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22 Nov 2021, 06:15
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C
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Difficulty:
15%
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Question Stats:
81% (01:28) correct
19%
(01:53)
wrong
based on 32
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a, b, c, d, e are five natural numbers all 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
A. 4
B. 5
C. 6
D. 7
E. More than one value possible
22 Nov 2021, 08:19
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Bunuel
Note: The GMAT Official Guide doesn't define natural numbers, so it's worth noting that natural numbers are positive integers
This means we can say: 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
22 Nov 2021, 11:57
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Bunuel
Breaking Down the Info:
Sum of smallest three is 11 : a + b + c = 11.
Sum of largest three is 23 : c + d + e = 23.
We may observe adding these two up gives us: a + b + 2c + d + e = 34.
Sum of these five numbers is 28: a + b + c + d + e = 28.
Subtracting the two equations above gives us \(c = 6\).
Answer: C
