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The question below is followed by two statements I and II. You have to determine whether the data given is sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. Is the positive integer X always divisible by 6? I. When X is divided by 15, the remainder is 3. II. When X is divided by 20, the remainder is 8.

The question below is followed by two statements I and II. You have to determine whether the data given is sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. Is the positive integer X always divisible by 6? I. When X is divided by 15, the remainder is 3. II. When X is divided by 20, the remainder is 8. Correct Answer If the data in both the statements I and II are not sufficient to answer the question.

Given that x is divisible by 6, it is also divisible by 2 and 3 as per the divisibility rule of 6.

Considering statement I,

We can write x in form of 15k + 3 where k is some natural number.

15k + 3 will always be divisible by 3 but it won’t be always divisible by 2. (We can check this by taking different values of k starting from 1)

Hence, the number x may or may not be divisible by 6.

∴ Statement I alone is not sufficient.

Considering statement II,

We can write x in form of 20m + 8 where m is some natural number.

But 20m + 8 will always be divisible by 2 but it won’t always be divisible by 3. (We can check this by taking different values of m starting from 1)

Hence, the number x may or may not be divisible by 6.

∴ Statement II alone is not sufficient.

 

Mistaken points:

Even multiple of 15 i.e.

⇒ 15 × 2 = 30

⇒ 15 × 4 = 60

According to question

When 3 is add to them then they are not multiple of 6

i.e. 30 + 3 = 33 (not divisible of 6)

⇒ 60 + 3 = 63 (not divisible of 6)

Odd multiple of 20 i.e

⇒ 20 × 3 = 60

⇒ 20 × 7 = 140

According to question

When 8 is added to them then they are not multiple of 6

i.e. 60 + 8 = 68 (not multiple of 6)

⇒ 140 + 8 = 148 (not multiple of 6)

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