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The security personnel of a leading employment organization insisted on developing a new system of allotting the unique ID numbers to its employees to prevent the tampering of ID numbers by any of the unscrupulous members. They insisted that the 10 digit number must include all the numbers from 0-9 exactly once. Further, all the ID numbers should also be exactly divisible by all the numbers from 1-9.
What would be the sum of first four digits of the largest ID number generated?
  • a)
    27
  • b)
    30
  • c)
    28
  • d)
    26
Correct answer is option 'B'. Can you explain this answer?
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The security personnel of a leading employment organization insisted o...
Hence, option 2.
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To find the largest ID number that satisfies the given conditions, we need to first understand the divisibility rules for each number from 1 to 9.

- The number should be divisible by 1: All numbers are divisible by 1.
- The number should be divisible by 2: The last digit of the number should be even.
- The number should be divisible by 3: The sum of all its digits should be divisible by 3.
- The number should be divisible by 4: The last two digits of the number should be divisible by 4.
- The number should be divisible by 5: The last digit of the number should be 0 or 5.
- The number should be divisible by 6: The number should be divisible by 2 and 3.
- The number should be divisible by 7: There is no simple rule for divisibility by 7.
- The number should be divisible by 8: The last three digits of the number should be divisible by 8.
- The number should be divisible by 9: The sum of all its digits should be divisible by 9.

To find the largest ID number, we can start with the largest digit, which is 9, and place it in the first available position.

- The first digit: Since the sum of the four digits should be divisible by 9, we can choose the largest digit that is less than or equal to 9, which is 9 itself.
- The second digit: Since the number should be divisible by 8, the last three digits should be divisible by 8. The largest three-digit number that is divisible by 8 is 992. So, the second digit is 9.
- The third digit: Since the sum of the three digits should be divisible by 3, and we have already used the digit 9, we can choose the next largest digit, which is 8.
- The fourth digit: Since the number should be divisible by 2, the last digit should be even. The largest even digit that is not used yet is 6.

So, the largest ID number that satisfies all the conditions is 99826.

The sum of the first four digits (9 + 9 + 8 + 2) is 28.

Therefore, the correct answer is option (c) 28.
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When people react to their experiences with particular authorities, those authorities and the organizations or institutions that they represent often benefit if the people involved begin with high levels of commitment to the organization or institution represented by the authorities. First, in his studies of people's attitudes toward political and legal institutions, Tyler found that attitudes after an experience with the institution were strongly affected by prior attitudes. Single experiences influence post experience loyalty but certainly do not overwhelm the relationship between pre-experience and post experience loyalty. Thus, the best predictor of loyalty after an experience is usually loyalty before that experience. Second, people with prior loyalty to the organization or institution judge their dealings with the organization's or institution's authorities to be fairer than do those with less prior loyalty, either because they are more fairly treated or because they interpret equivalent treatment as fairer.Although high levels of prior organizational or institutional commitment are generally beneficial to the organization or institution, under certain conditions high levels of prior commitment may actually sow the seeds of reduced commitment. When previously committed individuals feel that they were treated unfavourably or unfairly during some experience with the organization or institution, they may show an especially sharp decline in commitment. Two studies were designed to test this hypothesis, which, if confirmed, would suggest that organizational or institutional commitment has risks, as well as benefits. At least three psychological models offer predictions of how individuals' reactions may vary as a function of (1) their prior level of commitment and (2) the favorability of the encounter with the organization or institution. Favorability of the encounter is determined by the outcome of the encounter and the fairness or appropriateness of the procedures used to allocate outcomes during the encounter. First, the instrumental prediction is that because people are mainly concerned with receiving desired outcomes from their encounters with organizations, changes in their level of commitment will depend primarily on the favorability of the encounter. Second, the assimilation prediction is that individuals' prior attitudes predispose them to react in a way that is consistent with their prior attitudes.The third prediction, derived from the group-value model of justice, pertains to how people with high prior commitment will react when they feel that they have been treated unfavorably or unfairly during some encounter with the organization or institution. Fair treatment by the other party symbolizes to people that they are being dealt with in a dignified and respectful way, thereby bolstering their sense of self-identity and self-worth. However, people will become quite distressed and react quite negatively if they feel that they have been treated unfairly by the other party to the relationship. The group-value model suggests that people value the information they receive that helps them to define themselves and to view themselves favorably. According to the instrumental viewpoint, people are primarily concerned with the more material or tangible resources received from the relationship. Empirical support for the group-value model has implications for a variety of important issues, including the determinants of commitment, satisfaction, organizational citizenship, and rule following. Determinants of procedural fairness include structural or interpersonal factors. For example, structural determinants refer to such things as whether decisions were made by neutral, fact-finding authorities who used legitimate decision-making criteria. The primary purpose of the study was to examine the interactive effect of individuals (1) commitment to an organization or institution prior to some encounter and (2) perceptions of how fairly they were treated during the encounter, on the change in their level of commitment. A basic assumption of the group-value model is that people generally value their relationships with people, groups, organizations, and institutions and therefore value fair treatment from the other party to the relationship. Specifically, highly committed members should have especially negative reactions to feeling that they were treated unfairly, more so than (1) less-committed group members or (2) highly committed members who felt that they were fairly treated.The prediction that people will react especially negatively when they previously felt highly committed but felt that they were treated unfairly also is consistent with the literature on psychological contracts. Rousseau suggested that, over time, the members of work organizations develop feelings of entitlement, i.e., perceived obligations that their employers have toward them. Those who are highly committed to the organization believe that they are fulfilling their contract obligations. However, if the organization acted unfairly, then highly committed individuals are likely to believe that the organization did not live up to its end of the bargain.For summarizing the passage, which of the following is most appropriate

