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N = abc where a, b and c are the hundreds, tens and units digit respectively. If a, b and c are non-zero consecutive numbers such that a < b < c, then which of the following must be true?
I. N is always divisible by 2
II. N is always divisible by 3
III. N is divisible by 6 only if b is odd.
- a)I only
- b)II only
- c)I and II only
- d)II and III only
- e)I, II and III
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
N = abc where a, b and c are the hundreds, tens and units digit respec...
Solution:
Given, N = abc where a, b and c are the hundreds, tens and units digit respectively and a, b and c are non-zero consecutive numbers such that a < b="" />< />
I. N is always divisible by 2:
If c is an even number, then N is divisible by 2. Hence, option I is always true.
II. N is always divisible by 3:
The sum of three consecutive numbers is always divisible by 3. Hence, a + b + c is divisible by 3. Therefore, N is always divisible by 3. Hence, option II is always true.
III. N is divisible by 6 only if b is odd:
For N to be divisible by 6, it must be divisible by both 2 and 3. From I, we know that N is always divisible by 2. From II, we know that N is always divisible by 3. Therefore, N is divisible by 6 only if b is odd. Hence, option III is true.
Therefore, the correct option is D.
Given, N = abc where a, b and c are the hundreds, tens and units digit respectively and a, b and c are non-zero consecutive numbers such that a < b="" />< />
I. N is always divisible by 2:
If c is an even number, then N is divisible by 2. Hence, option I is always true.
II. N is always divisible by 3:
The sum of three consecutive numbers is always divisible by 3. Hence, a + b + c is divisible by 3. Therefore, N is always divisible by 3. Hence, option II is always true.
III. N is divisible by 6 only if b is odd:
For N to be divisible by 6, it must be divisible by both 2 and 3. From I, we know that N is always divisible by 2. From II, we know that N is always divisible by 3. Therefore, N is divisible by 6 only if b is odd. Hence, option III is true.
Therefore, the correct option is D.
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Community Answer
N = abc where a, b and c are the hundreds, tens and units digit respec...
A,b,c are consecutive (continues) it means that b= a+1 and c= a+2, if a is odd then b is even and c is odd, if a is even then b is odd and c is even.
statement I : n is not always divisible by 2 because when a is odd then c is odd which is unit digit then N is an odd and not divisible by 2.
statement II: any number is divisible by 3, if sum of digits divisible by 3. therefore a+b+c = a+(a+1)+(a+2)= 3a+3= 3(a+1) hence divisible by 3.
statement III: any number is divisible by 6 if it is divisible by both 2 and 3. N is divisible by 3. it is divisible by 2 when b is odd because then c is even.
statement I : n is not always divisible by 2 because when a is odd then c is odd which is unit digit then N is an odd and not divisible by 2.
statement II: any number is divisible by 3, if sum of digits divisible by 3. therefore a+b+c = a+(a+1)+(a+2)= 3a+3= 3(a+1) hence divisible by 3.
statement III: any number is divisible by 6 if it is divisible by both 2 and 3. N is divisible by 3. it is divisible by 2 when b is odd because then c is even.
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N = abc where a, b and c are the hundreds, tens and units digit respectively. If a, b and c are non-zero consecutive numbers such that a < b < c, then which of the following must be true? I. N is always divisible by 2 II. N is always divisible by 3 III. N is divisible by 6 only if b is odd.a)I onlyb)II onlyc)I and II onlyd)II and III onlye)I, II and IIICorrect answer is option 'D'. Can you explain this answer?
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N = abc where a, b and c are the hundreds, tens and units digit respectively. If a, b and c are non-zero consecutive numbers such that a < b < c, then which of the following must be true? I. N is always divisible by 2 II. N is always divisible by 3 III. N is divisible by 6 only if b is odd.a)I onlyb)II onlyc)I and II onlyd)II and III onlye)I, II and IIICorrect answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about N = abc where a, b and c are the hundreds, tens and units digit respectively. If a, b and c are non-zero consecutive numbers such that a < b < c, then which of the following must be true? I. N is always divisible by 2 II. N is always divisible by 3 III. N is divisible by 6 only if b is odd.a)I onlyb)II onlyc)I and II onlyd)II and III onlye)I, II and IIICorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for N = abc where a, b and c are the hundreds, tens and units digit respectively. If a, b and c are non-zero consecutive numbers such that a < b < c, then which of the following must be true? I. N is always divisible by 2 II. N is always divisible by 3 III. N is divisible by 6 only if b is odd.a)I onlyb)II onlyc)I and II onlyd)II and III onlye)I, II and IIICorrect answer is option 'D'. Can you explain this answer?.
N = abc where a, b and c are the hundreds, tens and units digit respectively. If a, b and c are non-zero consecutive numbers such that a < b < c, then which of the following must be true? I. N is always divisible by 2 II. N is always divisible by 3 III. N is divisible by 6 only if b is odd.a)I onlyb)II onlyc)I and II onlyd)II and III onlye)I, II and IIICorrect answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about N = abc where a, b and c are the hundreds, tens and units digit respectively. If a, b and c are non-zero consecutive numbers such that a < b < c, then which of the following must be true? I. N is always divisible by 2 II. N is always divisible by 3 III. N is divisible by 6 only if b is odd.a)I onlyb)II onlyc)I and II onlyd)II and III onlye)I, II and IIICorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for N = abc where a, b and c are the hundreds, tens and units digit respectively. If a, b and c are non-zero consecutive numbers such that a < b < c, then which of the following must be true? I. N is always divisible by 2 II. N is always divisible by 3 III. N is divisible by 6 only if b is odd.a)I onlyb)II onlyc)I and II onlyd)II and III onlye)I, II and IIICorrect answer is option 'D'. Can you explain this answer?.
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