Question:medium

What is the unit’s digit of the number (8pqr)64 where p, q and r are the hundredth, tenth and units digits of the number?
Statement 1: The product of p and q is 12 
Statement 2: The product of q and r is 24 and r is greater than 4
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: Jun 30, 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 C

Solution and Explanation

The correct answer is option (C): both the statements together are needed to answer the question

Here's the breakdown of why the correct answer is "both the statements together are needed to answer the question":

The problem asks for the unit's digit of (8pqr)64. The unit digit of a power depends only on the unit digit of the base, which here is r.

Statement 1: The product of p and q is 12.

This tells us something about p and q, but nothing directly about r. Statement 1 alone is insufficient.

Statement 2: The product of q and r is 24 and r > 4.

Since r is a single digit greater than 4 and q·r = 24, the only feasible pair is (q,r) = (3,8). Thus r = 8. The units digit pattern for powers of 8 is: 8, 4, 2, 6 (cycle length 4). Because 64 is a multiple of 4, 864 ends in 6. Statement 2 alone is sufficient to determine the unit digit.

Both statements together: Statement 1 (p·q = 12) plus statement 2 (q·r = 24, r > 4) gives q = 3 and r = 8 (and makes p = 4), but the additional information about p is irrelevant to the unit digit question. Statement 2 already suffices.

Conclusion: Statement 2 alone is sufficient; statement 1 is not necessary. Therefore the correct logical choice is that statement 2 alone is sufficient. (If you must select from the original options and they list option (C) as "both together needed", please check the exam key — mathematically the unit digit is determined by statement 2 alone.)

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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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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.
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