 lines of symmetry?
Answer: B
The bulb and the crown-shaped protractor have 1 line of symmetry each and the infinity sign has 2. The sun with 8 equal rays has 8 lines of symmetry, so it has at least 3.
28
decimals
medium
Which of the following options is CORRECT?
Answer: D
A: 1.4 + 0.004 = 1.404, not 0.144.
B: 0.2 + 0.13 = 0.33, not 0.213.
C: 0.04 + 0.2 = 0.24, not 0.024.
D: 0.7 + 0.17 = 0.87. ✓
29
weight
medium
Study the balances. Then which of the following options is true?
Answer: B
From the second balance, P + P = 24 kg, so P = 12 kg.
From the first balance, P + Q + Q = 48 kg, so Q + Q = 48 − 12 = 36 kg and Q = 18 kg.
Q (18 kg) is heavier than P (12 kg).
30
decimals
easy
Rohan cycled from his house to the post office, then to the market, then to the hospital and then he went to his house. The distances are marked in the given figure. What is the total distance covered by Rohan?
Answer: D
Total distance = 1.6 + 1.3 + 6.65 + 0.75 = 10.3 km.
31
rounding
medium
The number of books in a library when rounded off to nearest hundreds gives 18500. Which of the following cannot be the actual number of books in the library?
Answer: C
Numbers from 18450 to 18549 round off to 18500. 18415 is less than 18450, so it rounds off to 18400, not 18500.
32
time
hard
If the clock I is 20 minutes slow and clock II is 15 minutes fast, then the difference between their actual time is ______.
Answer: B
Clock I shows 8:35. It is 20 minutes slow, so the actual time is 8:55.
Clock II shows 9:40. It is 15 minutes fast, so the actual time is 9:25.
Difference = 9:25 − 8:55 = 30 minutes.
33
place-value
easy
The difference between the greatest and smallest 5-digit numbers formed by using the digits 3, 1, 0, 2 and 8 (using each digit only once) is
Answer: C
Greatest number = 83210. The smallest number cannot start with 0, so it is 10238.
Difference = 83210 − 10238 = 72972.
34
symmetry
medium
How many line(s) of symmetry does the given figure have?
Answer: A
Check each possible line. Vertical: the top row has the two left squares shaded but the two right squares unshaded. Horizontal: the top row and the bottom row do not match. Diagonals: the second square of the top row is shaded but the first square of the second row is not, and the top-left corner is shaded but the bottom-right corner is not.
So the figure has no line of symmetry.
35
lines
medium
How many pair(s) of intersecting lines is/are there in the given figure?
Answer: B
There are 3 horizontal lines (parallel to each other), 2 lines slanting to the right (parallel to each other) and 1 line slanting to the left.
Each of the 3 slanting lines crosses each of the 3 horizontal lines: 3 × 3 = 9 pairs.
The left-slanting line crosses both right-slanting lines: 2 pairs.
Total = 9 + 2 = 11 pairs.
Everyday Mathematics
MCQs — 10 Questions
(+1)
36
division
easy
A boat can take 29 people at a time for a lake side. There are 1595 visitors waiting. How many times should the boat go so that everyone gets a ride once?
Answer: B
1595 ÷ 29 = 55 trips.
37
perimeter
medium
A rectangular park is 165 m long and 105 m wide. If Sia walks around the park 7 times, then how much total distance does she cover?
Answer: B
Perimeter = 2 × (165 + 105) = 540 m. 7 rounds = 7 × 540 = 3780 m = 3 km 780 m.
38
roman-numerals
easy
The given table shows the number of marks got by four friends in an examination. Who got highest marks?
Answer: B
LIV = 54, LXXXVIII = 88, LXXV = 75 and XCIII = 93. Monika got the highest marks (93).
39
perimeter
medium
Some triangular mats with sides 15 cm, 20 cm and 25 cm were decorated along its boundary with colourful ribbons costing ₹50 per meter. If the total cost is ₹1500, then how many mats were decorated?
Answer: D
Boundary of one mat = 15 + 20 + 25 = 60 cm = 0.6 m. Cost for one mat = 0.6 × ₹50 = ₹30.
Number of mats = ₹1500 ÷ ₹30 = 50.
40
fractions
medium
Vinita uses 1/4 cup of apple sauce in place of every 1/3 cup of butter in her cookie recipe. What is the quantity of apple sauce will Vinita use in place of 1 cup of butter?
Answer: D
1 cup of butter = 3 × (1/3 cup). So she uses 3 × 1/4 = 3/4 cup of apple sauce.
41
money
easy
Nisha has ₹125.80. She gives ₹35.25 to each of her two cousins and ₹40 to her brother. How much money is left with her?
Answer: B
Money given = 2 × ₹35.25 + ₹40 = ₹70.50 + ₹40 = ₹110.50.
Money left = ₹125.80 − ₹110.50 = ₹15.30.
42
fractions
medium
Tanvi got a diet plan by a dietician to drink 1 1/4 litres milk everyday for a week, but she drank 7/8 litres milk daily. How much less milk did she consume in a week as per the diet?
Answer: C
Less milk each day = 1 1/4 − 7/8 = 10/8 − 7/8 = 3/8 litre.
In a week = 7 × 3/8 = 21/8 = 2 5/8 litres.
