Question 25 A store owner decided to increase the price of an item by exactly 10%.
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A store owner decided to increase the price of an item by exactly 10%. Which of the following cannot be the price of the new item? The original price of the item was a whole number of dollars.
Select any one of the following options
Show answer & explanation
Answer: C. C) $78
The new price is 1.10 * P = (11/10) * P. For original price P to be a whole number of dollars, the new price multiplied by 10/11 must be an integer. 78 * 10/11 = 70.91, which is not an integer.
Step-by-step Derivation:
Step 1: Let P be the original integer price. New price N = P * 1.10 = (11/10)P => P = (10/11)N.
Step 2: Check each option:
- $22: P = 22 * 10/11 = 20 (integer)
- $132: P = 132 * 10/11 = 120 (integer)
- $78: P = 780 / 11 = 70.909... (not an integer)
- $99: P = 99 * 10/11 = 90 (integer)
Step 3: Hence, $78 cannot be the price of the new item.