Question

A number is such that when divided by 3, 5, 6, or 7 it leaves the remainder 1, 3, 4, or 5 respectively. Which is the largest number below 4000 that satisfies this property? Explain. (a) 3358 (b) 3988 (c) 3778 (d) 2938

Answer 1

Answer:

(b) 3988

Step-by-step explanation:

B) add 3 to 3988 and divide by 6 we will get remainder=1.

Answer 2

Answer:

Option (b) $3998$ is the largest number below $4000$ that satisfies the given hypothesis.

Step-by-step explanation:

Given: A number when divided by $3,5,6$ or $7$ leaves the remainder $1,3,4$ or $5$ respectively.

(a) $3358$

When $3358$ is divided by $3$.

$3+3+5+8=19$

Here the number $19$ when divides by $3$ leaves 1 as a remainder.

Hence, the number $3358$ when divisible by $3$ leaves $1$ as a remainder.

When $3358$ is divided by $5$.

Using divisional algorithm,

$3358=5\cdot671+3$

Thus, the number $3358$ when divisible by $5$ leaves $3$ as a remainder.

When $3358$ is divided by $6$.

Using divisional algorithm,

$3358=6\cdot559+4$

Thus, the number $3358$ when divisible by $6$ leaves $4$ as a remainder.

When $3358$ is divided by $7$.

Using divisional algorithm,

$3358=7\cdot479+5$

Thus, the number $3358$ when divisible by $7$ leaves $5$ as a remainder.

(b) $3988$

$3+9+8+8=28$

Here the number $28$ when divides by $3$ leaves 1 as a remainder.

Hence, the number $3988$ when divisible by $3$ leaves $1$ as a remainder.

When $3988$ is divided by $5$.

Using divisional algorithm,

$3988=5\cdot797+3$

Thus, the number $3988$ when divisible by $5$ leaves $3$ as a remainder.

When $3988$ is divided by $6$.

Using divisional algorithm,

$3988=6\cdot664+4$

Thus, the number $3988$ when divisible by $6$ leaves $4$ as a remainder.

When $3988$ is divided by $7$.

Using divisional algorithm,

$3988=7\cdot569+5$

Thus, the number $3988$ when divisible by $7$ leaves $5$ as a remainder.

Among four options, option (b) is the largest number below $4000$ that satisfies the given hypothesis.

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