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Directions: The data sufficiency problem consists of a question and two statements, labeled (1)
and (2), in which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question. Using the data given in the statements plus
your knowledge of mathematics and everyday facts (such as the number of days in July or the
meaning of counterclockwise), you must indicate whether
Q.
x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?
1) 5 is a factor of x.
2) x is an integer.
and (2), in which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question. Using the data given in the statements plus
your knowledge of mathematics and everyday facts (such as the number of days in July or the
meaning of counterclockwise), you must indicate whether
Q.
x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?
1) 5 is a factor of x.
2) x is an integer.
- 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) TO GETHER are sufficient to answer the question
asked, but NEITHER statement ALONE is sufficient; - d)EACH statement ALONE is suffi cient to answer the question asked;
- e)statements (1} and (2) TOGETHER are NOT sufficient to answer the question
asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Directions: The data sufficiency problem consists of a question and tw...
The key to this problem is to recognize that in order for any integer to be divisible by 5, it
must end in 0 or 5. Since we are adding a string of powers of 9, the question becomes
"Does the sum of these powers of 9 end in 0 or 5?" If we knew the units digits of each
power of nine, we'd be able to figure out the units digit of their sum.
9 raised to an even exponent will result in a number whose units digit is 1 (e.g., 92 = 81,
94 = 6561, etc.). If 9 raised to an even exponent always gives 1 as the units digit, then 9
raised to an odd exponent will therefore result in a number whose units digit is 9 (think
about this: 92 = 81, so 93 will be 81 x 9 and the units digit will be 1 x 9).
Since our exponents in this case are x, x+1, x+2, x+3, x+4, and x+5, we need to know
whether x is an integer in order to be sure the pattern holds. (NEVER assume that an
unknown is an integer unless expressly informed). If x is in fact an integer, we will have
6 consecutive integers, of which 3 will necessarily be even and 3 odd. The 3 even
exponents will result in 1's and the 3 odd exponents will result in 9's. Since the three 1's
can be paired with the three 9's (for a sum of 30), the units digit of y will be 0 and y
will thus be divisible by 5. But we don't know whether x is an integer. For that, we need
to check the statements.
Statement (1) tells us that 5 is a factor of x, which means that x must be an integer.
Sufficient.
Statement (2) tells us that x is an integer. Sufficient.
The correct answer is D: EACH statement ALONE is sufficient to answer the question.
must end in 0 or 5. Since we are adding a string of powers of 9, the question becomes
"Does the sum of these powers of 9 end in 0 or 5?" If we knew the units digits of each
power of nine, we'd be able to figure out the units digit of their sum.
9 raised to an even exponent will result in a number whose units digit is 1 (e.g., 92 = 81,
94 = 6561, etc.). If 9 raised to an even exponent always gives 1 as the units digit, then 9
raised to an odd exponent will therefore result in a number whose units digit is 9 (think
about this: 92 = 81, so 93 will be 81 x 9 and the units digit will be 1 x 9).
Since our exponents in this case are x, x+1, x+2, x+3, x+4, and x+5, we need to know
whether x is an integer in order to be sure the pattern holds. (NEVER assume that an
unknown is an integer unless expressly informed). If x is in fact an integer, we will have
6 consecutive integers, of which 3 will necessarily be even and 3 odd. The 3 even
exponents will result in 1's and the 3 odd exponents will result in 9's. Since the three 1's
can be paired with the three 9's (for a sum of 30), the units digit of y will be 0 and y
will thus be divisible by 5. But we don't know whether x is an integer. For that, we need
to check the statements.
Statement (1) tells us that 5 is a factor of x, which means that x must be an integer.
Sufficient.
Statement (2) tells us that x is an integer. Sufficient.
The correct answer is D: EACH statement ALONE is sufficient to answer the question.
Most Upvoted Answer
Directions: The data sufficiency problem consists of a question and tw...
Understanding the Problem
The question asks if the expression y = 9^x + 9^(x+1) + 9^(x+2) + 9^(x+3) + 9^(x+4) + 9^(x+5) is divisible by 5.
Analyzing the Expression
- The expression can be rewritten as y = 9^x (1 + 9 + 9^2 + 9^3 + 9^4 + 9^5).
- The sum inside the parentheses can be simplified using the formula for a geometric series.
Divisibility by 5
- To determine if y is divisible by 5, we need to check if both components (9^x and the geometric series sum) influence divisibility.
- The term 9^x is crucial since 9 is not divisible by 5; we need to check the sum.
Evaluating Statement (1)
- Statement (1): "5 is a factor of x."
- If x is a multiple of 5, then 9^x mod 5 = 4, and 9^1 mod 5 = 4.
- The geometric series sum mod 5 needs to be evaluated separately.
- Thus, statement (1) alone does not provide sufficient information.
Evaluating Statement (2)
- Statement (2): "x is an integer."
- While x being an integer confirms that 9^x is a whole number, it does not give information about divisibility by 5.
- This statement alone does not help in concluding whether y is divisible by 5.
Conclusion
- Since neither statement alone provides sufficient information, but both together do not either, the correct answer is option 'D': EACH statement ALONE is sufficient to answer the question asked.
The question asks if the expression y = 9^x + 9^(x+1) + 9^(x+2) + 9^(x+3) + 9^(x+4) + 9^(x+5) is divisible by 5.
Analyzing the Expression
- The expression can be rewritten as y = 9^x (1 + 9 + 9^2 + 9^3 + 9^4 + 9^5).
- The sum inside the parentheses can be simplified using the formula for a geometric series.
Divisibility by 5
- To determine if y is divisible by 5, we need to check if both components (9^x and the geometric series sum) influence divisibility.
- The term 9^x is crucial since 9 is not divisible by 5; we need to check the sum.
Evaluating Statement (1)
- Statement (1): "5 is a factor of x."
- If x is a multiple of 5, then 9^x mod 5 = 4, and 9^1 mod 5 = 4.
- The geometric series sum mod 5 needs to be evaluated separately.
- Thus, statement (1) alone does not provide sufficient information.
Evaluating Statement (2)
- Statement (2): "x is an integer."
- While x being an integer confirms that 9^x is a whole number, it does not give information about divisibility by 5.
- This statement alone does not help in concluding whether y is divisible by 5.
Conclusion
- Since neither statement alone provides sufficient information, but both together do not either, the correct answer is option 'D': EACH statement ALONE is sufficient to answer the question asked.
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Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?
Question Description
Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. 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 Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?.
Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. 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 Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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Here you can find the meaning of Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwise), you must indicate whetherQ.x is a positive number. If 9x + 9x+1 + 9x+2 + 9x+3 + 9x+4 + 9x+5 = y, is y divisible by 5?1) 5 is a factor of x.2) x is an integer.a)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient toanswer the question asked;b)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient toanswer the question asked;c)BOTH statements (1) and (2) TO GETHER are sufficient to answer the questionasked, but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is suffi cient to answer the question asked;e)statements (1} and (2) TOGETHER are NOT sufficient to answer the questionasked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
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