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18 Oct 2021, 07:59
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Walkabout
Answer: Option B
Step-by-Step Video solution by GMATinsight
05 Nov 2022, 10:45
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Given: For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b.
Asked: If k is a positive integer and 2^k||72, then k is equal to
72 = 2^3*3^2
2^3 is a divisor of 72 but 2^4 is not a divisor of 72
k = 3
IMO B
Asked: If k is a positive integer and 2^k||72, then k is equal to
72 = 2^3*3^2
2^3 is a divisor of 72 but 2^4 is not a divisor of 72
k = 3
IMO B
22 Jan 2026, 23:08
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Hi Walkabout,
I understand the notation can be confusing! Let me break down what a^k||b means in simple terms:
The notation a^k||b means:
• a^kdividesb evenly (no remainder)
• a^(k+1) does NOT divide b evenly
In other words, k is the highest power of a that divides b.
For this problem:
We need to find k such that 2^k||72
This means:
• 2^k divides 72
• 2^(k+1) does NOT divide 72
Solution:
Let's find the prime factorization of 72:
72 = 8 × 9 = 2^3 × 3^2
Since 72 contains exactly 2^3 (and no higher powers of 2):
• 2^3 divides 72 ✓
• 2^4 does NOT divide 72 ✓
Therefore,k = 3
Answer: B
Hope this clarifies the notation!
I understand the notation can be confusing! Let me break down what a^k||b means in simple terms:
The notation a^k||b means:
• a^kdividesb evenly (no remainder)
• a^(k+1) does NOT divide b evenly
In other words, k is the highest power of a that divides b.
For this problem:
We need to find k such that 2^k||72
This means:
• 2^k divides 72
• 2^(k+1) does NOT divide 72
Solution:
Let's find the prime factorization of 72:
72 = 8 × 9 = 2^3 × 3^2
Since 72 contains exactly 2^3 (and no higher powers of 2):
• 2^3 divides 72 ✓
• 2^4 does NOT divide 72 ✓
Therefore,k = 3
Answer: B
Hope this clarifies the notation!
sebarm95
