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Bunuel
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Bunuel
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rishi02
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I think this is a high-quality question and I agree with explanation.
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Its great question and I'd like to practice a few more of these!
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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vedha0
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pretty easy but worded trickily. nice question.
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I did not quite understand the solution. There is no explanation on why N needs to be 0
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Silcodio
I did not quite understand the solution. There is no explanation on why N needs to be 0

Here is an explanation:

Since both \(2^{90}\) and \(m\) are integers, then \(\frac{n}{2^8}\) must also be an integer. Considering the constraint \(0 \le n \le 4\), this is only possible when \(n = 0\).

So, n can only be 0, 1, 2, 3, or 4. Only if n is 0 do we get an integer value for n/2^8.
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I like the solution - it’s helpful.
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I did not quite understand the solution. how will n=0 make n/2^8 an integer
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manvisaiwal
I did not quite understand the solution. how will n=0 make n/2^8 an integer

If n = 0, then n/2^8 = 0/2^8 = 0, which is an integer.

ZERO:

1. Zero is an INTEGER.

2. Zero is an EVEN integer.

3. Zero is neither positive nor negative (the only one of this kind)

4. Zero is divisible by EVERY integer except 0 itself (\(\frac{0}{x} = 0\), so 0 is a divisible by every number, x).

5. Zero is a multiple of EVERY integer (\(x*0 = 0\), so 0 is a multiple of any number, x)

6. Zero is NOT a prime number (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed: anything/0 is undefined.

8. Any non-zero number to the power of 0 equals 1 (\(x^0 = 1\))

9. \(0^0\) case is NOT tested on the GMAT.

10. If the exponent n is positive (n > 0), \(0^n = 0\).

11. If the exponent n is negative (n < 0), \(0^n\) is undefined, because \(0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0}\), which is undefined. You CANNOT take 0 to the negative power.

12. \(0! = 1! = 1\).
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This is a great question that’s helpful for learning.
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I like the solution - it’s helpful.
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I like the solution - it’s helpful.
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I like the solution - it’s helpful.
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I like the solution - it’s helpful.
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