TANCET 2014 DS 66: Numbers
Directions
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. Comparing numbers 2 concepts
In 1988, was the number of people in city X greater than three times the number of people in city Y?
 Statement 1: In 1998, there were approximately 1.1 million more people in city X than in city Y.
 Statement 2: In 1988, the 300,000 Hindus in city X made up for 20 percent of its population and the 141,000 Buddhists in city Y made up 30 percent of its population.
Correct Answer Choice (2). Statement (2) ALONE is 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 "Was the number of people in city X greater than three times the number of people in city Y in the year 1988?"
For questions that start with "is", "was", "does", the answer to the question is an YES or a NO.
When is the data sufficient?
If we are able to come up with a definite yes or no the data is sufficient.
If there is any ambiguity in our answer  if we say that the answer could be an yes in some cases and it could be a no in others, the data is NOT sufficient.
When is the answer an YES and when is it a NO?
If the number of people in city X is greater than three times the number of people in city Y, the answer is YES.
If the number of people in city X is LESS THAN three times or EQUAL to three times the nuumber of people in city Y in 1988, the answer is NO.
The important thing to note is that the answer is a NO when the number of people in city X is equal to 3 times the number of people in city Y.

Statement (1) ALONE
In 1998, there were approximately 1.1 million more people in city X than in city Y.
Scenario 1: If city Y had a population of 0.1 million, then city X will have a population of 1.2 million. The population of city X will be greater than 3 times the population of city Y. The answer to the question is YES.
Scenario 2: Alternatively, if city Y had a population of 4 million, city X will have a population of 5.1 million. The population of city X is not greater than 3 times the population of city Y. The answer to the question is NO.
The answer is YES for some values of the population of Y and the answer is NO for other values of the population of Y.
We could NOT find a UNIQUE answer using statement (1) ALONE.
Statement (1) ALONE is NOT sufficient.
If statement (1) ALONE is NOT sufficient, we can eliminate choices 1 and 4.
Choices narrow down to 2, 3, or 5.

Statement (2) ALONE
In 1988, the 300,000 Hindus in city X made up for 20 percent of its population and the 141,000 Buddhists in city Y made up 30 percent of its population.
Remember: When you are evaluating statement (2) ALONE, please do not recall information that you read in statement (1). Anything said about the population of city X or city Y in statement (1) should not be used while evaluating statement (2).
300,000 Hindus in city X made up for 20% of its population. So, we can deduce that the population of city X in 1988 was 1,500,000.
141,000 Buddhists in city Y made up for 30% of its population. So, we can deduce that the population of city Y in 1988 was 470,000
Using statement (2) we were able to determine the population of the two cities. With this information, we can conclusively answer the question YES.
We could answer the question with a DEFINITE Yes using the information given in statement (2).
Statement (2) ALONE is sufficient. Hence, choice (2) is the answer.
Video Explanation
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 Number Theory
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