In the number 74,825, how many times greater is the value of digit 8 than the value of digit 2?
Explanation: The place value of 8 is 800 (hundreds place). The place value of 2 is 20 (tens place). 800 ÷ 20 = 40 times.
An L-shaped garden has outer sides measuring 12 m and 10 m. All corners are right angles. What is the total perimeter of the garden?
Explanation: Sum of horizontal sides = 12 + 12 = 24 m. Sum of vertical sides = 10 + 10 = 20 m. Total perimeter = 24 + 20 = 44 m.
Which fraction is strictly greater than 3/5 but smaller than 4/5?
Explanation: Expressing with denominator 10: 3/5 = 6/10 and 4/5 = 8/10. The fraction 7/10 lies between 6/10 and 8/10.
A movie starts at 4:35 PM and lasts for 2 hours and 40 minutes. At what time does the movie end?
Explanation: 4:35 PM + 2 hours = 6:35 PM. Adding 25 minutes brings it to 7:00 PM. Adding remaining 15 minutes gives 7:15 PM.
Which operations fill the boxes to make this true? (15 □ 3) □ 4 = 24
Explanation: (15 ÷ 3) × 4 = 5 × 4 = 20. Checking +, ×: (15 + 3) × 4 = 18 × 4 = 72. Wait, (15 - 3) + 12 = 24. With B: 15 ÷ 3 = 5, 5 × 4 = 20. Let's adjust: (15 + 3) + 6 = 24. For Option A: (15 + 3) - 4? If choices give: 15 + 3 = 18... Wait, 15 + 3 + 6 = 24. Using +, × on 15 + 3 = 18? Correct choice matching 24: (15 - 3) + 12 = 24.
How many lines of symmetry does a regular hexagon have?
Explanation: A regular polygon with n sides has exactly n lines of symmetry. A regular hexagon has 6 lines of symmetry.
A jug contains 3 L 450 mL of water. If 1 L 800 mL is poured out, how much water remains in the jug?
Explanation: Convert to mL: 3450 mL - 1800 mL = 1650 mL = 1 L 650 mL.
A class voted for favorite fruits: Apple (8), Banana (12), Mango (16), Orange (4). What fraction of the total votes went to Mango?
Explanation: Total votes = 8 + 12 + 16 + 4 = 40. Fraction for Mango = 16/40 = 2/5.
Each box contains 24 boxes of crayons. Each crayon box contains 8 crayons. How many crayons are in 15 full boxes?
Explanation: Total crayons = 15 × 24 × 8 = 360 × 8 = 2,880 crayons.
What is the 25th term in the repeating pattern: ■, ▲, ◉, ■, ▲, ◉, ...?
Explanation: The pattern repeats every 3 terms. 25 ÷ 3 = 8 with a remainder of 1. The 1st item in the sequence is Square.
Ananya bought 3 notebooks for $4.50 each and a pen for $2.75. She paid with a $20 bill. How much change did she receive?
Explanation: Total cost = (3 × 4.50) + 2.75 = 13.50 + 2.75 = $16.25. Change = 20.00 - 16.25 = $3.75.
What type of angle is formed by the hands of a clock at 3:00?
Explanation: At 3:00, the hour hand points at 3 and the minute hand points at 12, forming a 90° right angle.
A figure is drawn on a grid of 1 cm square units. It consists of 7 full squares and 4 half squares. What is its total area?
Explanation: Area = (7 × 1) + (4 × 0.5) = 7 + 2 = 9 cm².
Which number is a common factor of both 36 and 48?
Explanation: Factors of 36: 1,2,3,4,6,9,12,18,36. Factors of 48: 1,2,3,4,6,8,12,16,24,48. Common factor listed is 12.
What is the Hindu-Arabic numeral for XLVII?
Explanation: XL = 40, VII = 7. XLVII = 40 + 7 = 47.
When 257 is divided by 6, what is the quotient and remainder?
Explanation: 257 = (6 × 42) + 5 = 252 + 5.
Which fraction is equivalent to 3/4?
Explanation: Multiply numerator and denominator of 3/4 by 3: (3×3)/(4×3) = 9/12.
If 2 identical apples balance 6 strawberries, how many strawberries balance 5 apples?
Explanation: 1 apple = 6 ÷ 2 = 3 strawberries. Therefore, 5 apples = 5 × 3 = 15 strawberries.
Rohan's school bag weighs 3 kg 250 g and his lunchbox weighs 850 g. What is the total weight of both items?
Explanation: 3,250 g + 850 g = 4,100 g = 4 kg 100 g.
How many vertices does a triangular prism have?
Explanation: A triangular prism has 2 triangular bases and 3 rectangular sides, totaling 5 faces, 9 edges, and 6 vertices.
What is the value of the digit 7 in the number 43.57?
Explanation: The digit in the second place to the right of the decimal point is in the hundredths place (0.07).
If August 4th is a Tuesday, what day of the week will August 28th be?
Explanation: 28 - 4 = 24 days. 24 ÷ 7 = 3 weeks and 3 days. Tuesday + 3 days = Wednesday, Thursday, Friday.
Find the missing number in the series: 4, 9, 16, 25, □, 49
Explanation: Sequence of perfect squares: 2², 3², 4², 5², 6² (36), 7².
A square wire frame has an area of 64 cm². What is the perimeter of the frame?
Explanation: Side of square = √64 = 8 cm. Perimeter = 4 × 8 = 32 cm.
A pizza is divided into 12 equal slices. Kabir ate 3 slices and Meera ate 4 slices. What fraction of the pizza is left?
Explanation: Total eaten = 3 + 4 = 7 slices. Remaining slices = 12 - 7 = 5 slices. Fraction left = 5/12.
Which product is closest to 3,000?
Explanation: 59 ≈ 60 and 51 ≈ 50. 60 × 50 = 3,000 (Exact = 3,009).
Which capital letter has BOTH horizontal and vertical lines of symmetry?
Explanation: 'H' can be folded horizontally and vertically into identical halves.
A farmer collected 180 eggs. He packed them into cartons of 6 eggs each. He sold each carton for $3. How much total money did he make?
Explanation: Number of cartons = 180 ÷ 6 = 30 cartons. Total earnings = 30 × $3 = $90.
What is a polygon with 5 sides called?
Explanation: A 5-sided closed figure is called a pentagon.
Priya ran 4 laps around a rectangular park that is 50 m long and 30 m wide. What is the total distance she ran?
Explanation: Perimeter of 1 lap = 2 × (50 + 30) = 160 m. 4 laps = 4 × 160 = 640 m.
What is 4,852 rounded to the nearest hundred?
Explanation: Tens digit is 5, so we round up the hundreds digit from 8 to 9, giving 4,900.
Solve: 2/9 + 4/9 + 1/9 = ?
Explanation: With common denominators, add numerators: (2 + 4 + 1) / 9 = 7/9.
A train left Station A at 10:15 AM and reached Station B at 2:45 PM. How long did the journey take?
Explanation: From 10:15 AM to 2:15 PM is 4 hours. Adding 30 minutes gives 2:45 PM. Total = 4 hrs 30 mins.
A toy shop sold 45 cars on Mon, 30 on Tue, 60 on Wed. What is the average number of cars sold per day?
Explanation: Total = 45 + 30 + 60 = 135. Average = 135 ÷ 3 = 45 cars.
Find the value of XV + IX - IV in Hindu-Arabic numerals.
Explanation: XV = 15, IX = 9, IV = 4. Equation: 15 + 9 - 4 = 24 - 4 = 20.
If 1 cat eats 1 mouse in 5 minutes, how many minutes will it take 5 cats to eat 5 mice?
Explanation: Each cat takes 5 minutes to eat its mouse. Operating simultaneously, 5 cats eat 5 mice in 5 minutes.
How many right angles are there inside a standard rectangle?
Explanation: Every rectangle has 4 internal corners, each forming a 90° right angle.
4 friends share a total prize money of $124 equally. How much money does each friend receive?
Explanation: $124 ÷ 4 = $31.
Find the rule for the pattern: 3, 7, 15, 31, 63, ...
Explanation: 3×2+1=7; 7×2+1=15; 15×2+1=31; 31×2+1=63.
How many meters are in 4 kilometers and 75 meters?
Explanation: 4 km = 4,000 m. Total = 4,000 + 75 = 4,075 m.
Rectangle A is 6 cm by 4 cm. Square B has a side length of 5 cm. Which statement is true?
Explanation: Area A = 6 × 4 = 24 cm². Area B = 5 × 5 = 25 cm². 24 < 25.
Which of the following is NOT a factor of 42?
Explanation: 42 is not divisible by 8 (42 ÷ 8 = 5 remainder 2).
Find the sum of 12.45 and 8.7?
Explanation: Align decimals: 12.45 + 8.70 = 21.15.
How many square faces make up the net of a cube?
Explanation: A 3D cube has 6 identical square faces, so its net contains 6 squares.
A book has 144 pages. If Meena reads 16 pages every day, how many days will she take to finish the book?
Explanation: Total days = 144 ÷ 16 = 9 days.
Subtract: 5/6 - 1/3 = ?
Explanation: Convert 1/3 to common denominator 6: 2/6. 5/6 - 2/6 = 3/6 = 1/2.
Which quadrilateral has only ONE pair of parallel sides?
Explanation: By definition, a trapezium has exactly one pair of opposite parallel sides.
What is the smallest non-zero number that is a multiple of both 6 and 8?
Explanation: Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... Least common multiple is 24.
If a digital clock shows 18:45, what time is it on a 12-hour clock?
Explanation: 18:45 - 12:00 = 6:45 PM.
If the word 'MOM' is reflected across a vertical mirror, how does it appear?
Explanation: M and O possess vertical reflectional symmetry, so 'MOM' stays 'MOM'.
Evaluate: 20 + 8 ÷ 2 × 3 - 5
Explanation: First 8 ÷ 2 = 4. Next 4 × 3 = 12. Then 20 + 12 - 5 = 27.
How many 250 mL cups are needed to fill a 2-liter container?
Explanation: 2 liters = 2,000 mL. 2,000 ÷ 250 = 8 cups.
In the addition problem: 4,□82 + 1,354 = 5,836, what digit belongs in the square?
Explanation: 5,836 - 1,354 = 4,482. The missing digit in the hundreds place is 4.
What is the straight line segment passing through the center of a circle and connecting two points on its boundary called?
Explanation: A straight line through the center connecting two points on the circle is the diameter.
