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Both Betty and Wilma earn annual salaries of more than $5000

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Both Betty and Wilma earn annual salaries of more than $5000

by BTGmoderatorLU » Sat Oct 27, 2018 2:22 pm

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Source: GMAT Prep

Both Betty and Wilma earn annual salaries of more than $50000. Is Wilma's annual salary greater than Betty's?

1) Betty's annual salary is closer to $50,000 than is Wilma's.
2) Betty's annual salary is closer to $35,000 than it is to Wilma's annual salary.

The OA is D.
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by fskilnik@GMATH » Sat Oct 27, 2018 6:58 pm

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BTGmoderatorLU wrote:Source: GMAT Prep
Both Betty and Wilma earn annual salaries of more than $50000. Is Wilma's annual salary greater than Betty's?

1) Betty's annual salary is closer to $50,000 than is Wilma's.
2) Betty's annual salary is closer to $35,000 than it is to Wilma's annual salary.
All numbers presented below are annual salaries expressed in thousands of dollars.
$$B,W\,\, > \,\,50\,\,\left( * \right)$$
$$W\,\,\mathop > \limits^? \,\,B$$
$$\left( 1 \right)\,\,{\rm{and}}\,\,\left( * \right)\,\,\,B - 50 < W - 50\,\,\,\, \Rightarrow \,\,\,\,B < W\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$
$$\left( 2 \right)\,\,{\rm{and}}\,\,\left( * \right)\,\,\,B - 35 < \left| {B - W} \right|$$
$$W \le B\,\,\,\, \Rightarrow \,\,\,\,B - 35 < \left| {B - W} \right| = B - W\,\,\,\, \Rightarrow \,\,\,\,35 > W\,\,\,\,{\rm{impossible}}$$
$$W \le B\,\,\,{\rm{impossible}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by GMATGuruNY » Sun Oct 28, 2018 2:34 am

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BTGmoderatorLU wrote:Source: GMAT Prep

Both Betty and Wilma earn annual salaries of more than $50000. Is Wilma's annual salary greater than Betty's?

1) Betty's annual salary is closer to $50,000 than is Wilma's.
2) Betty's annual salary is closer to $35,000 than it is to Wilma's annual salary.
Statement 1: Betty's annual salary is closer to $50000 than Wilma's is.
On a number line:
-----50,000---B---W
Thus, W > B.
SUFFICIENT.

Statement 2: Betty's annual salary is closer to $35000 than it is to Wilma's annual salary.
Case 1: -----35,000-----50,000---B---W
Case 2: -----35,000-----50,000---W---B

In Case 2, B is closer to W than to 35,000.
Thus, Case 2 is not viable.
Since only Case 1 is viable, W > B.
SUFFICIENT.

The correct answer is D.
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