ISEE Quantitative Comparisons Question 157: Answer and Explanation
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Question: 157
4. A piggy bank contains $2.40 cents in nickels and pennies and contains three times as many pennies as nickels.
(Note: 1 nickel = $0.05; 1 penny = $0.01)
- A. The quantity in Column A is greater.
- B. The quantity in Column B is greater.
- C. The two quantities are equal.
- D. The relationship cannot be determined from the information given.
Correct Answer: A
Explanation:
The answer is A
Let n represent the number of nickels and p represent the number of pennies. Each nickel is, therefore, worth $0.05n, and each penny is worth $0.01p. As the total value of the coins is $2.40, write an equation: $0.05n + $0.01p = $2.40. As there are three times as many pennies as nickels, 3n = p. Substitute 3n for p: $0.05n + $0.01(3n) = $2.40. Simplify: $0.05n + $0.03n = $0.08n = $2.40. Thus n = 30. The value of these 30 nickels is 30 × 0.05 = $1.50.
Test the value in choice (B). If the nickels are worth $1.20, then there are 24 nickels. As there are three times as many pennies as nickels, there are 72 pennies. Add these $0.72 to $1.20 to get $1.92. There should be $2.40, so there are more than 24 nickels.