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If x, y and z are integers with x < y < z, is z > 4

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by Max@Math Revolution » Thu Apr 25, 2019 12:13 am

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[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
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Source: — Data Sufficiency |
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by Max@Math Revolution » Mon Apr 29, 2019 5:12 pm
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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
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by deloitte247 » Tue Apr 30, 2019 12:19 pm
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
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