[GMAT math practice question]
If x, y, and z are integers, is xyz a multiple of 6?
1) x+y+z is a multiple of 6
2) x, y, and z are consecutive
If x, y, and z are integers, is xyz a multiple of 6?
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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.
Since the product of three consecutive integers is a multiple of 6, condition 2) is sufficient. Without loss of generality, since condition 2) tells us that x, y and z are consecutive, we can write y = x + 1 and z = x + 2. Then xyz = x(x+1)(x+2) is a multiple of 6 since x(x+1) is a multiple of 2 and x(x+1)(x+2) is a multiple of 3.
Condition 1)
If x = 1, y = 2 and z = 3, then xyz = 6 and the answer is 'yes'.
If x = 2, y = 2 and z = 2, then xyz = 8 and the answer is 'no'.
Condition 1) is not sufficient, since it doesn't yield a unique answer.
Therefore, B is the answer.
Answer: B
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.
Since the product of three consecutive integers is a multiple of 6, condition 2) is sufficient. Without loss of generality, since condition 2) tells us that x, y and z are consecutive, we can write y = x + 1 and z = x + 2. Then xyz = x(x+1)(x+2) is a multiple of 6 since x(x+1) is a multiple of 2 and x(x+1)(x+2) is a multiple of 3.
Condition 1)
If x = 1, y = 2 and z = 3, then xyz = 6 and the answer is 'yes'.
If x = 2, y = 2 and z = 2, then xyz = 8 and the answer is 'no'.
Condition 1) is not sufficient, since it doesn't yield a unique answer.
Therefore, B is the answer.
Answer: B
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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]