Convert 17/5 into a mixed fraction.
Explanation: 17 ÷ 5 gives quotient 3 and remainder 2. So, 17/5 = 3 2/5.
A bicycle travels at a speed of 12 km per hour. How far will it travel in 3 hours and 30 minutes?
Explanation: 3.5 hours × 12 km/h = 42 km.
If 1 star = 3 circles, and 2 circles = 4 squares, how many squares equal 1 star?
Explanation: 1 circle = 2 squares. Since 1 star = 3 circles, 1 star = 3 × 2 = 6 squares.
In a test, Rahul scored 85, 90, and 80 in three subjects. What score must he get in the fourth subject to have an average of 86?
Explanation: Target total = 4 × 86 = 344. Current sum = 85 + 90 + 80 = 255. Required = 344 - 255 = 89.
A triangle has side lengths 6 cm, 6 cm, and 8 cm. What type of triangle is it?
Explanation: A triangle with two sides of equal length is an isosceles triangle.
There are 3 identical-looking coins, but 1 is lighter than the others. What is the minimum number of weighings on a balance scale needed to guarantee finding the lighter coin?
Explanation: Place 1 coin on each pan of the balance scale, keeping 1 aside. If balanced, the unweighed coin is lighter. If unbalanced, the higher pan holds the lighter coin. Total = 1 weighing.
I am a 4-digit number. My thousands digit is 8 and my hundreds digit is 4. My tens digit and ones digit are the same, and the sum of all my digits is 20. Who am I?
Explanation: 8 + 4 = 12, so the tens and ones digits must add up to 20 − 12 = 8. Since they are equal, each is 4. The number is 8444.
Using each of the digits 3, 0, 7 and 5 exactly once, make the largest and the smallest possible 4-digit numbers. What is their difference?
Explanation: Largest = 7530. Smallest = 3057 (a 4-digit number cannot start with 0). Difference = 7530 − 3057 = 4,473.
The number line below goes from 4,200 to 4,600 and is divided into 8 equal parts. Which number does the red arrow point to?
Explanation: The distance 4,600 − 4,200 = 400 is split into 8 equal parts, so each part is 400 ÷ 8 = 50. The arrow is at the 5th mark: 4,200 + 5 × 50 = 4,450.
The number 8,647 is rounded to the nearest hundred and then separately to the nearest thousand. What is the sum of the two rounded numbers?
Explanation: Nearest hundred: 8,647 → 8,600. Nearest thousand: 8,647 → 9,000. Sum = 8,600 + 9,000 = 17,600.
Add XLIV and XXVIII. Which Roman numeral shows the answer?
Explanation: XLIV = 44 and XXVIII = 28. 44 + 28 = 72 = 50 + 10 + 10 + 2 = LXXII.
A shop had 2,450 pencils. It sold 875 pencils on Monday and 1,020 pencils on Tuesday. On Wednesday it bought 500 new pencils. How many pencils does the shop have now?
Explanation: 2,450 − 875 = 1,575. 1,575 − 1,020 = 555. Then 555 + 500 = 1,055 pencils.
A bus had some passengers at the start. At the first stop 18 got off and 7 got on. At the second stop 9 got off and 15 got on. Now there are 40 passengers on the bus. How many passengers were on the bus at the start?
Explanation: Work backwards. Second stop: net change = +15 − 9 = +6, so before it there were 40 − 6 = 34. First stop: net change = +7 − 18 = −11, so at the start there were 34 + 11 = 45.
A box holds 24 chocolates. A school orders 35 boxes and gives 4 chocolates to each child. How many children get chocolates?
Explanation: Total chocolates = 24 × 35 = 840. Children = 840 ÷ 4 = 210.
When a number is divided by 9, the quotient is 47 and the remainder is 5. What is the number?
Explanation: Number = divisor × quotient + remainder = 9 × 47 + 5 = 423 + 5 = 428.
The 3-digit number 47★ is divisible by 3. What is the largest digit that can replace ★?
Explanation: A number is divisible by 3 when its digit sum is. 4 + 7 = 11, so 11 + ★ must be in the 3-table. ★ can be 1, 4 or 7 (sums 12, 15, 18). The largest is 7 (477 ÷ 3 = 159).
How many factors does the number 36 have?
Explanation: Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. That makes 9 factors.
Bell A rings every 6 minutes and Bell B rings every 8 minutes. They ring together at 10:00 AM. At what time will they next ring together?
Explanation: The bells ring together after the LCM of 6 and 8. LCM(6, 8) = 24 minutes. 10:00 AM + 24 minutes = 10:24 AM.
Two ropes are 36 m and 48 m long. Both are cut into pieces of the same longest possible length, with nothing left over. How many pieces are there in all?
Explanation: Longest equal length = HCF(36, 48) = 12 m. Rope 1 gives 36 ÷ 12 = 3 pieces and Rope 2 gives 48 ÷ 12 = 4 pieces. Total = 7 pieces.
How many multiples of 7 are there from 1 to 60 (both included)?
Explanation: Multiples: 7, 14, 21, 28, 35, 42, 49, 56. The next one, 63, is more than 60. So there are 8 multiples.
What is the smallest 3-digit number that is exactly divisible by 4, 6 and 9?
Explanation: LCM(4, 6, 9) = 36. Multiples of 36: 36, 72, 108, … The first 3-digit multiple is 36 × 3 = 108.
A pizza is cut into 8 equal slices. Riya ate the blue slices and Sam ate the orange slices, as shown. What fraction of the pizza is left?
Explanation: Riya ate 3 slices and Sam ate 2 slices, so 5 slices were eaten. Slices left = 8 − 5 = 3, which is 3/8 of the pizza.
Which fraction is equal to 3/5?
Explanation: Multiply the top and bottom of 3/5 by 3: (3 × 3)/(5 × 3) = 9/15. The others are not equal to 3/5 (6/9 = 2/3, and 12/25 is close to 1/2).
Which is the greatest of the fractions 5/8, 3/4, 2/3 and 7/12?
Explanation: Change all to 24ths: 5/8 = 15/24, 3/4 = 18/24, 2/3 = 16/24, 7/12 = 14/24. The largest numerator is 18, so 3/4 is the greatest.
Aman spent 1/3 of his money on a book and 1/4 of his money on a toy. He has ₹25 left. How much money did he have at first?
Explanation: Fraction spent = 1/3 + 1/4 = 7/12, so the fraction left = 5/12. If 5/12 of the money is ₹25, then 1/12 is ₹5 and the whole is 12 × 5 = ₹60 (book ₹20, toy ₹15, left ₹25).
Find the value of 0.6 + 0.35 + 1.4.
Explanation: Write each with 2 decimal places: 0.60 + 0.35 + 1.40. 0.60 + 0.35 = 0.95, and 0.95 + 1.40 = 2.35.
Kabir buys 3 pens and 2 notebooks at the prices shown and pays with two ₹100 notes. How much change should he get back?
Explanation: 3 pens = 3 × 18 = ₹54. 2 notebooks = 2 × 35 = ₹70. Total = ₹124. Change = 200 − 124 = ₹76.
Using only ₹10, ₹5, ₹2 and ₹1 coins, what is the smallest number of coins needed to make exactly ₹37?
Explanation: Take as many big coins as possible: 3 × ₹10 = ₹30, then ₹5 (total 35), then ₹2 (total 37). That is 3 + 1 + 1 = 5 coins. Four coins cannot do it: three ₹10 coins leave ₹7, and there is no single ₹7 coin.
A train leaves the station at 6:45 AM. The journey takes 5 hours 40 minutes. At what time does the train arrive?
Explanation: 6:45 AM + 5 hours = 11:45 AM. 11:45 AM + 40 minutes = 12:25 PM. The train arrives at 12:25 PM.
The clock shows the time Priya left home for school. She reached school 45 minutes later. At what time did she reach school?
Explanation: The clock shows 4:20. 4:20 + 40 minutes = 5:00, and 5 more minutes make 5:05. So Priya reached school at 5:05.
The calendar of a 30-day month is shown below. On which date does the third Friday fall?
Explanation: Fridays are in the F column: 3rd, 10th, 17th and 24th. The third Friday is the 17th.
How many days are there from 15 March to 2 April, counting both 15 March and 2 April?
Explanation: 15 March to 31 March = 31 − 15 + 1 = 17 days. Add 1 April and 2 April = 2 days. Total = 19 days.
A container has 5 L 250 mL of water. Three bottles of 750 mL each are filled from it. How much water is left in the container?
Explanation: 5 L 250 mL = 5,250 mL. Water used = 3 × 750 = 2,250 mL. Left = 5,250 − 2,250 = 3,000 mL = 3 L.
Sana has a ribbon of length 2 m 35 cm. Her sister gives her another ribbon of length 1 m 80 cm. What is the total length of the ribbons?
Explanation: 235 cm + 180 cm = 415 cm. Since 100 cm = 1 m, 415 cm = 4 m 15 cm.
A square garden has a side of 12 m. A farmer fences it with wire going around it 3 times. What is the total length of wire used?
Explanation: Perimeter of the square = 4 × 12 = 48 m. For 3 rounds, wire = 3 × 48 = 144 m.
A rectangular floor is 8 m long and 6 m wide. It is covered with square tiles of side 2 m, as shown. How many tiles are needed?
Explanation: Along the length: 8 ÷ 2 = 4 tiles. Along the width: 6 ÷ 2 = 3 tiles. Total = 4 × 3 = 12 tiles. (Check: floor area 48 ÷ tile area 4 = 12.)
The L-shaped figure below is a 10 cm × 8 cm rectangle with a 4 cm × 3 cm corner cut out. What is the perimeter of the figure?
Explanation: Slide the two sides of the cut-out corner to the outer edges: the perimeter is the same as that of the full rectangle. 2 × (10 + 8) = 36 cm. (Check: 6 + 3 + 4 + 5 + 10 + 8 = 36.)
How many squares of all sizes can you find in this 3 × 3 grid?
Explanation: Small squares (1 × 1): 9. Medium squares (2 × 2): 4. Big square (3 × 3): 1. Total = 9 + 4 + 1 = 14.
Two lines are drawn from the top corner of a triangle to its base, dividing the base into 3 parts as shown. How many triangles are there in the figure?
Explanation: Single small triangles: 3. Triangles made of 2 small ones: 2. The whole big triangle: 1. Total = 3 + 2 + 1 = 6.
Which of these capital letters has both a horizontal and a vertical line of symmetry?
Explanation: A and M have only a vertical line of symmetry, and E has only a horizontal one. The letter H can be folded both ways along a line and the two halves match exactly.
The minute hand of a clock starts at 12 and stops at 9. Through how many right angles has it turned (clockwise)?
Explanation: 12 to 3 is 1 right angle, 3 to 6 is another and 6 to 9 is a third. So the minute hand turned through 3 right angles (a full turn is 4 right angles).
The perimeter of a rectangle is 40 cm and its length is 12 cm. What is its area?
Explanation: Length + width = 40 ÷ 2 = 20 cm, so width = 20 − 12 = 8 cm. Area = 12 × 8 = 96 sq cm.
The staircase shape below is made of unit squares. What are its area and its perimeter?
Explanation: Area = 1 + 2 + 3 + 4 = 10 unit squares. For the perimeter, the steps do not add extra length: the horizontal parts add up to 4 + 4 and the vertical parts to 4 + 4, so the perimeter is 4 + 4 + 4 + 4 = 16 units.
A square and a rectangle both have a perimeter of 24 cm. The rectangle is 8 cm long. Which one has the greater area, and by how much?
Explanation: Square: side = 24 ÷ 4 = 6 cm, area = 36 sq cm. Rectangle: width = 12 − 8 = 4 cm, area = 32 sq cm. The square is bigger by 36 − 32 = 4 sq cm.
Find the next number in the pattern: 2, 6, 12, 20, 30, ?
Explanation: The gaps are 4, 6, 8, 10, so the next gap is 12. 30 + 12 = 42.
Find the missing number: 1, 3, 7, 15, 31, ?
Explanation: Each number is (previous × 2) + 1. So 31 × 2 + 1 = 63.
A train of shapes repeats in the same order, as shown. Which shape will be in the 20th place?
Explanation: The pattern (triangle, square, circle) repeats every 3 shapes. 20 ÷ 3 = 6 remainder 2, so the 20th shape is the 2nd shape of the pattern: Square.
Squares are made in a row using matchsticks: 1 square needs 4 sticks, 2 squares need 7 sticks and 3 squares need 10 sticks. How many matchsticks are needed for 10 squares in a row?
Explanation: The first square needs 4 sticks, and each new square adds 3 more. For 10 squares: 4 + 9 × 3 = 4 + 27 = 31.
In this number pyramid, every box is the sum of the two boxes just below it. What number goes in the top box?
Explanation: Bottom row: 4, 7, 5, 9. Next row: 11, 12, 14. Next row: 23, 26. Top = 23 + 26 = 49.
In this magic square every row, every column and both diagonals add up to the same number. What number should replace the question mark?
Explanation: The middle row is 9 + 5 + 1 = 15, so every line adds up to 15. Top row: ? + 7 + 6 = 15, so ? = 15 − 13 = 2.
Each fruit stands for a number. Use the clues to find the value of the last line.
Explanation: 3 apples = 21, so an apple = 7. Apple + 2 bananas = 13, so 2 bananas = 6 and a banana = 3. Banana + grape = 8, so a grape = 5. Apple + banana + grape = 7 + 3 + 5 = 15.
How many times is the digit 1 written when we write all the numbers from 1 to 30?
Explanation: The digit 1 appears in: 1 (once), 10 (once), 11 (twice), 12 to 19 (once each, 8 times) and 21 (once). Total = 1 + 1 + 2 + 8 + 1 = 13.
Anu is taller than Bala. Bala is taller than Chitra. Dev is shorter than Chitra but taller than Esha. Who is the second shortest?
Explanation: Order from tallest to shortest: Anu > Bala > Chitra > Dev > Esha. The shortest is Esha, so the second shortest is Dev.
Tara is 7th from the left and 12th from the right in a line of children. How many children are in the line?
Explanation: Tara is counted in both positions, so we subtract 1: 7 + 12 − 1 = 18 children.
Six friends meet at a party. Every friend shakes hands exactly once with every other friend. How many handshakes are there in all?
Explanation: Each friend shakes hands with 5 others: 6 × 5 = 30. But every handshake is counted twice (once by each person), so 30 ÷ 2 = 15. (5 + 4 + 3 + 2 + 1 = 15.)
Ravi is 8 years old and his mother is 4 times as old as he is. After how many years will his mother be exactly 3 times as old as Ravi?
Explanation: Mother is 4 × 8 = 32 years old. After 4 years, Ravi will be 12 and his mother 36, and 36 = 3 × 12. So the answer is 4 years.
I think of a number, multiply it by 4 and subtract 6. The answer is 30. What is my number?
Explanation: Work backwards: 30 + 6 = 36, and 36 ÷ 4 = 9. Check: 9 × 4 = 36, 36 − 6 = 30.
The sum of two numbers is 45 and their difference is 9. What is the larger number?
Explanation: Larger = (sum + difference) ÷ 2 = (45 + 9) ÷ 2 = 27. The smaller is 18, and 27 + 18 = 45, 27 − 18 = 9.
12 fence posts are put in a straight line with 3 m between one post and the next. What is the distance from the first post to the last post?
Explanation: 12 posts make only 11 gaps. Distance = 11 × 3 = 33 m.
A clock takes 4 seconds to strike 3 times. How long will it take to strike 6 times?
Explanation: 3 strikes have 2 gaps, so each gap is 4 ÷ 2 = 2 seconds. 6 strikes have 5 gaps: 5 × 2 = 10 seconds.
The bar graph shows the number of storybooks read by five children in a month. How many books did the five children read altogether?
Explanation: Reading the bars: Amit 12, Bina 8, Chetan 20, Divya 4, Esha 16. Total = 12 + 8 + 20 + 4 + 16 = 60.
Using the same bar graph, Chetan read how many more books than Bina and Divya read together?
Explanation: Bina + Divya = 8 + 4 = 12 books. Chetan read 20 books, so the difference is 20 − 12 = 8.
Ria builds a staircase from identical cubes, as shown. How many cubes did she use in all?
Explanation: The columns have 4, 3, 2 and 1 cubes. Total = 4 + 3 + 2 + 1 = 10 cubes.
A big cube is made by joining 27 small cubes (3 × 3 × 3). The whole outside of the big cube is painted red. How many small cubes have no red paint on any face?
Explanation: Every small cube touching the outside gets paint. Only the single cube hidden right in the centre is completely inside, so 1 small cube has no paint (27 − 26 = 1).
The shape on the left is placed next to a vertical mirror. Which picture shows its mirror image?
Explanation: A vertical mirror swaps left and right. The upright bar of the L is on the left and the foot points right, so in the mirror the bar is on the right and the foot points left.
On a standard die, the numbers on opposite faces always add up to 7. A die is placed so that 2 is on top and 3 is at the front. What is the sum of the numbers on the bottom face and the back face?
Explanation: Bottom is opposite to top: 7 − 2 = 5. Back is opposite to front: 7 − 3 = 4. Sum = 5 + 4 = 9.
A rectangular garden is 15 m long and 9 m wide. What is the perimeter of the garden?
Explanation: Perimeter of a rectangle = 2 × (Length + Breadth) = 2 × (15 + 9) = 2 × 24 = 48 m.
A square-shaped table top has each side measuring 7 cm. What is the total length of the wooden border needed to go around it?
Explanation: A square has 4 equal sides. Perimeter = 4 × side = 4 × 7 = 28 cm.
Look at the L-shaped playground below. Its outer sides are 10 m and 8 m, and the notch cut out is 4 m by 3 m. What is the perimeter of the playground?
Explanation: Even though the shape has a notch, the total horizontal distance still equals 10 m (top and bottom together = 10+10=20) and vertical distance equals 8 m (left and right together = 8+8=16). Total Perimeter = 20 + 16 = 36 m. (A neat trick: for an L-shape, perimeter is always the same as the surrounding rectangle!)
A rectangle is divided into small identical squares as shown, forming a 4-by-3 grid. How many small squares are there in total?
Explanation: The grid has 4 columns and 3 rows. Total squares = 4 × 3 = 12.
A triangular flag has three sides measuring 18 cm, 24 cm, and 30 cm. A ribbon is sewn all around the edge of the flag. What length of ribbon is required?
Explanation: Perimeter of a triangle = sum of all three sides = 18 + 24 + 30 = 72 cm.
Look at the clock shown below. What time does it show?
Explanation: The hour hand is just past the 3, and the minute hand points at the 3 (which marks 15 minutes). So the clock shows 3:15.
School assembly starts at 8:05 AM and lasts for 25 minutes. At what time does the assembly end?
Explanation: End time = Start time + Duration = 8:05 AM + 25 minutes = 8:30 AM.
A movie begins at 6:40 PM and ends at 8:55 PM. How long is the movie?
Explanation: From 6:40 PM to 8:40 PM is 2 hours. From 8:40 PM to 8:55 PM is 15 more minutes. Total duration = 2 hours + 15 minutes = 2 hours 15 minutes.
How many minutes are there in 1 whole day (24 hours)?
Explanation: There are 60 minutes in 1 hour. In 24 hours, total minutes = 24 × 60 = 1440 minutes.
A train leaves the station at 10:50 AM and reaches the next city after travelling for 1 hour 35 minutes. At what time does it arrive?
Explanation: 10:50 AM + 1 hour = 11:50 AM. Then add 35 more minutes: 11:50 AM + 35 min = 12:25 PM.
A notebook costs ₹35. Riya buys 4 notebooks and gives the shopkeeper a ₹200 note. How much change should she get back?
Explanation: Cost of 4 notebooks = 4 × ₹35 = ₹140. Change = ₹200 - ₹140 = ₹60.
Three friends together have ₹450 in pocket money, shared equally. How much money does each friend have?
Explanation: Equal share = Total ÷ Number of friends = ₹450 ÷ 3 = ₹150.
Aryan's piggy bank has 12 coins of ₹5 each and 8 coins of ₹10 each. What is the total amount saved?
Explanation: Value of ₹5 coins = 12 × 5 = ₹60. Value of ₹10 coins = 8 × 10 = ₹80. Total = 60 + 80 = ₹140.
A toy costs ₹280. Meera has already saved ₹165. How much more money does she need to save to buy the toy?
Explanation: Amount still needed = Cost of toy - Amount saved = ₹280 - ₹165 = ₹115.
A fruit seller sells apples for ₹18 per kg and oranges for ₹12 per kg. If a customer buys 3 kg of apples and 5 kg of oranges, what is the total bill?
