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What is the greatest integer x for which

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by VJesus12 » Thu Nov 16, 2017 7:31 am
What is the greatest integer x for which $$\frac{24,300,000,000}{2^x}$$ is an integer?

A. 8
B. 9
C. 10
D. 11
E. 12

The OA is A .

How can I find the correct answer? Should I try number by number? Experts, may you help me?
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by GMATGuruNY » Thu Nov 16, 2017 7:57 am
VJesus12 wrote:What is the greatest integer x for which $$\frac{24,300,000,000}{2^x}$$ is an integer?

A. 8
B. 9
C. 10
D. 11
E. 12

The OA is A .

How can I find the correct answer? Should I try number by number? Experts, may you help me?
(24,300,000,000)/(2^x)

= (243 * 10�)/(2^x)

= (243 * 2� * 5�)/(2^x).

The values in blue indicate that the greatest possible value for x is 8.

The correct answer is A.
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by Scott@TargetTestPrep » Wed Oct 16, 2019 6:09 pm
VJesus12 wrote:What is the greatest integer x for which $$\frac{24,300,000,000}{2^x}$$ is an integer?

A. 8
B. 9
C. 10
D. 11
E. 12

The OA is A .

How can I find the correct answer? Should I try number by number? Experts, may you help me?

Simplifying the numerator, we have:

243 x 10^8 = 243 x 2^8 x 5^8

Therefore, we see that the maximum value of x is 8.

Answer: A
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