Consider a three-digit positive integer x, where the hundreds, tens, and units digits are represented by a, b, and c, respectively. Another three-digit positive integer y has its hundreds, tens, and units digits as k, l, and m. Given that (2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m), what is the difference x – y?

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310

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Official Explanation

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Let x be represented as abc, where a, b, and c denote the hundreds, tens, and units digits, respectively. Similarly, let y be represented as klm, where k, l, and m are the hundreds, tens, and units digits. The equation (2^a)(3^b)(5^c) = 12(2^k)(3^l)(5^m) can be rewritten as…

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PrashantNov 20, 2024

Thanks for sharingThank you for sharing!!thanks for sharing

What this question tests

What it tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Common trap

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).