Solutions

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Question

If 0<x<y, is y-x < 0.00005

I  x>1/60,000

II. y<1/15,000


 

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Difficulty Level

Medium

Solution

Option C is the correct answer.


Option Analysis

Notice that 0.00005=5/100,000=3/60,000, and 1/15,000=4/60,000.

So, we can rewrite the question as: If 0<x<y, is y-x<3

Statement I is insufficient: x>1 –> if x=2 and y=3 then the answer is YES but if x=2 and y=5 the answer is NO. Not sufficient.

Statement II is insufficient: y<4 –> if x=2 and y=3 then the answer is YES but if x=0.5 and y=3.5 the answer is NO. Not sufficient.

Together I and II, Remember we can subtract inequalities if their signs are in opposite directions –> subtract (1) from (2): y−x<4−1 –> y−x<3. Sufficient.


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