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27 Nov 2023, 23:32
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How many different positive two-digit integers are there such that the sum of the two digits is a prime number greater than 11?
A) Four
B) Five
C) Six
D) Seven
E) Eight
A) Four
B) Five
C) Six
D) Seven
E) Eight
27 Nov 2023, 23:52
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pablovaldesvega
How many different positive two-digit integers are there such that the sum of the two digits is a prime number greater than 11?
A) Four
B) Five
C) Six
D) Seven
E) Eight
A) Four
B) Five
C) Six
D) Seven
E) Eight
The maximum sum of two digits is 9 + 9 = 18. Thus, we are looking for primes greater than 11 and less than 18. There are only two such primes: 13 and 17. Each can be expressed as the sum of two digits in various ways:
- 13 = 9 + 4 = 8 + 5 = 7 + 6 = 6 + 7 = 5 + 8 = 4 + 9. This gives us six combinations, forming the numbers 94, 85, 76, 67, 58, and 49.
- 17 = 9 + 8 = 8 + 9. This yields two combinations, forming the numbers 98 and 89.
In total, there are eight such numbers.
Answer: E.
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playthegame
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19 May 2024, 14:23
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Interesting question, I could not think of a creative path to solve this during the mock test, so listed out all the numbers quickly and counted the sum. It took me 3.6mins which was not great but I got the question right.
