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Five friends went for a trip where each carried a certain number of apples with them. The number of apples carried by C was 1 less than that by D, which was 5 more than the number of apples carried by E. The total number of apples carried by A and B both was equal to the average number of apples carried by C, D and E. If D carried more apples than B and they together carried 14 apples, which of the following is a possible value of the apples carried by A?

Five friends went for a trip where each carried a certain number of apples with them. The number of apples carried by C was 1 less than that by D, which was 5 more than the number of apples carried by E. The total number of apples carried by A and B both was equal to the average number of apples carried by C, D and E. If D carried more apples than B and they together carried 14 apples, which of the following is a possible value of the apples carried by A? Correct Answer 6

Given:

Five friends went for a trip where each carried a certain number of apples with them. The number of apples carried by C was 1 less than that by D, which was 5 more than the number of apples carried by E. The total number of apples carried by A and B both was equal to the average number of apples carried by C, D and E. D carried more apples than B and they together carried 14 apples.

Concept Used:

If the sum of a and b is even, it implies either both a and b are even or that both a and b are odd.

In both the cases, difference of a and b will be even too.

Calculation:

Let the apples with A, B, C, D and E be ‘a’, ‘b’, ‘c’, ‘d’, and ‘e’ respectively.

⇒ c = d – 1, e = d – 5

⇒ a + b = (c + d + e)/3

⇒ 3a + 3b = c + d + e = d – 1 + d + d – 5

⇒ 3a + 3b = 3d – 6

⇒ a + b = d – 2

⇒ a = (d - b) – 2 ….(i)

Using above concept, we get, d – b = positive and even.

Hence, a should also be even. Only option D satisfies the above condition in equation (i)

6 is only possible value among the given options. 

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