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16 Sep 2014, 00:27
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If \(2^{98} = 256*m + n\), where \(m\) and \(n\) are integers and \(0 \le n \le 4\), what is the value of \(n\)?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
16 Sep 2014, 00:27
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Bookmarks
Official Solution:
If \(2^{98} = 256*m + n\), where \(m\) and \(n\) are integers and \(0 \le n \le 4\), what is the value of \(n\)?
A. 0
B. 1
C. 2
D. 3
E. 4
Given:
\(2^{98} = 2^8 * m + n\).
Divide both sides by \(2^8\):
\(2^{90} = m + \frac{n}{2^8}\).
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 \(n = 0\).
Answer: A
If \(2^{98} = 256*m + n\), where \(m\) and \(n\) are integers and \(0 \le n \le 4\), what is the value of \(n\)?
A. 0
B. 1
C. 2
D. 3
E. 4
Given:
\(2^{98} = 2^8 * m + n\).
Divide both sides by \(2^8\):
\(2^{90} = m + \frac{n}{2^8}\).
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 \(n = 0\).
Answer: A
09 Mar 2025, 11:22
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manvisaiwal
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. \(0! = 1! = 1\).
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. \(0! = 1! = 1\).
