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How many of the numbers a, b, and c are positive if each of these

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Sisrikhya
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How many of the numbers a, b, and c are positive if each of these [#permalink] New post   06 Aug 2023, 19:09
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How many of the numbers a, b, and c are positive if each of these numbers is less than 20?

(1) a + b + c = 30
(2) a + b = 24

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.
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JHR2021
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Re: How many of the numbers a, b, and c are positive if each of these [#permalink] New post   06 Aug 2023, 21:12
Sisrikhya wrote:
How many of the numbers a, b, and c are positive if each of these numbers is less than 20?

(1) a + b + c = 30
(2) a + b = 24

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

i think it is E. even if we combine both statements we only get info about c, and a, b can still be positive or negative so can't tell for sure. Therefore E.
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Bunuel
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Re: How many of the numbers a, b, and c are positive if each of these [#permalink] New post   07 Aug 2023, 01:28
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Sisrikhya wrote:
How many of the numbers a, b, and c are positive if each of these numbers is less than 20?

(1) a + b + c = 30
(2) a + b = 24

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.


Similar question to practice: https://gmatclub.com/forum/how-many-of- ... 32562.html Hope it helps.
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Re: How many of the numbers a, b, and c are positive if each of these [#permalink] New post   07 Aug 2023, 03:14
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Bunuel wrote:
Sisrikhya wrote:
How many of the numbers a, b, and c are positive if each of these numbers is less than 20?

(1) a + b + c = 30
(2) a + b = 24

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.


Similar question to practice: https://gmatclub.com/forum/how-many-of- ... 32562.html Hope it helps.

hi in the question you suggested one cannot make 'a' negative as explained by you in that answer. but here 'a' or 'b' can become negative and the other two still can add up to 30 while each being less than 20 e.g -5,+16, +19. so in this question Statement A is not sufficient. So i think answer is E. Please correct me if i am wrong.
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Re: How many of the numbers a, b, and c are positive if each of these [#permalink] New post   12 Aug 2023, 03:18
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JHR2021 wrote:
Bunuel wrote:
Sisrikhya wrote:
How many of the numbers a, b, and c are positive if each of these numbers is less than 20?

(1) a + b + c = 30
(2) a + b = 24

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.


Similar question to practice: https://gmatclub.com/forum/how-many-of- ... 32562.html Hope it helps.

hi in the question you suggested one cannot make 'a' negative as explained by you in that answer. but here 'a' or 'b' can become negative and the other two still can add up to 30 while each being less than 20 e.g -5,+16, +19. so in this question Statement A is not sufficient. So i think answer is E. Please correct me if i am wrong.


Statements alone are clearly insufficient. When combining the statements, we deduce that c = 6. Given that each of the numbers a, b, and c is less than 20, and knowing that a + b = 24, we can infer that neither a nor b can be negative or 0. If they were, their sum would not reach 24. Thus, we can conclude that all three numbers are positive. Therefore, the answer is C.

Hope it helps.
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Re: How many of the numbers a, b, and c are positive if each of these [#permalink]
12 Aug 2023, 03:18
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Bunuel
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