If x, y and z are positive numbers, is z between x and y ?
1) x< 2z < y
2) 2x< z < 2y
thanks
x, y, z, inequalities ....
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Target question: Is z between x and y?If x, y, and z are positive numbers, is z between x and y?
(1) x < 2z < y
(2) 2x < z < 2y
Statement 1: x < 2z < y
There are several set values of x, y and z that satisfy this condition. Here are two:
Case a: x = 3, y = 10, and z = 2, in which case z is NOT between x and y
Case b: x = 1, y = 10, and z = 3, in which case z IS between x and y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 2x < z < 2y
There are several set values of x, y and z that satisfy this condition. Here are two:
Case a: x = 1, y = 2, and z = 3, in which case z is NOT between x and y
Case b: x = 1, y = 10, and z = 3, in which case z IS between x and y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1: x < 2z < y
Statement 2: 2x < z < 2y
Since the two inequalities are facing the same direction, we can ADD them to get:
3x < 3z < 3y
Divide all three parts by 3 to get: x < z < y
As we can see, z IS definitely between x and y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
- Max@Math Revolution
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.
If x, y and z are positive numbers, is z between x and y ?
1) x< 2z < y
2) 2x< z < 2y
==> Since there are 3 variables (x,y,z) in the original condition, we need 3 equations to match the number of variables and since we have only 2 equations overall (1 each in (1), (2)), E is likely the answer. Using both (1) & (2)3x<3z<3y thus x<y<z, and the solution to the question is yes. Therefore the answer is C. Using both (1) & (2) together can save us time.
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If x, y and z are positive numbers, is z between x and y ?
1) x< 2z < y
2) 2x< z < 2y
==> Since there are 3 variables (x,y,z) in the original condition, we need 3 equations to match the number of variables and since we have only 2 equations overall (1 each in (1), (2)), E is likely the answer. Using both (1) & (2)3x<3z<3y thus x<y<z, and the solution to the question is yes. Therefore the answer is C. Using both (1) & (2) together can save us time.
If you know our own innovative logics to find the answer, you don't need to actually solve the problem.
www.mathrevolution.com
l The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.
l The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.
l The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare
l Hitting a score of 45 is very easy and points and 49-51 is also doable.
l Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson
l Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8