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Applications of Dot Product

Suppose we ha...

Question

Suppose we have ${6, 2, 1, 3}$ . If $k$ is a number so that the sum of $k$ and any number in the set above is also in the set, what is the value of $k$ ?

5

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4

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1

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0

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- 1

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Solution

The correct option is D $0$
Let $k$ be any number
Given that sum of $k$ and any number in the set must lie in that set.
Consider $k = 5$ , $k + 2 = 7$ is not present in the set
Consider $k = 4$ , $k + 3 = 7$ is not present in the set
Consider $k = 1$ , $k + 3 = 4$ is not present in the set
Consider $k = 0$ , All elements in the set when added to $0$ remains same and present in that set
Consider $k = - 1$ , $k + 1 = 0$ is not present in the set
Therefore correct option is $D$

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Suppose we have {6,2,1,3}. If k is a number so that the sum of k and any number in the set above is also in the set, what is the value of k?

Suppose we have ${6, 2, 1, 3}$ . If $k$ is a number so that the sum of $k$ and any number in the set above is also in the set, what is the value of $k$ ?