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by GMATGuruNY » Sun Sep 28, 2014 2:49 am
If (a + 12b)/4b = 18/5, which of the following can be determined?

I: a/b
II: 5b/(a + 7b)
III: (a + 3)/(b + 5)
(a + 12b)/4b = 18/5.
Cross-multiplying, we get:
5a + 60b = 72b
5a = 12b
a/b = 12/5.

I: a/b
a/b = 12/5.
The value of I can be determined.

To evaluate II and III, test TWO CASES.

II: 5b/(a + 7b)
Case 1: a=12, b=5
In this case, 5b/(a + 7b) = (5*5)/(12 + 7*5) = 25/47.

Case 2: a=24, b=10
In this case, 5b/(a + 7b) = (5*10)/(24 + 7*10) = 50/94 = 25/47.

Since in each case the result is the same -- 25/47 -- the value of II can be determined.

III: (a + 3)/(b + 5)
Case 1: a=12, b=5
In this case, (a + 3)/(b + 5) = (12+3)/(5+5) = 15/10 = 3/2.

Case 2: a=24, b=10
In this case, (a + 3)/(b + 5) = (24+3)/(10+5) = 27/15 = 9/5.

Since the result is NOT the same in each case, the value of III cannot be determined.
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by fermar84 » Sun Sep 28, 2014 6:26 am
Thank you, one more question, why do you test for two values (12/5 and 24/10)? I know they are multiples of each other but why is needed to test them?

Thanks again,
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by [email protected] » Sun Sep 28, 2014 10:17 am
Hi Fernando,

This question requires the same type of work as a typical DS question. When it asks "which of the following can be determined..." what it's really asking is "which of the following has just one answer, regardless of the values you use for A and B."

Mitch went about dealing with Roman Numerals II and III in the most efficient way possible - TESTing VALUES for A and B and using the smallest integer values that were possible. Roman Numeral III showed inconsistent results, so THAT value cannot be determined.

If you had included the 5 answer choices, then we might have been able to stop there (Roman Numeral I can be determined, while III cannot - it's possible that just one of the answer choices would "match" that evidence). Without the answer choices, we have to assess Roman Numeral II. Notice that the end result stays the same - thus, it's consistent and CAN be determined.

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