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Expert's post 00:00

Question Stats: 73% (01:02) correct 26% (00:55) wrong based on 53 sessions

$$a + \frac{b}{10} > 0$$

$$b + \frac{a}{10} < 0$$

 Quantity A Quantity B a b

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
[Reveal] Spoiler: OA

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Intern Joined: 15 May 2018
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Carcass wrote:
$$a + \frac{b}{10} > 0$$

$$b + \frac{a}{10} < 0$$

 Quantity A Quantity B a b

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

My Anwer is A GRE Instructor Joined: 10 Apr 2015
Posts: 3838
Followers: 149

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Expert's post
Carcass wrote:

$$a + \frac{b}{10} > 0$$

$$b + \frac{a}{10} < 0$$

 Quantity A Quantity B a b

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Take: $$a + \frac{b}{10} > 0$$
Multiply both sides by 10 to get: $$10a + b > 0$$

Take: $$b + \frac{a}{10} < 0$$
Multiply both sides by 10 to get: $$10b + a < 0$$
Multiply both sides by -1 to get: $$-10b - a > 0$$ [since I multiplied both sides by a NEGATIVE value, I had to REVERSE the direction of the inequality symbol]
Rearrange to get: $$-a - 10b > 0$$

We now have:
$$10a + b > 0$$
$$-a - 10b > 0$$

Since the inequality symbols are facing the SAME DIRECTION, we can ADD the inequalities to get: $$9a - 9b > 0$$
Divide both sides by 9 to get: $$a - b > 0$$
Add b to both sides to get: $$a > b$$

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If you enjoy my solutions, you'll like my GRE prep course. Intern Joined: 24 Aug 2019
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A Re: a + b/10>0   [#permalink] 25 Aug 2019, 06:55
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