Free Practice Question
PS · Problem Solving
705-805
percent
On day 1, a shopkeeper increases the price of an item by k%, and on day 2, he decreases the increased price by k%. By the end of the day 2, the price of the item drops by $1. On day 3, he again increases the decreased price by k%, and on day 4, he again decreases the increased price by k%. If, at the end of day 4, the price of the item comes to $398, what was the approximate initial price of the item?
Answer Choices
Correct answer marked belowA
$325
B
$350
C
$375
$400
Correct
E
$450
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Explanation
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Official Explanation
Official
Let's assume initial price = (Day 0).
Day 1:
Day 2:
It's given that:
On solving:
Plugging in in all equations:
Day 0 =
Day 1 =
Day 2 =
Now:
Day 3 = …
Day 1:
Day 2:
It's given that:
On solving:
Plugging in in all equations:
Day 0 =
Day 1 =
Day 2 =
Now:
Day 3 = …
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What it tests
Your ability to apply GMAT math concepts to solve a multi-step problem quickly and accurately. At the 705-805 level, accuracy and speed both matter.
Common trap
Overcomplicating the setup — most GMAT problems reward a direct, organized approach over brute calculation.
Related GMAT Topic Guides
Quant
TopicGMAT Quantitative Reasoning
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Difficulty
705-805
Type
PS
Category