IF $N=5^5\times10^{10}\times15^{15}\times20^{20}\times25^{25}\times30^{30}\times35^{35}\times40^{40}\times45^{45}\times50^{50}$ , then how many zeroes exist between decimal and first non zero digit of N?

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150

200

250

Correct

300

350

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Explanation

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Official Explanation

Official

For calculating zeros at the end we should calculate quantity of "2" and "5" in the final number.

In all numbers which end at 5 we don't have any "2" but have a lot of "5". So in final number we will have more "5" than "2" and we need to calculate quantity of "2" in each number:

10

– one "2" in 10, exponent = 10 →

1 \times 10 = 10

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What this question tests

What it tests

Your handling of square and higher roots, including simplifying radicals.

Common trap

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.