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by candygal79 » Thu Mar 13, 2014 6:43 am
A certain number of people wait in line at a bank until served. How many people are presently in line?

(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.

(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.
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Source: — Data Sufficiency |
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by Bill@VeritasPrep » Thu Mar 13, 2014 8:34 am
I assigned L to represent the number of people in line.

From Statement 1, we add 2 people to the line, so L + 2 >= 10. We can simplify to L >=8, but we can't find an exact value for L. Insufficient.

From Statement 2, we remove 4 people from the line, so L - 4 < 5. We can simplify to L < 9, but we can't find an exact value for L. Insufficient.

When we combine them, we need a value that satisfies both statements: L must be less than 9 but greater than or equal to 8. This leaves 8 as the only possibility.
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by candygal79 » Thu Mar 13, 2014 3:00 pm
Thank you so much for the explanation !
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by Bill@VeritasPrep » Fri Mar 14, 2014 2:41 pm
No problem! That's why we're here :D
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by [email protected] » Sat Mar 15, 2014 12:13 pm
Hi candygal79,

Bill's approach to this question focused on translating the sentences into algebra. You can also work through the "logic" behind each statement and break it into real-world terms.

We're asked how many people are in a line.

Fact 1: If 2 more people joined the line and none left, there would be AT LEAST 10 people in line.

If adding 2 more people puts 10 (or more) people into the line, then the current number of people has to be 8 or greater (9, 10, 11, etc.)
Fact 1 is INSUFFICIENT

Fact 2: If no more people joined the line and 4 were served (meaning they left), there would be FEWER than 5 people in line.

"fewer than 5 people" would be 0 to 4 people. This means that right now there must be 4, 5, 6, 7 or 8 people in line.
Fact 2 is INSUFFICIENT

When combining Facts, we have to look for "overlap"; the only answer that overlaps is 8.
Combined, SUFFICIENT

Final Answer: C

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