GMAT Exam  >  GMAT Questions  >  If X is a positive integer, is X divisible by... Start Learning for Free
If X is a positive integer, is X divisible by 4?
(1) X has at least two 2s in its prime factorization
(2) X is divisible by 2
  • 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 'A'. Can you explain this answer?
Most Upvoted Answer
If X is a positive integer, is X divisible by 4?(1) X has at least two...
  1. A number is divisible by any of its prime factors or any combination of its prime factors. For a number to be divisible by four, it must have two 2s in its prime factorization since 2 x 2 = 4 and, if 4 is a factor of X, X will be divisible by 4.
  2. Evaluate Statement (1) alone.
    1. Since X has two 2s in its prime factorization, 4 must be a factor of X and, consequently, X must be divisible by 4. Statement (1) is SUFFICIENT.
    2. If this seems too abstract, consider the following examples which show that whenever X has at least two 2s in its prime factorization (which it must as per Statement (1)), X is divisible by 4:
      X = 4: has two 2s in its prime factorization and, as a result, is divisible by 4
      X = 6: has only one 2 in its prime factorization and, as a result, is not divisible by 4
      X = 8: has at least two 2s in its prime factorization and, as a result, is divisible by 4
      X = 10: has only one 2 in its prime factorization and, as a result, is not divisible by 4
    3. Since X cannot be 6, 10, etc. as these values do not have at least two 2s as prime factors (as is required by Statement (1)), X can only be 4, 8, etc. and will always be divisible by 4.
    4. Statement (1) alone is SUFFICIENT.
  3. Evaluate Statement (2) alone.
    1. If X is divisible by 2, you know that X must have at least one 2 in its prime factorization. However, you do not know that X has two 2s in its prime factorization and, as a result, you cannot be sure that X is divisible by 4.
    2. If this seems too abstract, consider the following examples, all of which are divisible by 2 in keeping with the requirements of Statement (2):
      X = 4: has two 2s in its prime factorization and, as a result, is divisible by 4
      X = 6: has only one 2 in its prime factorization and, as a result, is not divisible by 4
      X = 8: has at least two 2s in its prime factorization and, as a result, is divisible by 4
      X = 10: has only one 2 in its prime factorization and, as a result, is not divisible by 4
    3. Statement (2) alone is NOT SUFFICIENT.
  4. Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
Free Test
Community Answer
If X is a positive integer, is X divisible by 4?(1) X has at least two...
  1. A number is divisible by any of its prime factors or any combination of its prime factors. For a number to be divisible by four, it must have two 2s in its prime factorization since 2 x 2 = 4 and, if 4 is a factor of X, X will be divisible by 4.
  2. Evaluate Statement (1) alone.
    1. Since X has two 2s in its prime factorization, 4 must be a factor of X and, consequently, X must be divisible by 4. Statement (1) is SUFFICIENT.
    2. If this seems too abstract, consider the following examples which show that whenever X has at least two 2s in its prime factorization (which it must as per Statement (1)), X is divisible by 4:
      X = 4: has two 2s in its prime factorization and, as a result, is divisible by 4
      X = 6: has only one 2 in its prime factorization and, as a result, is not divisible by 4
      X = 8: has at least two 2s in its prime factorization and, as a result, is divisible by 4
      X = 10: has only one 2 in its prime factorization and, as a result, is not divisible by 4
    3. Since X cannot be 6, 10, etc. as these values do not have at least two 2s as prime factors (as is required by Statement (1)), X can only be 4, 8, etc. and will always be divisible by 4.
    4. Statement (1) alone is SUFFICIENT.
  3. Evaluate Statement (2) alone.
    1. If X is divisible by 2, you know that X must have at least one 2 in its prime factorization. However, you do not know that X has two 2s in its prime factorization and, as a result, you cannot be sure that X is divisible by 4.
    2. If this seems too abstract, consider the following examples, all of which are divisible by 2 in keeping with the requirements of Statement (2):
      X = 4: has two 2s in its prime factorization and, as a result, is divisible by 4
      X = 6: has only one 2 in its prime factorization and, as a result, is not divisible by 4
      X = 8: has at least two 2s in its prime factorization and, as a result, is divisible by 4
      X = 10: has only one 2 in its prime factorization and, as a result, is not divisible by 4
    3. Statement (2) alone is NOT SUFFICIENT.
  4. Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
Attention GMAT Students!
To make sure you are not studying endlessly, EduRev has designed GMAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GMAT.
Explore Courses for GMAT exam

Top Courses for GMAT

If X is a positive integer, is X divisible by 4?(1) X has at least two 2s in its prime factorization(2) X is divisible by 2a)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 'A'. Can you explain this answer?
Question Description
If X is a positive integer, is X divisible by 4?(1) X has at least two 2s in its prime factorization(2) X is divisible by 2a)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 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If X is a positive integer, is X divisible by 4?(1) X has at least two 2s in its prime factorization(2) X is divisible by 2a)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 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If X is a positive integer, is X divisible by 4?(1) X has at least two 2s in its prime factorization(2) X is divisible by 2a)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 'A'. Can you explain this answer?.
Solutions for If X is a positive integer, is X divisible by 4?(1) X has at least two 2s in its prime factorization(2) X is divisible by 2a)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 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of If X is a positive integer, is X divisible by 4?(1) X has at least two 2s in its prime factorization(2) X is divisible by 2a)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 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of If X is a positive integer, is X divisible by 4?(1) X has at least two 2s in its prime factorization(2) X is divisible by 2a)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 'A'. Can you explain this answer?, a detailed solution for If X is a positive integer, is X divisible by 4?(1) X has at least two 2s in its prime factorization(2) X is divisible by 2a)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 'A'. Can you explain this answer? has been provided alongside types of If X is a positive integer, is X divisible by 4?(1) X has at least two 2s in its prime factorization(2) X is divisible by 2a)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 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice If X is a positive integer, is X divisible by 4?(1) X has at least two 2s in its prime factorization(2) X is divisible by 2a)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 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.
Explore Courses for GMAT exam

Top Courses for GMAT

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev