Note: The questions provided in this document are similar to the questions that were asked in the actual Olympiad exam. So, we recommend you study these for your Olympiad preparation
Logical Reasoning
Q1: Bipin is the son of Ashok. Ishu is the brother of Bipin, and Krishna is the wife of Ashok. Bipin is married to Aarti, then how is Ishu related to Aarti? (a) Brother (b) Brother-in-law (c) Husband (d) Father
Solution:
Ans: (b)
Ishu is the brother of Bipin.
Bipin is married to Aarti.
This means that Ishu is Aarti's brother-in-law because he is the brother of her husband.
Thus, the correct relationship is that Ishu is Aarti's brother-in-law.
Q2: The value of (1.5)³ is __________. (a) 5.375 (b) 3.375 (c) 4.375 (d) 7.375
Solution:
Ans: (1.5)3 =3.375
Q3: If '+' denotes '×', '÷' denotes '-', '-' denotes '+', and '×' denotes '÷', then find the value of 125 - 6 × 3 + 5 ÷ 18. (a) 104 (b) 109 (c) 238 (d) 117
Solution:
Ans: (d)
First, we need to replace the operations according to the given rules:
Now, we perform the operations in the correct order: division and multiplication first, then addition and subtraction.
Calculating 6 ÷ 3 gives 2, then 2 × 5 gives 10. Finally, we compute 125 + 10 - 18, which equals 117.
Q4: The distance of the point (3, 4) from the y-axis is: (a) 1 (b) 4 (c) 2 (d) 3
Solution:
Ans: (d) Perpendicular distance of point (3, 4) from y-axis is 3.
Q5: In a certain code language "BIRTHDAY" is written as "XENHTZWU." How is "PLEASURE" written in that code language? (a) QMFBTVSE (b) TPIEWYVI (c) SOHDVXUH (d) LHASAQNA
Solution:
Ans: (d)
The code language involves a specific pattern of shifting letters. Each letter in "BIRTHDAY" is replaced by another letter a certain number of places down the alphabet.
For example, 'B' becomes 'X', which is 22 letters back in the alphabet. This pattern continues for each letter.
Applying the same shifting pattern to "PLEASURE" results in "LHASAQNA."
Thus, the correct answer is option (d) LHASAQNA.
Q6: The cube root of 1.331 is: (a) 0.11 (b) 0.011 (c) 11 (d) 1.1
Solution:
Ans: (d)
Q7: Which of the following statements is false? (a) The x-coordinates of all points to the right of the y-axis are positive. (b) The y-coordinates of all points above the x-axis are positive. (c) The y-coordinates of all points below the x-axis are positive. (d) The x-coordinates of all points to the left of the y-axis are negative.
Solution:
Ans: (c) y-coordinates of all the points below the x-axis are negative.
Q8: The product 864 × n is a perfect cube. What is the smallest possible value of 'n'? (a) 2 (b) 1 (c) 4 (d) 3
Solution:
Ans: (a) 864 × n is a perfect cube. 864 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 ⇒ n=2
Q9: Abscissa of a point is positive in (a) I and II quadrants (b) I and IV quadrants (c) II quadrant only (d) III quadrant only
Solution:
Ans: (b) Abscissa of a point is positive in I and IV quadrants.
Q10: The smallest number by which 16384 must be divided so that the quotient is a perfect cube, is: (a) 2 (b) 4 (c) 12 (d) None of these.
Solution:
Ans: (b)
Q11: Study the graph and answer the questions that follow.
Which was the hottest day? (a) Sunday (b) Wednesday (c) Monday (d) Friday
Solution:
Ans: (d) On Friday, the temperature was high, so it was the hottest day.
Q12: The smallest number which when multiplied with 7200 will make the product a perfect cube, is: (a) 10 (b) 20 (c) 30 (d) None of these
Solution:
Ans: (c) Expressing 7200 as its prime factors 7200 = 2×2×2×2×2×3×3×5×5 7200 = (2×2×2)×(2×2)×(3×3)×(5×5) We find that prime factors 2, 3 & 5 appear in groups of two, so to make the given number a perfect cube, we must multiply it with 2×3×5=30 ∴ 7200 × 30 =(2×2×2)×(3×3×3)×(2×2×2)×(5×5×5) is a perfect cube.
Q13: The line graph shows the sale of dolls by Suhas from Monday to Saturday on a particular week. Given that the cost of one doll is ₹35, how much did Suhas receive from the sale of dolls on Saturday? (a) ₹200 (b) ₹700 (c) ₹1050 (d) ₹1400
Solution:
Ans: (d) Number of dolls sold on Saturday = 40 Cost of 1 doll = ₹35 Total cost of 35 dolls = 40 × 35 = ₹1400
Q14: The digit in the units place for the cube of a four-digit number of the form xyz8 is __________. (a) 2 (b) 4 (c) 8 (d) 6
Solution:
Ans: (b) Since the unit's place digit of xyz8 is 8 ∴ unit's place digit of cube of xyz8 is 2.
Mathematical Reasoning
Q15: The line graph shows the monthly expenditure of the Vasu family. The difference between their highest and lowest monthly expenditure is: (a) ₹100 (b) ₹200 (c) ₹300 (d) ₹400
Solution:
Ans: (d) Month with highest expenditure = February Month with lowest expenditure = April Difference in expenditure: 600 - 200 = 400
Q16: The value of (-9) × (7) + (-15) ÷ (-3) × 6 + 9 × 3 is ______. (a) -12 (b) 10 (c) -6 (d) 8
Solution:
Ans: (c)
First, calculate (-9) × (7) which equals -63.
Next, compute (-15) ÷ (-3) which gives 5, and then multiply by 6 to get 30.
Now, calculate 9 × 3 which equals 27.
Finally, combine all parts: -63 + 30 + 27 = -6.
Q17: Point (-10, 0) lies (a) on the negative direction of the x-axis (b) on the negative direction of the y-axis (c) in the third quadrant (d) in the fourth quadrant
Solution:
Ans: (a) Point (-10, 0) lies on the negative direction of x-axis.
Q18: Which of the following figures is/are formed by joining the points (1,1), (3,0), (4,2), and (2,3)?
(a) Figure III (b) Figure I (c) Figure I and II (d) Figure II
Solution:
Ans: (b) Figure I is formed by the given coordinates.
Q19: What needs to be taken away from (x^3 + 4x² + 3x - 2) to result in (x^3 - 2x² + 4)? (a) (2x3 + 6x² + 3x + 2) (b) (-2x3 + 3x - 2) (c) (4x² + 3x + 4) (d) (6x² + 3x - 6)
Solution:
Ans: (d)
To find what to subtract, we set up the equation: (x3 + 4x² + 3x - 2) - ? = (x^3 - 2x² + 4).
When we simplify this, we combine like terms: 4x² + 2x² + 3x - 2 - 4 = 6x² + 3x - 6.
Thus, the expression we need to subtract is (6x² + 3x - 6), which matches option (d).
Q20: Which of the following steps is incorrect while constructing a triangle PQR in which ∠PQR = 120° and PQ = QR = 6.5 cm? (a) Step I (b) Step II (c) Step III (d) Step IV
Solution:
Ans: (c)
The construction of triangle PQR involves specific steps to ensure the correct angles and lengths are achieved.
In this case, we need to create an angle of 120° at point Q and ensure both sides PQ and QR are 6.5 cm long.
Step III is identified as incorrect, possibly due to a mistake in measuring or drawing the angle or sides.
It's crucial to follow the construction steps accurately to form the triangle as specified.
Q21: In a single roll of a die, what is the chance of rolling a number that is more than 2? (a) 1/6 (b) 2/3 (c) 5/6 (d) 4/5
Solution:
Ans: (b)
The total possible outcomes when rolling a die are 6: {1, 2, 3, 4, 5, 6}.
The numbers greater than 2 are {3, 4, 5, 6}, which gives us 4 favorable outcomes.
To find the probability, we use the formula: Probability = (Number of favorable outcomes) / (Total outcomes).
So, the probability = 4/6 = 2/3.
Q22: A point both of whose coordinates are negative will lie in __________ quadrant. (a) I (b) III (c) IV (d) II
Solution:
Ans: (b) Abscissa and ordinate of a point are negative in III quadrants.
Q23: If we add 15 to one-fourth of a number, then we will get the same number. Find the number. (a) 30 (b) 40 (c) 20 (d) 25
Solution:
Ans: (c)
Let the number be represented as x.
According to the statement, we can write the equation: (1/4)x + 15 = x.
To solve for x, first subtract (1/4)x from both sides: 15 = x - (1/4)x.
This simplifies to 15 = (3/4)x, and then multiplying both sides by (4/3) gives x = 20.
Thus, the number is 20.
Q24: Which of the following statements is NOT accurate? (a) (6)⁶ ÷ (3)³ can be expressed as (2)⁶ × (3)³ (b) The standard form of 10.342 × (10) ⁹ is 1.0342 × (10) ¹⁰ (c) The result of 20 x 30 + 40 is 1 (d) The value of P³ × P⁵ ÷ P⁴ is P⁴
Solution:
Ans: (c)
The statement "20 x 30 + 40 is 1" is incorrect because when you calculate it, 20 x 30 equals 600, and adding 40 gives you 640, not 1.
Option (a) is correct as it follows the rules of exponents.
Option (b) is also correct as it represents the proper conversion to standard form.
Option (d) is valid since P³ × P⁵ ÷ P⁴ simplifies to P(3+5-4) = P⁴.
Q25: Find the cube root of 42875. (a) 35 (b) 25 (c) 15 (d) 20
Solution:
Ans: (a) The factors of 42875 = 5 × 5 × 5 × 7 × 7 × 7 Make the factors of the number by taking three identical numbers. Now multiply each number of the factors.
Q26: The scores obtained by two different teams A and B are in the ratio 5:6. If the sum of scores obtained by team A and B together is 154, then find the scores obtained by team A and B respectively. (a) 75, 90 (b) 84, 70 (c) 70, 84 (d) 90, 75
Solution:
Ans: (c)
Let the scores of team A and B be 5x and 6x respectively, based on the ratio 5:6.
The total score is given as 154, so we can write the equation: 5x + 6x = 154.
This simplifies to 11x = 154, leading to x = 14.
Now, substituting x back, team A's score is 5x = 5 x 14 = 70, and team B's score is 6x = 6 x 14 = 84.
Q27: The mean weight of six students is 40.8 kg. If the weights of the first five students are 42.5 kg, 35.7 kg, 38.9 kg, 40.2 kg, and 44.5 kg, what is the weight of the sixth student? (a) 43 kg (b) 44.5 kg (c) 46.6 kg (d) 42 kg
Solution:
Ans: (a)
To find the weight of the sixth student, we first calculate the total weight of all six students. Since the mean weight is 40.8 kg, the total weight is 40.8 kg x 6 = 244.8 kg.
Next, we add the weights of the first five students: 42.5 kg + 35.7 kg + 38.9 kg + 40.2 kg + 44.5 kg = 201.8 kg.
Now, we can find the weight of the sixth student by subtracting the total weight of the first five students from the total weight of all six: 244.8 kg - 201.8 kg = 43 kg.
Thus, the weight of the sixth student is 43 kg.
Q28. Point (0, -7) lies (a) on the x-axis (b) in the second quadrant (c) on the y-axis (d) in the fourth quadrant
Solution:
Ans: (c) Point (0, -7) lies on the y-axis.
Q29: If (a : b = 2 : 3), then ((3a + 2b) : (5a + 3b)) is equal to ______. (a) 13/20 (b) 24/19 (c) 12/19 (d) 13/21
Solution:
Ans: (c)
Given the ratio (a : b = 2 : 3), we can express a and b in terms of a common variable. Let a = 2x and b = 3x.
Now, substituting these values into the expression (3a + 2b) and (5a + 3b) gives us (3(2x) + 2(3x)) and (5(2x) + 3(3x)).
This simplifies to (6x + 6x) : (10x + 9x), which is (12x : 19x).
Thus, the ratio simplifies to 12/19, confirming that the answer is (c).
Q30: What digit should replace * (where * is a single digit number) to ensure that 478265* is divisible by 6? (a) 6 (b) 8 (c) 2 (d) 4
Solution:
Ans: (d)
For a number to be divisible by 6, it must be divisible by both 2 and 3.
To check for divisibility by 2, the last digit (which is *) must be even. The options that are even are 2, 4, 6, and 8.
To check for divisibility by 3, the sum of the digits must be divisible by 3. The sum of the digits in 478265* is 32 + *.
Testing the options: If * = 4, the sum is 36, which is divisible by 3. Thus, the correct answer is 4.
Q31. The square of a natural number when subtracted from its cube results in 48. The number is (a) 6 (b) 5 (c) 4 (d) 8
Solution:
Ans: (c) Let the natural number be 'x'. ∴ x3 -x2 =48 ⇒ x2 (x-1)=48 ⇒ 42 ( 4 - 1 ) = 48 ∴ 𝑥 = 4 x=4
Q32. In a five-digit number 1b 6a3, 'a' is the greatest single-digit perfect cube and twice of it exceeds 'b' by 7. Then find the sum of the number and its cube root. (a) 21970 (b) 11907 (c) 17190 (d) 19710
Solution:
Ans: (d) Since 'a' is the greatest single digit perfect cube, therefore a=8 according to the question, 2a-b=7 ⇒b=9
Q33: Which of the following statements is accurate? (a) The sum of a negative integer and a positive integer is always a negative integer. (b) The product of two negative integers is always a positive integer. (c) -27 is greater than -25. (d) There are four integers between -82 and -86.
Solution:
Ans: (b)
The product of two negative integers results in a positive integer. This is because when you multiply two negative numbers, the negatives cancel each other out, leading to a positive result.
For example, if you take -3 and -4, their product is 12, which is positive.
In contrast, the other options are incorrect: the sum of a negative and a positive integer can be negative, -27 is not greater than -25, and there are actually three integers between -82 and -86.
Q34: 11 oranges are purchased for ₹10 and 10 oranges are sold for ₹11. What is the gain or loss percentage? (a) 21% loss (b) 11% gain (c) 21% gain (d) 11% loss
Solution:
Ans: (c)
The cost price of 11 oranges is ₹10, so the cost price per orange is ₹10/11 = ₹0.91 (approximately).
The selling price of 10 oranges is ₹11, so the selling price per orange is ₹11/10 = ₹1.10.
The gain per orange is ₹1.10 - ₹0.91 = ₹0.19.
The gain percentage is calculated as (Gain/Cost Price) x 100 = (0.19/0.91) x 100 ≈ 20.88%, which rounds to 21% gain.
Ans: (d) Abscissa is zero, so it will lie on y-axis, but value of ordinate is negative. So it will lie on negative y-axis.
Everyday Mathematics
Q36. To draw the graph of a line, the least number of points required is _______. (a) One (b) Two (c) Three (d) Four
Solution:
Ans: (b) Least number of points required to draw graph of a line is two.
Q37: Karan is 4 times as old as Varun. Five years ago, Karan was 7 times as old as Varun. Find the present age of Karan. (a) 10 years (b) 42 years (c) 40 years (d) 28 years
Solution:
Ans: (c)
Let Varun's current age be represented as V. Therefore, Karan's current age is 4V.
Five years ago, Varun's age was V - 5 and Karan's age was 4V - 5.
According to the problem, five years ago, Karan was 7 times Varun's age: 4V - 5 = 7(V - 5).
Simplifying this gives: 4V - 5 = 7V - 35, leading to 3V = 30, so V = 10.
Thus, Karan's current age is 4V = 4 x 10 = 40 years.
Q38: Amit deposits an amount of ₹24,200 in a bank. After 3 years, he will get ₹2,904 as interest. Find the rate of interest. (a) 4% (b) 6% (c) 5% (d) 2%
Solution:
Ans: (a)
To find the rate of interest, we can use the formula: Interest = Principal x Rate x Time.
Here, the Principal is ₹24,200, the Interest earned is ₹2,904, and the Time is 3 years.
Rearranging the formula to find the Rate gives us: Rate = (Interest / (Principal x Time)) x 100.
Substituting the values: Rate = (2904 / (24200 x 3)) x 100 = 4%.
Q39: The price of a bat is ₹14 greater than three times the price of a ball. If a bat costs ₹176, what is the total expense for 3 bats and 4 balls? (a) ₹575 (b) ₹460 (c) ₹650 (d) ₹744
Solution:
Ans: (d)
Let the price of the ball be x. Then, the price of the bat can be expressed as 3x + 14.
According to the problem, the cost of the bat is ₹176, so we set up the equation: 3x + 14 = 176.
Solving for x, we find that 3x = 162, which gives x = 54. Thus, the price of the ball is ₹54.
