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What least number must be subtracted from 1936 so that the remainder when divided by 9.10,15 will leave in each case the same remainder unseen 7?
- a)30
- b)39
- c)23
- d)29
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
What least number must be subtracted from 1936 so that the remainder w...
The L.C.M. of 9.10 and 15 = 90.
On dividing 1936 by 90. the remainder = 46.
But 7 is also a pait of this remainder. Therefore, the required number = 46 - 7 = 39.
On dividing 1936 by 90. the remainder = 46.
But 7 is also a pait of this remainder. Therefore, the required number = 46 - 7 = 39.
Most Upvoted Answer
What least number must be subtracted from 1936 so that the remainder w...
To find the least number that must be subtracted from 1936 so that the remainder when divided by 9, 10, and 15 is the same remainder as unseen 7, we need to find the LCM (Least Common Multiple) of 9, 10, and 15.
Step 1: Find the LCM of 9, 10, and 15
The prime factorization of 9 is 3^2, the prime factorization of 10 is 2 * 5, and the prime factorization of 15 is 3 * 5. To find the LCM, we take the highest powers of each prime factor. So, the LCM of 9, 10, and 15 is 2 * 3^2 * 5 = 90.
Step 2: Find the remainder when 1936 is divided by 90
To find the remainder when 1936 is divided by 90, we divide 1936 by 90 and find the remainder. Using long division, we get:
21
______________
90 | 1936
- 1800
______________
136
The remainder when 1936 is divided by 90 is 136.
Step 3: Find the difference between the remainder and 7
The difference between the remainder (136) and 7 is 136 - 7 = 129.
Therefore, the least number that must be subtracted from 1936 so that the remainder when divided by 9, 10, and 15 is the same remainder as unseen 7 is 129.
Option B, which is 39, is the correct answer.
Step 1: Find the LCM of 9, 10, and 15
The prime factorization of 9 is 3^2, the prime factorization of 10 is 2 * 5, and the prime factorization of 15 is 3 * 5. To find the LCM, we take the highest powers of each prime factor. So, the LCM of 9, 10, and 15 is 2 * 3^2 * 5 = 90.
Step 2: Find the remainder when 1936 is divided by 90
To find the remainder when 1936 is divided by 90, we divide 1936 by 90 and find the remainder. Using long division, we get:
21
______________
90 | 1936
- 1800
______________
136
The remainder when 1936 is divided by 90 is 136.
Step 3: Find the difference between the remainder and 7
The difference between the remainder (136) and 7 is 136 - 7 = 129.
Therefore, the least number that must be subtracted from 1936 so that the remainder when divided by 9, 10, and 15 is the same remainder as unseen 7 is 129.
Option B, which is 39, is the correct answer.
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What least number must be subtracted from 1936 so that the remainder when divided by 9.10,15 will leave in each case the same remainder unseen 7?a)30b)39c)23d)29Correct answer is option 'B'. Can you explain this answer?
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