When people react to their experiences with particular authorities, those authorities and the organizations or institutions that they represent often benefit if the people involved begin with high levels of commitment to the organization or institution represented by the authorities. First, in his studies of people's attitudes toward political and legal institutions, Tyler found that attitudes after an experience with the institution were strongly affected by prior attitudes. Single experiences influence post experience loyalty but certainly do not overwhelm the relationship between pre-experience and post experience loyalty. Thus, the best predictor of loyalty after an experience is usually loyalty before that experience.Second, people with prior loyalty to the organization or institution judge their dealings with the organization's or institution's authorities to be fairer than do those with less prior loyalty, either because they are more fairly treated or because they interpret equivalent treatment as fairer.Although high levels of prior organizational or institutional commitment are generally beneficial to the organization or institution, under certain conditions high levels of prior commitment may actually sow the seeds of reduced commitment. When previously committed individuals feel that they were treated unfavourably or unfairly during some experience with the organization or institution, they may show an especially sharp decline in commitment. Two studies were designed to test this hypothesis, which, if confirmed, would suggest that organizational or institutional commitment has risks, as well as benefits. At least three psychological models offer predictions of how individuals' reactions may vary as a function of (1) their prior level of commitment and (2) the favorability of the encounter with the organization or institution. Favorability of the encounter is determined by the outcome of the encounter and the fairness or appropriateness of the procedures used to allocate outcomes during the encounter. First, the instrumental prediction is that because people are mainly concerned with receiving desired outcomes from their encounters with organizations, changes in their level of commitment will depend primarily on the favorability of the encounter. Second, the assimilation prediction is that individuals' prior attitudes predispose them to react in a way that is consistent with their prior attitudes.The third prediction, derived from the group-value model of justice, pertains to how people with high prior commitment will react when they feel that they have been treated unfavorably or unfairly during some encounter with the organization or institution. Fair treatment by the other party symbolizes to people that they are being dealt with in a dignified and respectful way, thereby bolstering their sense of self-identity and self worth. However, people will become quite distressed and react quite negatively if they feel that they have been treated unfairly by the other party to the relationship. The group-value model suggests that people value the information they receive that helps them to define themselves and to view themselves favorably. According to the instrumental viewpoint, people are primarily concerned with the more material or tangible resources received from the relationship. Empirical support for the group-value model has implications for a variety of important issues, including the determinants of commitment, satisfaction, organizational citizenship, and rule following. Determinants of procedural fairness include structural or interpersonal factors. For example, structural determinants refer to such things as whether decisions were made by neutral, fact finding authorities who used legitimate decision making criteria. The primary purpose of the study was to examine the interactive effect of individuals (1) commitment to an organization or institution prior to some encounter and (2) perceptions of how fairly they were treated during the encounter, on the change in their level of commitment. A basic assumption of the group-value model is that people generally value their relationships with people, groups, organizations, and institutions and therefore value fair treatment from the other party to the relationship. Specifically, highly committed members should have especially negative reactions to feeling that they were treated unfairly, more so than (1) less-committed group members or (2) highly committed members who felt that they were fairly treated.The prediction that people will react especially negatively when they previously felt highly committed but felt that they were treated unfairly also is consistent with the literature on psychological contracts. Rousseau suggested that, over time, the members of work organizations develop feelings of entitlement, i.e., perceived obligations that their employers have toward them. Those who are highly committed to the organization believe that they are fulfilling their contract obligations. However, if the organization acted unfairly, then highly committed individuals are likely to believe that the organization did not live up to its end of the bargain.For summarizing the passage, which of the following is most appropriate

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The security personnel of a leading employment organization insisted on developing a new system of allotting the unique ID numbers to its employees to prevent the tampering of ID numbers by any of the unscrupulous members. They insisted that the 10 digit number must include all the numbers from 0-9 exactly once. Further, all the ID numbers should also be exactly divisible by all the numbers from 1-9.What would be the sum of first four digits of the largest ID number generated?a)27b)30c)28d)26Correct answer is option 'B'. Can you explain this answer?
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