Explanation: Cost of apples = 3 × 18 = ₹54. Cost of oranges = 5 × 12 = ₹60. Total bill = 54 + 60 = ₹114.
A pizza is cut into 8 equal slices. Karan eats 3 slices. What fraction of the pizza is left?
Explanation: Fraction eaten = 3/8. Fraction left = 1 - 3/8 = 8/8 - 3/8 = 5/8.
Which of the following fractions is the greatest?
Explanation: When fractions have the same numerator (1), the fraction with the smaller denominator is greater, because the whole is divided into fewer, bigger parts. Comparing denominators 4, 3, 2, 6 — the smallest is 2. So 1/2 is the greatest.
A grid of 10 equal squares has 4 squares shaded blue. What fraction of the grid is shaded?
Explanation: Number of shaded squares = 4. Total squares = 10. Fraction shaded = 4/10 (which can also be written as 2/5).
Simran ate half of a chocolate bar. She then gave half of what remained to her brother. What fraction of the whole bar does her brother get?
Explanation: After Simran eats 1/2, the remaining piece is 1/2 of the bar. Her brother gets half of that remaining half: 1/2 × 1/2 = 1/4 of the whole bar.
Deepak has 24 marbles. He gives 1/4 of them to his friend. How many marbles does he give away?
Explanation: 1/4 of 24 = 24 ÷ 4 = 6 marbles.
Look at the number pattern: 4, 8, 12, 16, ___. What is the next number in the pattern?
Explanation: Each number increases by 4 (the pattern is the 4-times table: 4, 8, 12, 16...). The next number = 16 + 4 = 20.
A pattern of stars is arranged as: 20, 17, 14, 11, ___. What number comes next?
Explanation: Each number decreases by 3 (20 - 3 = 17, 17 - 3 = 14, and so on). The next number = 11 - 3 = 8.
Look at the repeating shape pattern below: Circle, Square, Square, Circle, Square, Square, Circle, ___. What shape comes next?
Explanation: The pattern repeats in a block of 3: Circle, Square, Square. After the 7th shape (Circle), the next one starts the block again: Square.
A pattern doubles each time: 3, 6, 12, 24, ___. What is the next number?
Explanation: Each term is double the one before it (3×2=6, 6×2=12, 12×2=24). The next term = 24 × 2 = 48.
In the table below, each output is found by adding 7 to the input. If the input is 15, what is the output?
Explanation: Output = Input + 7 = 15 + 7 = 22.
The bar graph shows the favorite fruits of students in a class: Apple = 8, Banana = 12, Mango = 15, Orange = 5. How many more students chose Mango than Banana?
Explanation: Students who chose Mango = 15. Students who chose Banana = 12. Difference = 15 - 12 = 3.
A picture graph shows books read by Anu: January = 4 books, February = 7 books, March = 3 books. How many books did Anu read in total over the three months?
Explanation: Total books = January + February + March = 4 + 7 + 3 = 14 books.
A survey of pets shows: Dogs = 18, Cats = 14, Fish = 9, Birds = 6. What is the total number of pets counted in the survey?
Explanation: Total pets = 18 + 14 + 9 + 6 = 47.
In a tally chart, the number of students who walk to school is shown as: |||| |||| ||. How many students walk to school?
Explanation: Each group of |||| represents 5. Two full groups = 5 + 5 = 10, plus 2 more marks = 10 + 2 = 12 students.
A bar graph shows rainfall (in mm) over 4 days: Mon = 10mm, Tue = 25mm, Wed = 15mm, Thu = 30mm. On which day did it rain the most, and how much more than Monday?
Explanation: The tallest bar is Thursday with 30 mm. Difference from Monday = 30 - 10 = 20 mm more, on Thursday.
A shopkeeper has 156 pencils. He packs them equally into boxes of 12 pencils each. How many full boxes can he make?
Explanation: Number of boxes = Total pencils ÷ Pencils per box = 156 ÷ 12 = 13 boxes.
For a school function, 18 rows of chairs are arranged with 15 chairs in each row. How many chairs are there in total?
Explanation: Total chairs = Number of rows × Chairs per row = 18 × 15 = 270 chairs.
A farmer collects 384 eggs and packs them into cartons that hold 8 eggs each. How many cartons does he need?
Explanation: Number of cartons = 384 ÷ 8 = 48 cartons.
5 buses are used for a school trip. Each bus carries 42 students. How many students went on the trip in total?
Explanation: Total students = Number of buses × Students per bus = 5 × 42 = 210 students.
A box contains 168 sweets, to be shared equally among 7 children. How many sweets does each child get?
Explanation: Sweets per child = 168 ÷ 7 = 24 sweets.
A rope is 3 metres 45 centimetres long. What is its length in centimetres only?
Explanation: 1 metre = 100 cm, so 3 m = 300 cm. Total length = 300 cm + 45 cm = 345 cm.
A shopkeeper has three bags of rice weighing 12 kg, 18 kg, and 25 kg. What is the total weight of rice?
Explanation: Total weight = 12 + 18 + 25 = 55 kg.
A water tank holds 60 litres when full. A bucket can carry 5 litres of water. How many buckets of water are needed to fill the empty tank?
Explanation: Number of buckets = Total capacity ÷ Bucket capacity = 60 ÷ 5 = 12 buckets.
Which of these lengths is the longest?
Explanation: Convert all to centimetres: A = 250 cm, B = 230 cm, C = 3 m = 300 cm, D = 280 cm. The greatest value is 300 cm (3 m).
A juice bottle holds 750 mL. If 4 such bottles are filled completely, how many millilitres of juice are used in total?
Explanation: Total juice = 4 × 750 mL = 3000 mL (which is the same as 3 litres).
In the number 4,587, what is the value of the digit 5?
Explanation: In the number 4,587: 4 is in the thousands place, 5 is in the hundreds place, 8 is in the tens place, and 7 is in the ones place. So the digit 5 stands for 500.
Round the number 486 to the nearest ten.
Explanation: The ones digit of 486 is 6, which is 5 or more, so we round up. 486 rounded to the nearest ten = 490.
Using the digits 3, 8, 1, and 6 (each used only once), what is the greatest 4-digit number that can be formed?
Explanation: To form the greatest number, arrange the digits in descending order: 8631.
What number does the Roman numeral XXIV represent?
Explanation: XX = 20 and IV = 4 (5 - 1 = 4, since I comes before V). So XXIV = 20 + 4 = 24.
Which of the following numbers is an odd number?
Explanation: A number is odd if its ones digit is 1, 3, 5, 7, or 9. Among the choices, 583 ends in 3, so 583 is the odd number.
A clock shows the time 3:00 as seen directly. When this clock face is viewed in a mirror, at what time will the reflected hands appear to point?
Explanation: A mirror flips an image left-to-right. The hour hand pointing at 3 (to the right) will appear to point at 9 (to the left) in the mirror. So the mirror image shows 9:00.
The solid block shown is built from small identical cubes stacked in 2 layers, each layer being a 3-by-2 grid of cubes. How many small cubes make up the whole block?
Explanation: Each layer has 3 × 2 = 6 cubes. There are 2 layers, so the total number of cubes = 6 × 2 = 12 cubes.
A square piece of paper has one hole punched near a corner. The paper is folded exactly in half along the dotted vertical line before punching. When unfolded, how many holes will the paper have?
Explanation: Folding the paper in half means the punch goes through both layers at once. When unfolded, the hole appears once on each half, mirrored across the fold line, giving 2 holes in total.
Which of these shapes has the greatest number of sides?
Explanation: Triangle = 3 sides, Square = 4 sides, Pentagon = 5 sides, Hexagon = 6 sides. The shape with the most sides is the Hexagon.
A triangle pointing UP is rotated a little to the right each time in a repeating sequence, as shown. Which pattern rule describes this sequence?
Explanation: Looking carefully at the three triangles shown, each one is turned a bit further in the clockwise direction than the one before it, while staying the same size and color. The rule is: it rotates clockwise a little each time.
How many factors does the number 12 have?
Explanation: The factors of 12 are the numbers that divide it exactly: 1, 2, 3, 4, 6, and 12. That makes 6 factors in total.
Which of the following numbers is a common factor of both 18 and 24?
Explanation: Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The number that appears in both lists is 6.
Which of the following numbers is NOT a multiple of 6?
Explanation: Multiples of 6 are found by multiplying 6 by whole numbers: 6, 12, 18, 24, 30, 36, 42... The number 32 does not appear in this list, so it is not a multiple of 6.
If two even numbers are multiplied together, what type of number will the answer always be?
Explanation: Any even number can be written as 2 × something. When two even numbers are multiplied, the answer always has a factor of 2 in it, so the product is always even. For example, 4 × 6 = 24, which is even.
If 7 × ___ = 56, what number goes in the blank?
Explanation: To find the missing factor, divide: 56 ÷ 7 = 8. Check: 7 × 8 = 56. ✓
Ravi is 4 years older than his sister Priya. If Priya is 9 years old, how old will Ravi be in 3 years?
Explanation: Ravi's current age = Priya's age + 4 = 9 + 4 = 13 years. In 3 years, Ravi's age = 13 + 3 = 16 years.
A shelf has 3 rows of books. The first row has 24 books, the second row has twice as many books as the first row, and the third row has 15 fewer books than the second row. How many books are on the third row?
Explanation: First row = 24 books. Second row = 2 × 24 = 48 books. Third row = 48 - 15 = 33 books.
I am a 2-digit number. My tens digit is 3 more than my ones digit. My ones digit is 4. What number am I?
Explanation: The ones digit is 4. The tens digit is 3 more than the ones digit = 4 + 3 = 7. Putting the tens digit first, the number is 74.
In a classroom, students sit in equal rows. There are 8 rows with an equal number of students in each row, and 56 students in total. If 2 more students join and are seated in new rows of 8 each, how many complete rows will there be in total?
Explanation: Currently, students per row = 56 ÷ 8 = 7 students in each of 8 rows. Adding 2 more students (total 58) is not enough to fill a 9th row of 8, so there are still 7 complete rows of 8, with 2 students left over.
A farmer picks 245 mangoes. He packs them into baskets that hold 9 mangoes each, filling as many baskets as possible. How many mangoes will be left over after filling the baskets?
Explanation: Divide 245 by 9: 9 × 27 = 243, with a remainder. 245 - 243 = 2 mangoes left over (27 full baskets are filled).