Quant Exam > Quant Questions > When a number is multiplied by 13 and 13 is a...
Start Learning for Free
When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?
- a)85
- b)130
- c)65
- d)90
- e)105
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
When a number is multiplied by 13 and 13 is added to the product, the ...
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
When a number is multiplied by 13 and 13 is added to the product, the ...
To find the smallest number that satisfies the given condition, we need to take into account the divisibility rule for 5. A number is divisible by 5 if its units digit is either 0 or 5.
Let's assume the number we are looking for is represented by 'x'. According to the given condition, when 'x' is multiplied by 13 and 13 is added to the product, the result should be divisible by 5.
So we can write the equation as:
13x + 13 ≡ 0 (mod 5)
Now, let's simplify the equation step by step:
Step 1: Subtract 13 from both sides of the equation:
13x ≡ -13 (mod 5)
Step 2: Simplify -13 (mod 5) to get the congruence in a more manageable form:
13x ≡ 2 (mod 5)
Step 3: Find the modular inverse of 13 with respect to 5:
The modular inverse of 13 (mod 5) is 2, since 13 * 2 ≡ 1 (mod 5).
Step 4: Multiply both sides of the congruence by the modular inverse of 13:
2 * 13x ≡ 2 * 2 (mod 5)
26x ≡ 4 (mod 5)
Step 5: Simplify 26 (mod 5) to get the congruence in a more manageable form:
x ≡ 4 (mod 5)
Now, we need to find the smallest number that satisfies this congruence. By trial and error, we can easily see that the smallest number that satisfies x ≡ 4 (mod 5) is 4 itself.
Therefore, the smallest number that satisfies the given condition is 4.
Since option C represents the number 65, which is not the correct answer, it seems there may be an error in the question or the options provided. Please double-check the options and the question statement.
Let's assume the number we are looking for is represented by 'x'. According to the given condition, when 'x' is multiplied by 13 and 13 is added to the product, the result should be divisible by 5.
So we can write the equation as:
13x + 13 ≡ 0 (mod 5)
Now, let's simplify the equation step by step:
Step 1: Subtract 13 from both sides of the equation:
13x ≡ -13 (mod 5)
Step 2: Simplify -13 (mod 5) to get the congruence in a more manageable form:
13x ≡ 2 (mod 5)
Step 3: Find the modular inverse of 13 with respect to 5:
The modular inverse of 13 (mod 5) is 2, since 13 * 2 ≡ 1 (mod 5).
Step 4: Multiply both sides of the congruence by the modular inverse of 13:
2 * 13x ≡ 2 * 2 (mod 5)
26x ≡ 4 (mod 5)
Step 5: Simplify 26 (mod 5) to get the congruence in a more manageable form:
x ≡ 4 (mod 5)
Now, we need to find the smallest number that satisfies this congruence. By trial and error, we can easily see that the smallest number that satisfies x ≡ 4 (mod 5) is 4 itself.
Therefore, the smallest number that satisfies the given condition is 4.
Since option C represents the number 65, which is not the correct answer, it seems there may be an error in the question or the options provided. Please double-check the options and the question statement.
|
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer?
Question Description
When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer?.
When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer?.
Solutions for When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer?, a detailed solution for When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest number possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant 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