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03 Jun 2026, 03:37
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Difficulty:
35%
(medium)
Question Stats:
73% (01:17) correct
27%
(01:35)
wrong
based on 59
sessions
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If w is an integer and \((21.6)(36)(0.0006)(60)(10^w)\) is an integer, what is the least possible value of w?
A. 4
B. 3
C. 0
D. -3
E. -4
A. 4
B. 3
C. 0
D. -3
E. -4
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03 Jun 2026, 15:13
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If w is an integer and \((21.6)(36)(0.0006)(60)(10^w)\) is an integer, what is the least possible value of w?
A. 4
B. 3
C. 0
D. -3
E. -4
No need to multiply everything out.
21.6 has 1 decimal place, and 0.0006 has 4 decimal places, so together they create 5 decimal places.
Now look for factors of 10 in the other factors. The factor 60 contributes one factor of 10, so it removes one decimal place.
The factor 36 has no factor of 5, so it cannot create another factor of 10. Therefore, no more decimal places are removed.
So we still need 10^4 to make the product an integer.
Therefore, the least possible value of w is 4.
Answer: A.
A. 4
B. 3
C. 0
D. -3
E. -4
No need to multiply everything out.
21.6 has 1 decimal place, and 0.0006 has 4 decimal places, so together they create 5 decimal places.
Now look for factors of 10 in the other factors. The factor 60 contributes one factor of 10, so it removes one decimal place.
The factor 36 has no factor of 5, so it cannot create another factor of 10. Therefore, no more decimal places are removed.
So we still need 10^4 to make the product an integer.
Therefore, the least possible value of w is 4.
Answer: A.