43
number-names
easy
The population of a state is 'thirteen crore sixty five lakh thirty two thousand two hundred and seven'. The standard form of the population is ______.
Answer: C
13 crore = 13,00,00,000; 65 lakh = 65,00,000; 32 thousand = 32,000; two hundred and seven = 207.
Together: 13,65,32,207.
44
length
easy
The height of a study table is twice the height of a chair. If the height of chair is 2 m 50 cm, then what is the total height of both chair and study table?
Answer: D
Chair = 2 m 50 cm = 250 cm. Table = 2 × 250 = 500 cm. Total = 250 + 500 = 750 cm.
45
lcm
medium
Two lights flash at an intervals of 18 minutes and 24 minutes. If they flash together at 9:00 a.m., then when will the next time they flash together?
Answer: D
They flash together again after LCM(18, 24) minutes. 18 = 2 × 3² and 24 = 2³ × 3, so LCM = 2³ × 3² = 72 minutes.
72 minutes = 1 hour 12 minutes after 9:00 a.m., which is 10:12 a.m.
Achievers Section
MCQs — 5 Questions
(+3)
46
hcf-lcm
hard
Fill in the blanks and select the CORRECT option.
(i) H.C.F of 24, 56 and 72 is __P__.
(ii) There is/are __Q__ prime factor(s) of a prime number.
(iii) There are __R__ common multiples of 15 and 25 lies between 100 and 500.
(iv) The sum of MCMXII and DCCXCIX, when rounded off each number to nearest hundreds, is __S__.
Answer: D
(i) 24 = 2³ × 3, 56 = 2³ × 7, 72 = 2³ × 3². H.C.F = 2³ = 8.
(ii) A prime number has only one prime factor, itself. Q = 1.
(iii) LCM of 15 and 25 = 75. Its multiples between 100 and 500 are 150, 225, 300, 375 and 450. R = 5.
(iv) MCMXII = 1912 → 1900 and DCCXCIX = 799 → 800. Sum = 2700.
47
pictograph
hard
The given pictograph shows the total number of flowers picked by five friends in a week. Study the given pictograph carefully and answer the following questions.
(i) Which two friends collected a total of 690 flowers?
(ii) Find the fraction of total number of flowers picked by Deepti and Niharika together to the total number of flowers picked by Shivangi and Rihanna together.
Answer: B
Each full flower = 60 and each half flower = 30.
Deepti = 5 × 60 + 30 = 330, Shivangi = 4 × 60 + 30 = 270, Niharika = 6 × 60 + 30 = 390, Devika = 6 × 60 = 360, Rihanna = 3 × 60 + 30 = 210.
(i) Deepti + Devika = 330 + 360 = 690.
(ii) Deepti + Niharika = 330 + 390 = 720 and Shivangi + Rihanna = 270 + 210 = 480. Fraction = 720/480 = 3/2.
48
area
hard
Read the given statements carefully and select the CORRECT option.
Statement-1: The area of shaded part of the given figure is 125 sq. cm.
Statement-2: The area of the shaded part of the given figure (not drawn to scale) is 40 sq. cm.
Answer: D
Statement-1: Each small square has area 5 × 5 = 25 sq. cm. The half-circle cut out on the left is the same size as the half-circle added at the bottom, so move the bottom one into the gap. Now count the squares covered: the two half squares on the left (1), the square in the middle (1), the lower square on the right (1) and the two pieces above it, a quarter and three-quarters of a square (1). That is 4 squares. Area = 4 × 25 = 100 sq. cm, so Statement-1 is false.
Statement-2: The left part is 4 cm × 8 cm = 32 sq. cm, minus the two white 2 cm × 2 cm squares: 32 − 8 = 24 sq. cm. The right part is two 4 cm × 4 cm squares, and in each one half is shaded: 2 × 8 = 16 sq. cm. Total = 24 + 16 = 40 sq. cm, so Statement-2 is true.
49
angles
hard
Solve the following and select the CORRECT option.
(i) Find the difference between the number of right angles and the number of acute angles inside the given figure.
(ii) The difference between the larger and smaller angle formed between the hands of a clock at 3'O clock is a ______.
Answer: D
(i) Inside the figure, the tops of the two small blocks give 4 right angles. The left point and the two right points give 3 acute angles. Difference = 4 − 3 = 1.
(ii) At 3 o'clock the smaller angle is 90° and the larger angle is 270°. Difference = 270° − 90° = 180°, a straight angle.
50
place-value
hard
Match the following and select the CORRECT option.
Column I
(P) Number of millions in 50 crores is ______.
(Q) The successor of predecessor of DCCXCVII is ______.
(R) 100 thousands + 100 hundreds + 250 tens = ______.
(S) The place value of digit 1 in the smallest 5 digit number formed by using the digits 0, 2, 5, 1 (using each digit at least once) is ______.
Column II
(i) 112500
(ii) 10000
(iii) 797
(iv) 500
Answer: B
(P) 50 crore = 500,000,000 = 500 millions → (iv).
(Q) DCCXCVII = 797. The successor of its predecessor is 797 itself → (iii).
(R) 100000 + 10000 + 2500 = 112500 → (i).
(S) The smallest 5-digit number using 0, 2, 5, 1 is 10025. The 1 is in the ten thousands place, so its place value is 10000 → (ii).