TANCET 2014 DS 79: Rates
Directions for TANCET Data Sufficiency Questions
The question is followed by two statements labeled (1) and (2) in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the problem plus your knowledge of mathematics and everyday facts, choose the answer as:
 Choice 1 if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
 Choice 2 if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
 Choice 3 if both the statements (1) and (2) TOGETHER are sufficient, but NEITHER statement alone is sufficient.
 Choice 4 if each statement ALONE is sufficient.
 Choice 5 if statements (1) and (2) TOGETHER are not sufficient, and additional data is needed.
Question
2. Solution to system of equations 2 concepts
Automobile A is travelling at \\frac{2}{3}\\)^{rd} of the speed that Automobile B is travelling at. How fast is Automobile A travelling?
 Statement 1: If both automobiles increased their speed by 10 km per hour, Automobile A would be travelling at \\frac{3}{4}\\)^{th} the speed of Automobile B.
 Statement 2: If both automobiles decreased their speed by 10 km per hour, Automobile A would be travelling at \\frac{1}{2}\\) the speed of Automobile B.
Correct Answer Choice (4). Each statement is INDEPENDENTLY SUFFICIENT.
Explanatory Answer  step by step

What should we know from the Question Stem?
Before evaluating the two statements, answer the following questions to get clarity on when the data is sufficient.
What kind of an answer will the question fetch?
The question is "How fast is Automobile A travelling?"
The answer to the question should be the speed of Automobile A, a number followed by a unit of speed.
When is the data sufficient?
If we are able to come up with a UNIQUE value for the speed of Automobile A, the data is sufficient.
If we are not able to come up with a unique value – either we cannot find an answer with the data in the statement(s) or if we find more than one value, the data is NOT sufficient.
What data is available from the question stem?
Automobile A is travelling at \\frac{2}{3}\\)^{rd} the speed of Automobile B.

Statement (1) ALONE
If both automobiles increased their speed by 10 km per hour, Automobile A would be travelling at \\frac{3}{4}\\)^{th} the speed of Automobile B.
Let the speed of Automobile B be ‘b’ kmph.
So, speed of Automobile A = \\frac{2}{3}\\)b.
If each increased its speed by 10 kmph, the speeds of A and B will be (\\frac{2}{3}\\)b + 10) and (b + 10) respectively.
From statement 1, (\\frac{2}{3}\\)b + 10) = \\frac{3}{4}\\)(b + 10)
\\frac{3}{4}\\)b – \\frac{2}{3}\\)b = 10 – 7.5
Solving the equation, we get b = 30 kmph.
So, speed of Automobile A = 20 kmph
We are able to find a UNIQUE value for the speed of Automobile A using data in statement 1.
Statement (1) ALONE is sufficient.
The moment we realize that statement (1) ALONE is sufficient, we can narrow down our choices to 1 or 4
To determine whether the answer is choice 1 or choice 4, we need to evaluate statement (2). Remember that you have to evaluate statement (2) even if statement (1) is sufficient.

Statement (2) ALONE
If both automobiles decreased their speed by 10 km per hour, Automobile A would be travelling at \\frac{1}{2}\\) the speed of Automobile B.
Remember: When you are evaluating statement (2) ALONE, please do not recall information that you read in statement (1). Anything said about the speeds of either automobile A or B in statement (1) should not be used while evaluating statement (2).
We know a = \\frac{2}{3}\\)b from the question stem.
If each decreased its speed by 10 kmph, the speeds of A and B will be (\\frac{2}{3}\\)b – 10) and (b – 10) respectively.
From statement 2, (\\frac{2}{3}\\)b – 10) = \\frac{1}{2}\\) (b – 10)
\\frac{2}{3}\\)b – \\frac{1}{2}\\)b = 10 – 5
Solving the equation, we get b = 30 kmph.
So, speed of Automobile A = 20 kmph.
Using statement (2) ALONE we could get a UNIQUE answer.
Statement (2) ALONE is ALSO sufficient.
Each statement is INDEPENDENTLY sufficient, we can eliminate choice 1.
Hence, choice (4) is the answer.
Video Explanation
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XAT TANCET Practice Questions  Listed Topic wise
 Number Theory
 Permutation Combination
 Probability
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 Geometry
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 Mensuration
 Trigonometry
 Data Sufficiency
 Percentages
 Profit Loss
 Ratio Proportion
 Mixtures & Alligation
 Speed Distance & Time
 Pipes, Cisterns & Work, Time
 Simple & Compound Interest
 Races
 Averages & Statistics
 Progressions : AP, GP & HP
 Set Theory
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