A and B are integers greater than 1 and A^3 x B is a multiple of 10.

Question

A and B are integers greater than 1 and A^3 x B is a multiple of 10. Which of the following must be a multiple of 8,000 ?

A. A*B^3
B. A^3 * B^3
C. A^3 * B^6
D. A^6 * B^3
E. A^6 * B^6

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ineedbananas · Answer

8000 = 2^6 * 5^3

for a multiple of 10 we are getting 2^1 and 5^1 from either A or B. Since we need at least 6 2s - A^6 B^6 is the only option that satisfies that.

E

Dereno · Answer

A and B are greater than 1.

A^3 x B is a multiple of 10 = 2*5*K

case 1: A=2 and B=5

case 2: A=5 and B=2.

Multiple of 8,000 = 2^3 * 100*10 = 2^3 * 5^2 * 2^2 * 2*5 = 2^6 * 5^3

Must be a multiple of 8000.

2^6 * 5^3 = A^6 * B^3

A. A*B^3.

This cannot be the answer.

B. A^3 * B^3.

But, we have a power of 6. Hence, wrong.

C. A^3 * B^6.

B can be 2 or 5. Hence, Wrong.

D. A^6 * B^3.

A can be 2 or 5. Hence, Wrong.

E. A^6 * B^6

Even with A or B being either of 2 or 5, will definitely be a multiple of 8000.

Hence,  Option E

ExpertsGlobal5 · Answer

Video explanation:

https://www.youtube.com/watch?v=odeb9HhDf04

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