The total cost for 3 bats and 4 balls is calculated as follows: 3 x 176 + 4 x 54 = 528 + 216 = 744.
Q40: A historical trip is organized by a school. There are 4620 students in the school, out of which only 24% of girls and 20% of boys go on the trip. If the number of girls in the school is 2075, then find the number of boys and girls, respectively, who go on the trip. (a) 402, 436 (b) 509, 498 (c) 506, 408 (d) 605, 421
Solution:
Ans: (b)
First, calculate the number of boys in the school: 4620 total students - 2075 girls = 2545 boys.
Next, find the number of girls going on the trip: 24% of 2075 = 0.24 x 2075 = 498.
Then, calculate the number of boys going on the trip: 20% of 2545 = 0.20 x 2545 = 509.
Thus, the number of boys and girls going on the trip is 509 and 498, respectively.
Q41: The height (in feet) of 10 students of Class 7 are: 5.4, 4.8, 4.6, 3.8, 5.7, 3.6, 4.2, 4.7, 3.8, 3.2. Find the average height of the students. (a) 3.48 (b) 7.02 (c) 5.42 (d) 4.38
Solution:
Ans: (d)
To find the average height, you need to add all the heights together and then divide by the number of students.
The total height is 5.4 + 4.8 + 4.6 + 3.8 + 5.7 + 3.6 + 4.2 + 4.7 + 3.8 + 3.2 = 43.8 feet.
Now, divide this total by the number of students, which is 10: 43.8 / 10 = 4.38 feet.
Thus, the average height of the students is 4.38 feet.
Q42: There are (6xy - 4x² - y² + 5) marbles in a box. If Ranjana takes (x² - 3xy + 7y² - 2) marbles, then how many marbles are left? (a) (-5x² - 8y² + 9xy + 7) (b) (6x² - 8y² + 9xy - 17) (c) (-15x² - 8y² + 19xy - 8) (d) (5x² + 8y² - 9xy - 7)
Solution:
Ans: (a)
To find the number of marbles left, we need to subtract the number of marbles Ranjana takes from the total number of marbles.
The total marbles are 6xy - 4x² - y² + 5 and the marbles taken are x² - 3xy + 7y² - 2.
Thus, the number of marbles left is (-5x² - 8y² + 9xy + 7).
Q43: A boy is standing 3 meters away from a wall. There is a window at a height of 4 meters on the wall. The boy uses a ladder to reach the window. Find the length of the ladder. (a) 4 m (b) 7 m (c) 6 m (d) 5 m
Solution:
Ans: (d)
To find the length of the ladder, we can use the Pythagorean theorem. The distance from the boy to the wall (3 meters) and the height of the window (4 meters) form a right triangle with the ladder as the hypotenuse.
According to the theorem, the length of the ladder (hypotenuse) can be calculated as: length = √(height² + distance²).
Thus, the length of the ladder needed to reach the window is 5 meters.
Q44: Ram's father's age is 3 years greater than twice Ram's age. If Ram's father is 45 years old, what equation can be formed to determine Ram's age? (a) (2x + 3 = 45) (b) (3x + 2 = 45) (c) (6x + 3 = 45) (d) (5x + 1 = 45)
Solution:
Ans: (a)
Let Ram's age be represented by x.
According to the problem, Ram's father's age is 3 years more than twice Ram's age, which can be expressed as 2x + 3.
Since Ram's father is 45 years old, we can set up the equation: 2x + 3 = 45.
This equation allows us to solve for Ram's age.
Q45: There are 255 boxes of various sizes - large, medium, and small. The ratio of these boxes is 2:8:5. Determine the quantity of medium-sized boxes. (a) 85 (b) 136 (c) 192 (d) 115
Solution:
Ans: (b)
To find the number of medium-sized boxes, first, we need to understand the total parts in the ratio 2:8:5. This adds up to 2 + 8 + 5 = 15 parts.
Next, we calculate the value of one part by dividing the total number of boxes (255) by the total parts (15): 255 ÷ 15 = 17.
Now, to find the number of medium-sized boxes, we multiply the number of parts for medium boxes (8) by the value of one part: 8 x 17 = 136.
Thus, the number of medium-sized boxes is 136.
