[GMAT math practice question]
If x, y and z are integers with x < y < z, is z > 4?
1) x+y+z=12
2) x < 4
If x, y and z are integers with x < y < z, is z > 4
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]
- 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
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
From condition 1), since x + y + z = 12, their average is 4.
The maximum of three numbers is greater than or equal to their average. Thus, z ≥ 4.
Indeed, we must have z > 4 since x, y and z are different for the following reasons.
If z = 4, then x + y = 8. But x < y < z (= 4), so this is impossible.
If z ≤ 4, then x < y < z ≤ 4, and we must have x < 4 and y < 4.
This implies that x + y + z < 4 + 4 + 4 = 12 and x + y + z ≠12 , which contradicts condition 1).
Thus, z > 4.
Condition 1) is sufficient.
Condition 2)
If x = 3, y = 4 and z = 5, then z > 4 and the answer is 'yes'.
If x = 1, y = 2 and z = 3, then z < 4 and the answer is 'no'.
Condition 2) is not sufficient since it does not yield a unique answer.
Therefore, A is the answer.
Answer: A
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
From condition 1), since x + y + z = 12, their average is 4.
The maximum of three numbers is greater than or equal to their average. Thus, z ≥ 4.
Indeed, we must have z > 4 since x, y and z are different for the following reasons.
If z = 4, then x + y = 8. But x < y < z (= 4), so this is impossible.
If z ≤ 4, then x < y < z ≤ 4, and we must have x < 4 and y < 4.
This implies that x + y + z < 4 + 4 + 4 = 12 and x + y + z ≠12 , which contradicts condition 1).
Thus, z > 4.
Condition 1) is sufficient.
Condition 2)
If x = 3, y = 4 and z = 5, then z > 4 and the answer is 'yes'.
If x = 1, y = 2 and z = 3, then z < 4 and the answer is 'no'.
Condition 2) is not sufficient since it does not yield a unique answer.
Therefore, A is the answer.
Answer: A
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]
-
- Legendary Member
- Posts: 2214
- Joined: Fri Mar 02, 2018 2:22 pm
- Followed by:5 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
The value of z is the greatest integer.
Question ===> is 2>4 ?
Statement 1: x+y+z=12
x and y are less than z (from x<y<z)
For x+y+z to = 12 maximum value of z can be gotten by inputting lowest value of x.
0+1+11=12 where x=0, y=1 and z =11
Minimum value of z can be gotten from
3+4+5=12 where x=3, y=4 and z=5
Hence, z>4 no matter the value of x and y. Thus, STATEMENT 1 IS SUFFICIENT
Statement 2: x<4
From x < y < z; x and y are less than 4.
From x < 4, the value of x can be 0, 1, 2, or 3.
x < y < z can be written as
0 < 1 < 2 where x=0, y=1 and z=2
OR
3 < 4 < 5 where x=3, y=4 and z=5.
Information given is not enough to arrive at a specific answer. Hence, STATEMENT 2 IS NOT SUFFICIENT
Therefore, STATEMENT 1 ALONE IS SUFFICIENT
ANSWER IS OPTION A
Question ===> is 2>4 ?
Statement 1: x+y+z=12
x and y are less than z (from x<y<z)
For x+y+z to = 12 maximum value of z can be gotten by inputting lowest value of x.
0+1+11=12 where x=0, y=1 and z =11
Minimum value of z can be gotten from
3+4+5=12 where x=3, y=4 and z=5
Hence, z>4 no matter the value of x and y. Thus, STATEMENT 1 IS SUFFICIENT
Statement 2: x<4
From x < y < z; x and y are less than 4.
From x < 4, the value of x can be 0, 1, 2, or 3.
x < y < z can be written as
0 < 1 < 2 where x=0, y=1 and z=2
OR
3 < 4 < 5 where x=3, y=4 and z=5.
Information given is not enough to arrive at a specific answer. Hence, STATEMENT 2 IS NOT SUFFICIENT
Therefore, STATEMENT 1 ALONE IS SUFFICIENT
ANSWER IS OPTION A