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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Two different primes may be said to "rhyme" around an integer if they
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15 Apr 2021, 00:54
15 Apr 2021, 00:54
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Two different primes may be said to "rhyme" around an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
A. 12
B. 15
C. 17
D. 18
E. 20
A. 12
B. 15
C. 17
D. 18
E. 20
Re: Two different primes may be said to "rhyme" around an integer if they
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15 Apr 2021, 02:07
15 Apr 2021, 02:07
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Test answer choices
A. 12
Possible cases:
11, 12, 13
7, 12, 17
5, 12, 19
B. 15
Possible cases:
13, 15, 17
11, 15, 19
In other answer choices, there cannot be more possible cases than option A, since more prime numbers on the right of the given number will not be available.
Hence, A is the correct answer.
A. 12
Possible cases:
11, 12, 13
7, 12, 17
5, 12, 19
B. 15
Possible cases:
13, 15, 17
11, 15, 19
In other answer choices, there cannot be more possible cases than option A, since more prime numbers on the right of the given number will not be available.
Hence, A is the correct answer.
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Re: Two different primes may be said to "rhyme" around an integer if they
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15 Apr 2021, 06:13
15 Apr 2021, 06:13
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GeminiHeat wrote:
Two different primes may be said to "rhyme" around an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
A. 12
B. 15
C. 17
D. 18
E. 20
A. 12
B. 15
C. 17
D. 18
E. 20
If two numbers are rhyming primes, then the integer they rhyme around will be the AVERAGE of the two primes.
For example, 3 and 7 rhyme around 5. Notice that the AVERAGE of 3 and 7 is 5.
Likewise, 5 and 23 rhyme around 14, and the AVERAGE of 5 and 23 is 14.
Now onto the solution...
List several primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,....
Now check the answer choices:
A)12
For 12 to be the integer that two primes rhyme around, we need 2 primes that have an AVERAGE of 12. In other words, we need 2 primes that ADD to 24. Now check the list of primes to find pairs that satisfy this condition.
We get: 5 & 19, 7 & 17, 11 & 13
Total of 3 pairs.
B)15
So, we need 2 distinct primes that ADD to 30.
We get: 7 & 23, 11 & 19, 13 & 17
Total of 3 pairs.
C)17
So, we need 2 distinct primes that ADD to 34.
We get: 3 & 31, 5 & 29, 11 & 23
Total of 3 pairs.
D)18
So, we need 2 distinct primes that ADD to 36.
We get: 5 & 31, 7 & 29, 13 & 23, 17 & 19
Total of 4 pairs.
E)20
So, we need 2 distinct primes that ADD to 40.
We get: 3 & 37, 11 & 29, 17 & 23
Total of 3 pairs.
Answer: D
Cheers,
Brent
