Q. The thing about electric cars is that they are wonderful. The internal combustion engine is a machine that creates a precise mixture of air and petrol, carefully ignites it, then uses the ongoing controlled explosion to generate mechanical revolutions, which it transmits from the engine through gears to a vehicle’s wheels. By contrast, an electric car contains an electric motor just whizzes along and can transmit revolutions directly anywhere it wants: no mix, no explosions, no gears. The result is smaller, lighter, safer, more efficient: in short, better. Which of the following undermines the above mentioned theory that an electric car is better than a car with an internal combustion engine? A. The battery of an electric car runs for only 20 kms on a single recharge. B. The car with an internal combustion engine is noisier as compared to an electric car. C. The car with an internal combustion engine needs to be filled with fuel every time. D. The car with an internal combustion engine is more stylish as compared to an electric car.
The conclusion of the argument is that electric cars are better than cars with an internal combustion engine. If we can point out a defect of electric cars, we may be able to negate this conclusion. Let's look at the options: A. If the battery lasts only for 20 kms, it's a severe disadvantage of electric cars and hence we cannot conclude that electric cars are better. B. This is in favour of electric cars and hence can be eliminated C. This is in favour of electric cars and hence can be eliminated D. 'Style' is not a criteria mentioned by the author in concluding that electric cars are better. Hence, this statement is irrelevant. Hence, the answer is A.
Q. What is the sum of all solutions to the equation |x² – 4x + 4| = x² + 10x – 24? A) -5 B) -3 C) -2 D) 2 E) 5
If |x| = a, then x= a or x=-a. We will apply this in the question. Hence, we will have 2 cases: i. x² – 4x + 4 = x² + 10x – 24 Cancelling out x² and bringing the like terms together: 14x = 28 x = 2 ii. x² – 4x + 4 = -(x² + 10x – 24) Bringing all the terms to the left hand side: 2x² + 6x - 20 = 0 2(x² + 3x - 10) = 0 2(x² + 5x - 2x + 10) = 0 2(x + 5)(x - 2) = 0 Hence, x= -5 and x=2 However, the solution doesn't end here. We need to insert these values back in the original equation and check if the equation is satisfied x = 2 |2² – 4(2) + 4| = 2² + 10(2) – 24 Hence, |0| = 0 The equation is satisfied in this case. Hence, x=2 is a solution. x = -5 |(-5)² – 4(-5) + 4| = (-5)² + 10(-5) – 2 |49| = -49 In this case, the left hand side is an absolute value and will always be positive. Hence, the equation is not satisfied in this case. Hence, x = -5 is NOT a solution Hence, the sum of all solutions will be 2. Answer: D
Q. If n is an integer greater than 50, then the expression (n^2 - 2n)(n^2 - 1) must be divisible by which of the following?
The equation can be written as n*(n-1)*(n-2)*(n+1). These are 4 consecutive numbers. This means 2 of them are even and 2 are odd. If 2 numbers are even then each of these will be divisible by 2 and hence the number as a whole will be divisible by 4. Any three consecutive integers contains one multiple of 3, so four consecutive integers would contain at least one. We have a multiple of 3, which has 3 as a factor, and at least one even number, which has 2 as a factor. Hence, 6 will be a factor. For the number to be divisible by 18, we need 2 factors of 3. We know for sure that there will be one factor of 3 in four consecutive numbers. However, we cannot be sure that there can be another factor of 3. Hence, we can't say for sure that the number will be divisible by 18. Hence, C is the answer