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Srini wrote his class 10th board examination this year. When the result came out he searched for his hall ticket to see his roll number but could not trace it. He could remember only the first three digits of the 6 digit number as 267. His father, however, remembered that the number was divisible by 11. His mother gave the information that the number was also divisible by 13. They tried to recollect the number when all of a sudden Srini told that the number was a multiple of 7. What was the unit digits of the number?
  • a)
    5
  • b)
    7
  • c)
    2
  • d)
    Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Srini wrote his class 10th board examination this year. When the resul...
His roll no. is divisible by 1001 (13x11x7)
and 1st three digit are 267. 
Hence, the Last three digits will also be 267. 
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Most Upvoted Answer
Srini wrote his class 10th board examination this year. When the resul...
If the number is divisible by 11 13 and 7 then the number will be also divisible by there product ie 1001 now we just need to see which option is dividing 1001 perfectly
7 is the number which divides 1001
therefore the number will contain 7 at its unit place
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Community Answer
Srini wrote his class 10th board examination this year. When the resul...
Solution:
Given, the first 3 digits of the 6 digit number are 267.

Let the 6 digit number be ABC267.

It is given that the number is divisible by 11.

Divisibility rule of 11 states that the difference between the sum of the digits in the odd places and the sum of the digits in the even places of the number should be either 0 or a multiple of 11.

So, (C + A + B) - (6 + 2 + 7) = C + A + B - 15 should be either 0 or a multiple of 11.

C + A + B = 26, 37, 48, 59, 70, 81, 92

It is also given that the number is divisible by 13.

So, 13 divides ABC267.

13 divides (267000 + ABC)

13 divides (2A7 + BC0)

13 divides (2A7 - BC)

We can check the values of (2A7 - BC) for the possible values of C + A + B.

For C + A + B = 26, (2A7 - BC) can be 079, 192, 2A5, 3B8, 4C1, 5A4, 6B7, 7C0, 8A3, 9B6.

For C + A + B = 37, (2A7 - BC) can be 2B9, 3C2, 4A5, 5B8, 6C1, 7A4, 8B7, 9C0.

For C + A + B = 48, (2A7 - BC) can be 4C3, 5A6, 6B9, 7C2, 8A5, 9B8.

For C + A + B = 59, (2A7 - BC) can be 6B5, 7C8, 8A1, 9B4.

For C + A + B = 70, (2A7 - BC) can be 8C7, 9A0.

For C + A + B = 81, (2A7 - BC) can be 0B3, 1C6.

For C + A + B = 92, (2A7 - BC) can be 2C9.

Now, we know that the number is a multiple of 7.

Divisibility rule of 7 states that if we remove the last digit of the number, double it, and subtract it from the remaining part of the number, then the resulting number should be either 0 or a multiple of 7.

Let the unit digit of the number be x.

So, (ABC26 - 2x) should be either 0 or a multiple of 7.

When C + A + B = 26, (ABC26 - 2x) can be 737, 1057, 2377, 3327, 4657, 6627, 7287, 8617, 9287.

When C + A + B = 37, (ABC26 - 2x) can be 1187, 2517, 346
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Srini wrote his class 10th board examination this year. When the result came out he searched for his hall ticket to see his roll number but could not trace it. He could remember only the first three digits of the 6 digit number as 267. His father, however, remembered that the number was divisible by 11. His mother gave the information that the number was also divisible by 13. They tried to recollect the number when all of a sudden Srini told that the number was a multiple of 7. What was the unit digits of the number?a)5b)7c)2d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?
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Srini wrote his class 10th board examination this year. When the result came out he searched for his hall ticket to see his roll number but could not trace it. He could remember only the first three digits of the 6 digit number as 267. His father, however, remembered that the number was divisible by 11. His mother gave the information that the number was also divisible by 13. They tried to recollect the number when all of a sudden Srini told that the number was a multiple of 7. What was the unit digits of the number?a)5b)7c)2d)Cannot be determinedCorrect answer is option 'B'. 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 Srini wrote his class 10th board examination this year. When the result came out he searched for his hall ticket to see his roll number but could not trace it. He could remember only the first three digits of the 6 digit number as 267. His father, however, remembered that the number was divisible by 11. His mother gave the information that the number was also divisible by 13. They tried to recollect the number when all of a sudden Srini told that the number was a multiple of 7. What was the unit digits of the number?a)5b)7c)2d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Srini wrote his class 10th board examination this year. When the result came out he searched for his hall ticket to see his roll number but could not trace it. He could remember only the first three digits of the 6 digit number as 267. His father, however, remembered that the number was divisible by 11. His mother gave the information that the number was also divisible by 13. They tried to recollect the number when all of a sudden Srini told that the number was a multiple of 7. What was the unit digits of the number?a)5b)7c)2d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
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