GATE Exam > GATE Questions > What is the least number which must be subtra...
Start Learning for Free
What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7?
Most Upvoted Answer
What is the least number which must be subtracted from 1936 so that th...
Community Answer
What is the least number which must be subtracted from 1936 so that th...
Understanding the Problem
To solve the problem, we need to find the least number that must be subtracted from 1936 so that the result leaves a remainder of 7 when divided by 9, 10, and 15.
Step 1: Setting Up the Equations
Let the number to be subtracted be x. We want:
- (1936 - x) % 9 = 7
- (1936 - x) % 10 = 7
- (1936 - x) % 15 = 7
This means:
- 1936 - x = 7 (mod 9)
- 1936 - x = 7 (mod 10)
- 1936 - x = 7 (mod 15)
Step 2: Finding the Remainders
We can rewrite the equations as:
- 1936 - 7 = x (mod 9)
- 1936 - 7 = x (mod 10)
- 1936 - 7 = x (mod 15)
Calculating 1936 - 7:
- 1936 - 7 = 1929
Now, we need to find x such that:
- 1929 % 9
- 1929 % 10
- 1929 % 15
Step 3: Calculate Remainders
- 1929 % 9 = 6
- 1929 % 10 = 9
- 1929 % 15 = 9
Step 4: Calculating x
To achieve a remainder of 7, we need:
- For mod 9: We need 1929 to be adjusted to 7. Thus, we subtract 6 from 1929.
- For mod 10: We need to adjust to 7, thus subtracting 2.
- For mod 15: We need to adjust to 7, thus subtracting 2.
The highest adjustment required is 6.
Conclusion
Therefore, the least number that must be subtracted from 1936 is:
- x = 6
Thus, the answer is 6, ensuring that the remainder when dividing by 9, 10, and 15 is consistently 7.
To solve the problem, we need to find the least number that must be subtracted from 1936 so that the result leaves a remainder of 7 when divided by 9, 10, and 15.
Step 1: Setting Up the Equations
Let the number to be subtracted be x. We want:
- (1936 - x) % 9 = 7
- (1936 - x) % 10 = 7
- (1936 - x) % 15 = 7
This means:
- 1936 - x = 7 (mod 9)
- 1936 - x = 7 (mod 10)
- 1936 - x = 7 (mod 15)
Step 2: Finding the Remainders
We can rewrite the equations as:
- 1936 - 7 = x (mod 9)
- 1936 - 7 = x (mod 10)
- 1936 - 7 = x (mod 15)
Calculating 1936 - 7:
- 1936 - 7 = 1929
Now, we need to find x such that:
- 1929 % 9
- 1929 % 10
- 1929 % 15
Step 3: Calculate Remainders
- 1929 % 9 = 6
- 1929 % 10 = 9
- 1929 % 15 = 9
Step 4: Calculating x
To achieve a remainder of 7, we need:
- For mod 9: We need 1929 to be adjusted to 7. Thus, we subtract 6 from 1929.
- For mod 10: We need to adjust to 7, thus subtracting 2.
- For mod 15: We need to adjust to 7, thus subtracting 2.
The highest adjustment required is 6.
Conclusion
Therefore, the least number that must be subtracted from 1936 is:
- x = 6
Thus, the answer is 6, ensuring that the remainder when dividing by 9, 10, and 15 is consistently 7.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7?
Question Description
What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7?.
What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7?.
Solutions for What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7? defined & explained in the simplest way possible. Besides giving the explanation of
What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7?, a detailed solution for What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7? has been provided alongside types of What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7? theory, EduRev gives you an
ample number of questions to practice What is the least number which must be subtracted from 1936 so that the remainder divided by 9,10,15 will leave in each case the same remainder 7? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE 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