Question:medium

A set contains six odd numbers. What is its median?
Statement 1: Sum of 6 odd numbers is 300 and they are consecutive
Statement 2: The mean of six numbers is 20
Directions: This question has a problem and two statements numbered (1) and (2) giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem. Indicate your answer :

Updated On: Jan 13, 2026
  • statement (1) alone is sufficient to answer the question
  • statement (2) alone is sufficient to answer the question
  • both the statements together are needed to answer the question
  • either statement (1) alone or statement (2) alone is sufficient to answer the question
  • neither statement (1) nor statement (2) suffices to answer the question
Show Solution

The Correct Option is A

Solution and Explanation

The correct answer is option (A):
statement (1) alone is sufficient to answer the question

Here's the breakdown of why the correct answer is "statement (1) alone is sufficient to answer the question":

The problem asks for the median of a set of six odd numbers. The median is the middle value when the numbers are arranged in order. Because there's an even number of values (six), the median will be the average of the 3rd and 4th values when the numbers are ordered.

Let's analyze the statements:

Statement 1: The sum of the six odd numbers is 300, and they are consecutive.

If the six odd numbers are consecutive and their sum is 300, we can determine the numbers. Let the first odd number be 'x'. The next five consecutive odd numbers are x+2, x+4, x+6, x+8, and x+10. Their sum can be expressed as: x + (x+2) + (x+4) + (x+6) + (x+8) + (x+10) = 300. Simplifying, we get 6x + 30 = 300. Solving for x: 6x = 270, and x = 45. The numbers are 45, 47, 49, 51, 53, and 55. The median is (49+51)/2 = 50. Therefore, statement 1 alone is sufficient.

Statement 2: The mean of the six numbers is 20.

Knowing the mean (average) of the numbers doesn't tell us the median. The mean is calculated by summing all the numbers and dividing by the count. Many different sets of six numbers can have a mean of 20. The set could even contain non-odd numbers. Therefore, statement 2 is not sufficient.

Conclusion: Only statement 1 provides enough information to determine the median of the set of six odd numbers.
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Top Questions on Statements and Inferences

Questions Asked in IBSAT exam

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The result is not just a lofty declaration of principles but a blueprint for a practical programme of action. The policy delineates a series of concrete measures to accord women a decision-making role in the political domain and greater control over their economic status. Of especially far-reaching impact are the devolution of control of economic infrastructure to women, notably at the gram panchayat level, and the amendments proposed in the Hindu Succession Act of 1956 to give women coparcenary rights.
 An enlightened aspect of the policy is its recognition that actual change in the status of women cannot be brought about by the mere enactment of socially progressive legislation. Accordingly, it focuses on reorienting development programmes and sensitizing administrations to address specific situations as, for instance, the growing number of households headed by women, which is a consequence of rural-urban migration. The proposal to create an equal-opportunity police force and give women greater control of police stations is an acknowledgement of the biases and callousness displayed by the generally all-male lawenforcement authorities in cases of dowry and domestic violence. While the mere enunciation of such a policy has the salutary effect of sensitizing the administration as a whole, it does not make the task of its implementation any easier. 
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  • IBSAT
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This anxiety does not dissipate, and in fact, it can increase to the level where it begins to change your behavior. That’s when it’s characterized as an anxiety disorder. Anxiety can keep you safe, helping you recognize danger, and cope with it, says Mooney. But if you begin to see danger lurking around every corner, or worry over and over again about the same events, then you might be dealing with something more substantial, like an anxiety disorder. 
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I am the family face; flesh perishes. I live on, projecting trait and trace through time to times anon, and leaping from place to place over oblivion.
So wrote Thomas Hardy in his poem, Heredity, describing direct descent of life from one generation to the next. Indeed, the poem reflects the DNA in our genome. Dr.Drew Endy of MIT quoted this when he described how people at the J. Craig Venter Institute (JCVI) bypass nature’s constraint of direct descent. Scientists there have used chemistry and biochemistry to produce the first synthetic genome in the laboratory. They chemically synthesized many fragments of the DNA, encoding the 582,970-units-long genome of a bacterium called Mycoplasma genitalium. Next, they assembled these fragments in perfect order to generate the genome of the bacterium.
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Now, they used the clever trick of exploiting the process called homologous recombination. This is a basic essential process in every cell, which physically rearranges the two strands of DN The JCVI researchers inserted the synthesized DNA fragments into yeast and utilized its homologous recombination ability to generate the whole 580,000 long genome of M.genitalium in one step. 
This is clearly a landmark work that leads into the brave new world of synthesizing life itself in the laboratory. It was hardly 200 years ago when Friedrich Wohler synthesized urea, an organic molecule, in the chemical laboratory, thus throwing out the notion of ‘vital forces’ involved in the components of living organisms. What is the next step, making life itself in the lab, bypassing nature? With single cell organisms like M.genitalium, it might not be far away. It is now possible in the lab to do so, by inserting the genome into a ‘host’ cell and asking the latter to make the bacterium of your choice. If only we find a way to insert the bacterial genome into this proto-cell, and somehow trigger it to make the bacterium itself! We would have chemically created life in the la This is not a pipedream; JCVI scientists are already on the job, and my bet is they will do it within a few years. 
This surely raises ethical questions, a matter that JCVI is keenly aware of and is already engaged in with ethicists. Even their present work on M.genitalium was done with prior approval of ethical experts. But then, today it is M.genitalium, tomorrow it could be a more advanced, multi-cellular organism, and that could flummox even the ethicist. Assisted reproduction, which is the other side of the coin and truly a recently initiated technology, has become ethically and morally acceptable. Cloning of Dolly, the sheep, has not raised any outrage, but cloning a human certainly does.
  • IBSAT
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