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18 Mar 2019, 02:19
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D
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Difficulty:
55%
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Question Stats:
70% (02:46) correct
30%
(02:51)
wrong
based on 222
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The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three numbers is 5. What is their sum?
(A) 5
(B) 20
(C) 25
(D) 30
(E) 36
(A) 5
(B) 20
(C) 25
(D) 30
(E) 36
18 Mar 2019, 03:04
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Bunuel
a+b+c/3 = 10+a = c-15
b=5
a= m-10
c=m+15
so
m-10+5+m+15 = 3m
10=m
sum
30
IMO D
Updated on: 17 May 2021, 09:41
Originally posted by BrentGMATPrepNow on 18 Mar 2019, 08:28.
Last edited by BrentGMATPrepNow on 17 May 2021, 09:41, edited 2 times in total.
Last edited by BrentGMATPrepNow on 17 May 2021, 09:41, edited 2 times in total.
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Bunuel
Let x, y and z be the 3 numbers such that x ≤ y ≤ z
The median of the three numbers is 5.
So, y = 5
The mean of three numbers is 10 more than the least of the numbers
We can write: (x + 5 + z)/3 = x + 10
Multiply both sides by 3 to get: x + 5 + z = 3x + 30
Subtract 5 from both sides to get: x + z = 3x + 25
Subtract x from both sides to get: z = 2x + 25
The mean of three numbers is 15 less than the greatest.
We can write: (x + 5 + z)/3 = z - 15
Multiply both sides by 3 to get: x + 5 + z = 3z - 45
Subtract 5 from both sides to get: x + z = 3z - 50
Subtract z from both sides to get: x = 2z - 50
What is the value of x + y + z?
We get: x + y + z = (2z - 50) + 5 + 2x + 25
Simplify to get: x + y + z = 2z + 2x - 20
Subtract y and z from both sides to get: y = z + x - 20
Since y = 5, we get: 5 = z + x - 20
Add 20 to both sides: 25 = z + x
Since y = 5, we get: 30 = x + y + z
Answer: D
Cheers,
Brent
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