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26 Apr 2018, 01:22
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D
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Difficulty:
25%
(medium)
Question Stats:
69% (00:54) correct
31%
(01:09)
wrong
based on 134
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[GMAT math practice question]
The minimum of the integers \(x, y\), and \(z\) is \(10\) and their average is \(11\). What is the greatest possible value of their maximum?
\(A. 10\)
\(B. 11\)
\(C. 12\)
\(D. 13\)
\(E. 14\)
The minimum of the integers \(x, y\), and \(z\) is \(10\) and their average is \(11\). What is the greatest possible value of their maximum?
\(A. 10\)
\(B. 11\)
\(C. 12\)
\(D. 13\)
\(E. 14\)
sashiim20
Joined: 04 Dec 2015
Last visit: 05 Jun 2024
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Location: India
Concentration: Technology, Strategy
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
WE:Information Technology (Consulting)
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
Posts: 608
26 Apr 2018, 01:34
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MathRevolution
Given minimum integer is \(= 10\)
Average of \(3\) integers \(x\), \(y\), and \(z\) \(= 11\)
Therefore Total \(= 11*3 = 33\)
ie; \(x + y + z = 33\)\(\)
Greatest value is possible if the other two values are minimum.
Let \(x\) and \(y\) \(= 10\)
Therefore greatest possible value of their maximum;
\(x + y + z = 33\)
\(10 + 10 + z = 33\)
\(20 + z = 33\)
\(z = 33-20 = 13\)
Answer D
26 Apr 2018, 12:25
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MathRevolution
I could not understand the question. (Maybe that's the point?)
REWRITE:
Each of three integers \(x, y,\) and \(z\) has a minimum value of \(10\). The integers' average is \(11.\) What is the greatest possible value of any one variable?
We know the sum, \(x + y + z\):
\(A*n = S\)
\(11*3 = 33\) = Sum of all three
In order to maximize one value, minimize the other two. Each integer must = at least 10
Let \(x=10, y=10\)
\(10, 10,\) z? . . .They sum to \(33\):
\(10 + 10 + z = 33\)
\(z = (33 - 20) = 13\)
Maximum value of the third integer = \(13\)
Answer D
