There is no additional data available about 'y' in the question stem. The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.ĭo we have any additional information about 'y' from the question stem? Answer to an "is" questions is either YES or NO. What kind of an answer will this GMAT DS question fetch? The basic fare of an adult ticket = 2X = 2*105 = $210ĭetailed Solution for Test: Basic Algebra - Question 5 The question is "What is the basic fare for an adult?" Multiply equation (1) by 2: 4X + 2Y = 432. Step 2 of solving this GMAT Algebra Question: Solve the simultaneous equations and determine basic fare for an adult. So, the ticket for an adult and a child will cost (2X + Y) + (X + Y) = 3X + 2Y = $327. Information 4: The cost of a reserved ticket for an adult and a child (aged between 3 and 10) is $327. Information 3: One reserved ticket for an adult costs $216. Hence, an adult ticket will cost (Basic fare + Reservation charges) = 2X + Y. Let the reservation charge per ticket be $YĪ child's ticket will cost (Basic fare + Reservation charges) = X + Y Information 2: Reservation charge is the same on the child's ticket as on the adult's ticket. Therefore, the basic fare for an adult = 2(basic one-way airfare for a child) = $2X. Information 1: Basic one-way air fare of a child costs half the regular fare for an adult. Step 1 : Assign variables and frame equations So, there will be NO solution to this system of linear equations in two variables.ĭetailed Solution for Test: Basic Algebra - Question 4 When k = 9, the system of equations will represent a pair of parallel lines (their y-intercepts are different). Or 'k' should be equal to 9 for the system of linear equations to NOT have a unique solution. In the question given above, a = 3, b = 4, d = k and e = 12. Slope of the first line is -a/b and that of the second line is -d/eįor a unique solution, the slopes of the lines should be different.Ĭondition for the equations to NOT have a unique solutionĪpply the condition in the given equations to find k I.e., if the two lines are neither parallel nor coincident.Įssentially, the slopes of the two lines should be different.Īx + by + c = 0 and dx + ey + g = 0 will intersect at one point if their slopes are different.Įxpress both the equations in the standardized y = mx + c format, where 'm' is the slope of the line and 'c' is the y-intercept. So, the farm has (130 - 70) = 60 more chickensĭetailed Solution for Test: Basic Algebra - Question 3Ī system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. Note:The question is "How many more chickens were there in the farm?" So, the farm has 130 chickens and 70 pigs. 'x' is the number of chickens in the farm. Step 2 of solving this GMAT Linear Equations Question: Solve the system of linear equations So, the sum of the number of legs of chickens and the number of legs of pigs is 540. The count of the legs in the farm is 540. 'x' chickens will therefore, have 2x legs and 'y' pigs will have 4y legs. So, the sum of the number of chickens and pigs is 200.Įach chicken has 2 legs and each pig has 4 legs The count of the heads in the farm is 200. Therefore, number of heads will be the same as the sum of the chickens and pigs in the farm. Let the number of pigs in the farm be 'y'. Let the number of chickens in the farm be 'x'. Step 1 : Assign Variables and Frame Equations This is a simple quiz with some basic maths questions to get your brain ticking.Detailed Solution for Test: Basic Algebra - Question 1 Lots of maths history to take in there, but never fear, we're not going to test you on that. If the word 'blam' existed back then, you would have heard it a lot when it came to mathematics. The introduction of Arabic numeral and the idea of zero was a total game-changer. In the 10th century, Islamic scientists worked on the ideas behind arithmetic, algebra and geometry. You may have learned about Pythagoras' theorem: "the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides". They truly were the influencers of their era and came up with theories that are still put in practice now. Early civilisations developed maths to help them in many aspects of every day life, like keeping an eye on their stock or working out how much land they needed to work on to ensure crops would sustain their community.īut it was the likes of BC boffins Euclid, Pythagoras, and Archimedes who did the groundwork for the maths we know and use today.
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