[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 aver
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
GMAT/MBA Expert
-
- Senior | Next Rank: 100 Posts
- Posts: 38
- Joined: Mon Mar 19, 2018 6:26 am
- Followed by:1 members
Hi Max,Max@Math Revolution wrote:[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 least of three integers is 10. Let's let x = 10.
The question stem provides the average of the three integers, so we can write the equation (10 + y + z)/3 = 11.
Simplify the equation, so that 10 + y + z = 33, and y + z = 23.
The question asks for the greatest possible value of the greatest integer.
To maximize the value of one of the remaining integers, minimize the value of the other.
Since the least of the three integers is 10, neither y nor z can have a value less than 10.
If y = 10, and y + z = 23, then z = 13.
The correct answer is choice D.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7285
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Since the average is 11, the sum of the three integers is 11 x 3 = 33.Max@Math Revolution wrote:[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
Since the smallest possible integer in the set is 10, we can let two of the integers equal 10, so the maximum integer is 33 - (2 x 10) = 13.
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
=>
Assume x ≤ y ≤ z.
( x + y + z ) / 3 = 11 and x = 10
We have 10 + y + z = 33 or y + z = 23.
In order to have the greatest maximum number, y must be the minimum which is 10.
10 + z = 23.
z = 13.
Therefore, D is the answer.
Answer : D
Assume x ≤ y ≤ z.
( x + y + z ) / 3 = 11 and x = 10
We have 10 + y + z = 33 or y + z = 23.
In order to have the greatest maximum number, y must be the minimum which is 10.
10 + z = 23.
z = 13.
Therefore, D is the answer.
Answer : D
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
Given minimum integer is = 10
Average of 3 integers x, y, and z =11
Therefore Total =11∗3=33
ie; (x + y + z = 33)
The greatest value is possible if the other two values are minimum.
Let xx and y= 10
Therefore the greatest possible value of their maximum;
x + y + z = 33
10 + 10 + z = 33
20 + z = 33
z = 33 - 20 = 13. Option D.
Regards!
Average of 3 integers x, y, and z =11
Therefore Total =11∗3=33
ie; (x + y + z = 33)
The greatest value is possible if the other two values are minimum.
Let xx and y= 10
Therefore the greatest possible value of their maximum;
x + y + z = 33
10 + 10 + z = 33
20 + z = 33
z = 33 - 20 = 13. Option D.
Regards!
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Key concept: If we know the sum of a set of numbers, and we want to MAXIMIZE the biggest number in the set, we must MINIMIZE all of the other numbers.Max@Math Revolution wrote:[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
GIVEN: Average of x, y, and z is 11
So, (x + y + z)/3 = 33
This means x + y + z = 33
Great! We know the sum of the values.
In order to MAXIMIZE the biggest number in the set, we must MINIMIZE all of the other numbers.
We're told that 10 is the MINIMUM value in the set.
So, let's let TWO of the values equal 10
Say x = 10 and y = 10
We have now MINIMIZED two of the three values.
Since we know that x + y + z = 33, we can now write 10 + 10 + z = 33
Solve to get: z = 13
So, the MAXIMUM value is 13.
Answer: D
Cheers,
Brent