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Was the number of candles sold at supermarket A greater?

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by gmatdriller » Wed Nov 07, 2012 2:01 am
Was the numberr of candles sold at supermarket A greater than the number of candles sold at supermarket B last week?
(1) last week, more than 1,000 candles were sold at supermarket A on Saturday and fewer than 1,000 candles were sold at supermarket B on Saturday.
(2) last week, less than 20% of the candles sold at supermarket A were sold on Saturday and more
than 20% of the candles sold at supermarket B were sold on Saturday

OA is C
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Source: — Data Sufficiency |

by GMATGuruNY » Wed Nov 07, 2012 7:46 am
gmatdriller wrote:Was the numberr of candles sold at supermarket A greater than the number of candles sold at supermarket B last week?
(1) last week, more than 1,000 candles were sold at supermarket A on Saturday and fewer than 1,000 candles were sold at supermarket B on Saturday.
(2) last week, less than 20% of the candles sold at supermarket A were sold on Saturday and more
than 20% of the candles sold at supermarket B were sold on Saturday

OA is C
Statement 1: No information about the other days of the week. INSUFFICIENT.
Statement 2: Since there is no upper or lower limit to the number of candles sold at each store, there is no way to determine whether more candles were sold at supermarket A. INSUFFICIENT.

Statements combined:
PLUG IN THE THRESHOLDS.
Here, the thresholds are 1000 and 20%.

Supermarket A:
If 1000 candles sold on Saturday were 20% of the weekly total, we get:
1000 = .2A
A = 1000/.2 = 5000.
Since the numerator here must actually be GREATER THAN 1000 (since MORE than 1000 candles were sold on Saturday), and the denominator must be LESS THAN .2 (since the number of candles sold on Saturday was LESS than 20% of the weekly total), the actual value of A must be GREATER THAN 5000.

Supermarket B:
If 1000 candles sold on Saturday were 20% of the weekly total, we get:
1000 = .2B
B = 1000/.2 = 5000.
Since the numerator here must actually be LESS THAN 1000 (since FEWER than 1000 candles were sold on Saturday), and the denominator must be GREATER THAN .2 (since the number of candles sold on Saturday was MORE than 20% of the weekly total), the actual value of B must be LESS THAN 5000.

Since A>5000 and B<5000, A>B.
SUFFICIENT.

The correct answer is C.
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by Jim@StratusPrep » Wed Nov 07, 2012 7:50 am
1) We don't know anything about the rest of the week
2) We don't know anything about the number on Saturday so this number cannot help us.

Together, we know that A sold more than 5,000 candles since 1,000 is 20% of 5,000 and B sold less than 5,000 for the same reason.

The answer is C.
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