JEE Exam > JEE Questions > The number of numbers between 105 and 1000 wh...
Start Learning for Free
The number of numbers between 105 and 1000 which are divisible by 7 is
- a)127
- b)142
- c)128
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The number of numbers between 105 and 1000 which are divisible by 7 is...
To find the number of numbers between 105 and 1000 that are divisible by 7, we need to determine the range of numbers that satisfy this condition.
Step 1: Find the smallest number greater than or equal to 105 that is divisible by 7.
The smallest number greater than or equal to 105 that is divisible by 7 is 105 itself.
Step 2: Find the largest number less than or equal to 1000 that is divisible by 7.
To find the largest number less than or equal to 1000 that is divisible by 7, we divide 1000 by 7 and take the integer part of the quotient. This is because the largest number divisible by 7 would be a multiple of 7.
1000 ÷ 7 = 142.857
Since we need to find the largest number less than or equal to 1000, we take the integer part of 142.857, which is 142.
Therefore, the largest number less than or equal to 1000 that is divisible by 7 is 7 * 142 = 994.
Step 3: Calculate the number of numbers divisible by 7 between 105 and 1000.
To calculate the number of numbers divisible by 7 between 105 and 1000, we subtract the smallest number divisible by 7 from the largest number divisible by 7 and divide the result by 7.
(994 - 105) ÷ 7 = 889 ÷ 7 = 127
Therefore, there are 127 numbers between 105 and 1000 that are divisible by 7.
Hence, the correct answer is option C) 128.
Step 1: Find the smallest number greater than or equal to 105 that is divisible by 7.
The smallest number greater than or equal to 105 that is divisible by 7 is 105 itself.
Step 2: Find the largest number less than or equal to 1000 that is divisible by 7.
To find the largest number less than or equal to 1000 that is divisible by 7, we divide 1000 by 7 and take the integer part of the quotient. This is because the largest number divisible by 7 would be a multiple of 7.
1000 ÷ 7 = 142.857
Since we need to find the largest number less than or equal to 1000, we take the integer part of 142.857, which is 142.
Therefore, the largest number less than or equal to 1000 that is divisible by 7 is 7 * 142 = 994.
Step 3: Calculate the number of numbers divisible by 7 between 105 and 1000.
To calculate the number of numbers divisible by 7 between 105 and 1000, we subtract the smallest number divisible by 7 from the largest number divisible by 7 and divide the result by 7.
(994 - 105) ÷ 7 = 889 ÷ 7 = 127
Therefore, there are 127 numbers between 105 and 1000 that are divisible by 7.
Hence, the correct answer is option C) 128.
Free Test
FREE
| Start Free Test |
Community Answer
The number of numbers between 105 and 1000 which are divisible by 7 is...
Clearly, the numbers between 105 and 1000 which are divisible by 7 are 112,119,126,...,994.
This is an AP with first term a=112, common difference d=7 and last term l = 994.
Let there be n terms in this AP. Then,
an = 994
Let there be n terms in this AP. Then,
an = 994
⇒ a + (n − 1)d
994 = 112 + (n − 1) × 7
994 = 105 + 7n
∴ 7n = 889
∴ n = 127
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Question Description
The number of numbers between 105 and 1000 which are divisible by 7 isa)127b)142c)128d)none of theseCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of numbers between 105 and 1000 which are divisible by 7 isa)127b)142c)128d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of numbers between 105 and 1000 which are divisible by 7 isa)127b)142c)128d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
The number of numbers between 105 and 1000 which are divisible by 7 isa)127b)142c)128d)none of theseCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of numbers between 105 and 1000 which are divisible by 7 isa)127b)142c)128d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of numbers between 105 and 1000 which are divisible by 7 isa)127b)142c)128d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The number of numbers between 105 and 1000 which are divisible by 7 isa)127b)142c)128d)none of theseCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The number of numbers between 105 and 1000 which are divisible by 7 isa)127b)142c)128d)none of theseCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The number of numbers between 105 and 1000 which are divisible by 7 isa)127b)142c)128d)none of theseCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The number of numbers between 105 and 1000 which are divisible by 7 isa)127b)142c)128d)none of theseCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The number of numbers between 105 and 1000 which are divisible by 7 isa)127b)142c)128d)none of theseCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The number of numbers between 105 and 1000 which are divisible by 7 isa)127b)142c)128d)none of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
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!
within 7 days!
Takes less than 10 seconds to signup