ISEE Quantitative Comparisons Question 165: Answer and Explanation

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Question: 165

6. The product of three consecutive whole numbers is 504.

  • 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:

A

You might start by setting up an equation, but you will see that it quickly becomes ugly: (x)(x + 1)(x + 2) = 504, so (x2 + x)(x + 2) = 504. So, try another approach, such as breaking 504 into its prime factors: 7 × 23 × 32. This means that the three numbers are 7, 8, and 9. As 7 > 6, choice (A) is correct.

As there is an unknown value in one column and a known value in the other, test the known value against the unknown value. That is, assume that 6 is the least of the three numbers. The numbers would be 6, 7, and 8, with a product of 336. As 336 < 504, the least of the three numbers is greater than 6.

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