Question

he points A, B, C, and D are on a number line, not necessarily in that order. If the distance between A and B is 18 and the distance between C and D is 8, what is the distance between B and D ? (1) The distance between C and A is the same as the distance between C and B. (2) A is to the left of D on the number line. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient. Next Help End Review Review Screen

Answer 1

Statements (1) and (2) TOGETHER are NOT sufficient.

Explanation:

If the point order is DCAB or CDAB (or the reverse of either of these), then the BD distance will be 36±8 units. It cannot be determined.

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If the point order is AD(BC) or A(BC)D, then the BD distance is the same as the CD distance, which is given as 8. In this scenario, point B and C lie at the same place on the number line.

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So, we have 3 possible values of BD, even when both statements are used together. TOGETHER, the statements aren NOT sufficient.