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If a and b are negative real numbers and c is a positive real number, then which of the following is/are correct?
1. a - b < a - c
2. If a < b, then a/c < b/c.
3. 1/b < 1/c
Select the correct answer using the code given below.
  • a)
    1 only
  • b)
    2 only 
  • c)
    3 only
  • d)
    2 and 3 only 
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If a and b are negative real numbers and c is a positive real number, ...
Statement I:
a - b will be moving in the positive number line because b is negative
a - c will move in negative direction because c is positive
⇒ a - b > a - c
⇒ Statement I is wrong
Statement II:
a < b         [Given]
⇒ ac < bc       [∵ c is a positive number]
⇒ a/c < b/c
⇒ Statement II is correct
Statement III:
1/b is negative and 1/c is positive
⇒ 1/b < 1/c
⇒ Statement III is correct
∴ Only statement II and III are correct
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Most Upvoted Answer
If a and b are negative real numbers and c is a positive real number, ...
Explanation:

1. a - b < a="" -="" />
When a and b are negative real numbers and c is a positive real number, the inequality a - b < a="" -="" c="" holds="" true.="" this="" is="" because="" subtracting="" a="" negative="" number="" from="" a="" results="" in="" a="" larger="" value,="" while="" subtracting="" a="" positive="" number="" results="" in="" a="" smaller="" value.="" therefore,="" a="" -="" b="" is="" less="" than="" a="" -="" />

2. If a < b,="" then="" a/c="" />< />
If a is less than b, dividing both sides by a positive number c will not change the direction of the inequality. Therefore, a/c will be less than b/c. This is because when a is smaller than b, dividing both by a positive number will result in a smaller value for a/c compared to b/c.

3. 1/b < />
When a and b are negative real numbers and c is a positive real number, the inequality 1/b < 1/c="" holds="" true.="" this="" is="" because="" when="" comparing="" the="" reciprocals="" of="" negative="" numbers,="" the="" reciprocal="" of="" the="" smaller="" negative="" number="" is="" larger.="" therefore,="" 1/b="" is="" less="" than="" />
Therefore, options 2 and 3 are correct. The correct answer is option 'D'.
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If a and b are negative real numbers and c is a positive real number, then which of the following is/are correct?1. a - b < a - c2. If a < b, then a/c < b/c.3. 1/b < 1/cSelect the correct answer using the code given below.a)1 onlyb)2 onlyc)3 onlyd)2 and 3 onlyCorrect answer is option 'D'. Can you explain this answer?
Question Description
If a and b are negative real numbers and c is a positive real number, then which of the following is/are correct?1. a - b < a - c2. If a < b, then a/c < b/c.3. 1/b < 1/cSelect the correct answer using the code given below.a)1 onlyb)2 onlyc)3 onlyd)2 and 3 onlyCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If a and b are negative real numbers and c is a positive real number, then which of the following is/are correct?1. a - b < a - c2. If a < b, then a/c < b/c.3. 1/b < 1/cSelect the correct answer using the code given below.a)1 onlyb)2 onlyc)3 onlyd)2 and 3 onlyCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are negative real numbers and c is a positive real number, then which of the following is/are correct?1. a - b < a - c2. If a < b, then a/c < b/c.3. 1/b < 1/cSelect the correct answer using the code given below.a)1 onlyb)2 onlyc)3 onlyd)2 and 3 onlyCorrect answer is option 'D'. Can you explain this answer?.
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