UPSC Exam > UPSC Questions > N = abc where a, b and c are the hundreds, te...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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.
Free Test
FREE
| Start Free Test |
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.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup