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If s and t are positive integers greater than 1 and s • t = 30, which
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17 Dec 2021, 06:59
17 Dec 2021, 06:59
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If s and t are positive integers greater than 1 and s • t = 30, which of the following must be true?
I. s + t is even
II. Either s or t is a prime number
III. s + t + 1 is divisible by 3
(A) I
(B) II
(C) III
(D) I and II
(E) II and III
I. s + t is even
II. Either s or t is a prime number
III. s + t + 1 is divisible by 3
(A) I
(B) II
(C) III
(D) I and II
(E) II and III
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Re: If s and t are positive integers greater than 1 and s • t = 30, which
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17 Dec 2021, 07:36
17 Dec 2021, 07:36
1
Carcass wrote:
If s and t are positive integers greater than 1 and s • t = 30, which of the following must be true?
I. s + t is even
II. Either s or t is a prime number
III. s + t + 1 is divisible by 3
(A) I
(B) II
(C) III
(D) I and II
(E) II and III
I. s + t is even
II. Either s or t is a prime number
III. s + t + 1 is divisible by 3
(A) I
(B) II
(C) III
(D) I and II
(E) II and III
Given: s and t are positive integers greater than 1 and s • t = 30
Since there aren't many possible pairs of values that meet the above conditions, let's start by listing all possible outcomes in the form (s, t):
(2, 15)
(3, 10)
(5, 6)
(6, 5)
(10, 3)
(15, 2)
Now we'll check the three statements...
I. s + t is even
This is definitely not true. In fact NONE of the 6 possible outcomes have an even sum.
So, statement I need not be true, which means we can eliminate answer choices A and D, since they say statement I must be true.
II. Either s or t is a prime number
Since every pair of possible values includes a prime number, statement II is definitely true.
This means we can eliminate answers choice C since it says statement II is not true.
III. s + t + 1 is divisible by 3
When we check the pairs of possible values, we see that s = 3 and t = 10 does not meet this condition.
That is, 3 + 10 + 1 is NOT divisible by 3.
So, statement III need not be true, which means we can eliminate answer choice E, since it says statement III must be true.
Answer: B
Re: If s and t are positive integers greater than 1 and s • t = 30, which
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17 Dec 2021, 08:31
17 Dec 2021, 08:31
1
I) s+t is even? Need not be, take s=5, t=6
I is incorrect
II) either s or t is prime? Yes. Factorize 30 into prime factors, we obtain: 2,3,5.
So we can take: 6 and 5, 15 and 2, 10 and 3, in each of the cases, we obtain a prime number. So either s or t MUST be a prime
II is correct
III) s + t + 1 is divisible by 3? No, take s and t as 10 and 3 respectively, 10+3+1 = 14 which is not divisible by 3
III incorrect
Answer: B
I is incorrect
II) either s or t is prime? Yes. Factorize 30 into prime factors, we obtain: 2,3,5.
So we can take: 6 and 5, 15 and 2, 10 and 3, in each of the cases, we obtain a prime number. So either s or t MUST be a prime
II is correct
III) s + t + 1 is divisible by 3? No, take s and t as 10 and 3 respectively, 10+3+1 = 14 which is not divisible by 3
III incorrect
Answer: B
