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Points P, Q, R, are S are situated on a number line in that order. What is the coordinate of S?

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Points P, Q, R, are S are situated on a number line in that order. What is the coordinate of S?

by Max@Math Revolution » Thu Jun 18, 2020 11:30 pm

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[GMAT math practice question]

Points P, Q, R, are S are situated on a number line in that order. What is the coordinate of S?

1) The coordinate of P is -8, and that of R is -2.
2) The length of QR and that of RS are equal.
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Source: — Data Sufficiency |
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Re: Points P, Q, R, are S are situated on a number line in that order. What is the coordinate of S?

by Max@Math Revolution » Sun Jun 21, 2020 6:19 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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Assume p, q, r, and s are coordinates of points P, Q, R, and S, respectively.

Since we have 4 variables (p, q, r, and s) and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2) together give us:
We have p = -8 and r = -2.
We have r – q = s – r or s = 2r – q = 2(-2) – q = -4 – q.
If p = -8, q = -6, and r = -2, we have s = -4 – (-6) = 2.
If p = -8, q = -4, and r = -2, we have s = -4 – (-4) = 0.

The answer is not unique, and both conditions 1) and 2) together are not sufficient according to Common Mistake Type 2, which states that the number of answers must be only one.

Therefore, E is the answer.
Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B, or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.
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