Achievers Section
Q46: Find the cube root of -13824. (a) 24 (b) -24 (c) 26 (d) -26
Solution:
Ans: (b)
=-(2×2×2×3) =-24
Q47: If the sum of cubes of digits of a number is equal to the number itself, the number is called 'Armstrong Number', then the Armstrong Number is (a) 367 (b) 470 (c) 153 (d) None of these
Solution:
Ans: (c) According to the definition of Armstrong number, 13+53+33=1+125+27 =126+27=153
Q48: Which of the following options is correct according to the given observations? 115, 120, 146, 148, 150, 145, 132, 136, 132 (a) Median of the given observations is less than the mean. (b) Mode of the given observations is 140. (c) Median of the given observations is more than the mode. (d) Mean of the observations is 138.
Solution:
Ans: (C)
The median is the middle value when the numbers are arranged in order. In this case, the median is greater than the mode, which is the most frequently occurring number.
The mode here is 132, as it appears most often in the list.
The mean is the average, but the question focuses on the relationship between median and mode.
Thus, the correct statement is that the median of the observations is indeed more than the mode.
Q49: State 'T' for true and 'F' for false and select the correct option. (i) The product of a whole number with a rational number is always a rational number. (ii) All rational numbers are fractions. (iii) If a rational number is multiplied by an integer, then it is always an integer. (a) T T F (b) T F F (c) F T T (d) F F T
Solution:
Ans: (b)
Statement (i) is true because when you multiply a whole number (like 2) with a rational number (like 1/2), the result (1) is still a rational number.
Statement (ii) is false because not all rational numbers are fractions; for example, the number 2 is rational but not a fraction.
Statement (iii) is false because multiplying a rational number (like 1/2) by an integer (like 2) gives a rational number (1), not an integer.
Q50: Read the given statements carefully and select the correct option. Statement I: If Sujata lost 5% on a laptop which was sold for ₹24,700, then the cost price of the laptop was ₹28,500. Statement II: 3% of 1 hour = 108 seconds. (a) Both Statement-I and Statement-II are true. (b) Both Statement-I and Statement-II are false. (c) Statement-I is true but Statement-II is false. (d) Statement-I is false but Statement-II is true.
Solution:
Ans: (d)
Statement I: To find the cost price, we can use the formula: Selling Price = Cost Price - Loss. Here, if the selling price is ₹24,700 and the loss is 5%, the cost price is actually ₹26,000, not ₹28,500. So, this statement is false.
Statement II: 3% of 1 hour (which is 3600 seconds) is calculated as 0.03 x 3600 = 108 seconds. This statement is true.
Since Statement I is false and Statement II is true, the correct option is (d).
1. What topics are covered in the Mathematics Olympiad Model Test Paper for Class 7?
Ans.The Mathematics Olympiad Model Test Paper for Class 7 typically covers topics such as Logical Reasoning, Mathematical Reasoning, and Everyday Mathematics. These subjects aim to enhance students' problem-solving skills and mathematical understanding.
2. How can I prepare effectively for the Mathematics Olympiad exam?
Ans.To prepare effectively for the Mathematics Olympiad exam, students should practice previous years' papers, focus on understanding concepts rather than rote memorization, and engage in group studies for collaborative learning. Additionally, using resources like mock tests and online quizzes can be beneficial.
3. What is the importance of Logical Reasoning in the Mathematics Olympiad?
Ans.Logical Reasoning is crucial in the Mathematics Olympiad as it helps students develop critical thinking and problem-solving skills. It encourages them to analyze situations, identify patterns, and make reasoned conclusions, which are essential skills in mathematics and everyday life.
4. Are there any specific strategies for solving Mathematical Reasoning problems in the Olympiad?
Ans.Yes, specific strategies for solving Mathematical Reasoning problems include breaking down complex problems into simpler parts, drawing diagrams to visualize the problem, and practicing various types of problems to become familiar with different techniques and approaches.
5. How can students benefit from participating in the Mathematics Olympiad?
Ans.Students can benefit from participating in the Mathematics Olympiad by enhancing their mathematical skills, boosting their confidence, and gaining experience in competitive exams. It also provides an opportunity to identify strengths and weaknesses in their mathematical understanding, guiding future learning efforts.
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Perpendicular distance of point (3, 4) from y-axis is 3.
Make the factors of the number by taking three identical numbers. Now multiply each number of the factors.
=-(2×2×2×3) =-24
