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If integer k > 0 and x2 − 7x + k = 0, what is the value of k?
(1) Both roots are prime number
(2) 2 is one of root of the equation
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
  • d)
    EACH statement ALONE is sufficient to answer the question asked
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If integer k > 0 and x2 − 7x + k = 0, what is the value of k?...
Viete's theorem states that for the roots x1 and xof a quadratic equation ax2 + bx + c = 0:
x1 + x2 = -b/a and x1∗x2 = c/a.
(1) Both roots are prime number.
According to the theorem:  x1 + x2 = -b/a = 7.7 can be expressed as the sum of two primes only in one way 2 + 5 = 7. Knowing the roots we can find the value of k. Sufficient.
(2) 2 is one of root of the equation. Plug x = 2: 22 − 7*2 + k = 0. We can find k. Sufficient.
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If integer k > 0 and x2 − 7x + k = 0, what is the value of k?(1) Both roots are prime number(2) 2 is one of root of the equationa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?
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If integer k > 0 and x2 − 7x + k = 0, what is the value of k?(1) Both roots are prime number(2) 2 is one of root of the equationa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If integer k > 0 and x2 − 7x + k = 0, what is the value of k?(1) Both roots are prime number(2) 2 is one of root of the equationa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If integer k > 0 and x2 − 7x + k = 0, what is the value of k?(1) Both roots are prime number(2) 2 is one of root of the equationa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?.
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