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a, b, c, d, e are five natural numbers all less than 10 such that a <

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Carcass
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a, b, c, d, e are five natural numbers all less than 10 such that a < [#permalink] New post   15 Feb 2022, 06:58
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a, b, c, d, e are five positive integers each less than 10 such that a < b < c < d < e. Sums of smallest three of these numbers and largest three of these numbers are 11 and 23 respectively. Sum of these five numbers is 28. What is the value of 'c'?

A. 4
B. 5
C. 6
D. 7
E. More than one value possible
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C
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Re: a, b, c, d, e are five natural numbers all less than 10 such that a < [#permalink] New post   15 Feb 2022, 07:15
Carcass wrote:
a, b, c, d, e are five positive integers each less than 10 such that a < b < c < d < e. Sums of smallest three of these numbers and largest three of these numbers are 11 and 23 respectively. Sum of these five numbers is 28. What is the value of 'c'?

A. 4
B. 5
C. 6
D. 7
E. More than one value possible


Given: 0< a < b < c < d < e < 10

The sum of smallest three numbers is 11
We can write: a + b + c = 11

The sum of largest three numbers is 23
We can write: c + d + e = 23

We have the following system:
a + b + c = 11
c + d + e = 23

Add the equations to get: a + b + 2c + d + e = 34

The sum of the five numbers is 28
We can write: a + b + c + d + e = 28

We now have the following system:
a + b + 2c + d + e = 34
a + b + c + d + e = 28

When we subtract the bottom equation from the top equation, we get: c = 6

Answer: C
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Re: a, b, c, d, e are five natural numbers all less than 10 such that a < [#permalink]
15 Feb 2022, 07:15
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