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This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -
Q. When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?
1. When 2x is divided by d, the remainder is 23.
2. When 3x is divided by d, the remainder is 22
2. When 3x is divided by d, the remainder is 22
- 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 to answer the question asked.
- 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 specific to the problem are needed.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
This data sufficiency problem consists of a question and two statement...
Step 1 of solving this GMAT DS question: Understand the Question Stem
What kind of an answer will the question fetch?
The question is a "What is the value?" question. For questions asking for a value, the answer should be a number.
The question is a "What is the value?" question. For questions asking for a value, the answer should be a number.
When is the data sufficient?
The data is sufficient if we are able to get a UNIQUE answer for the value of 'd' from the information in the statements.
If either the statements do not have adequate data to determine the value of 'd' or if more than one value of 'd' exists based on the information in the statement, the data is NOT sufficient.
The data is sufficient if we are able to get a UNIQUE answer for the value of 'd' from the information in the statements.
If either the statements do not have adequate data to determine the value of 'd' or if more than one value of 'd' exists based on the information in the statement, the data is NOT sufficient.
What do we know from the question stem?
'x' is a positive integer. Dividing x by d leaves a remainder of 24.
So, the value of 'd' is more than 24.
'x' is a positive integer. Dividing x by d leaves a remainder of 24.
So, the value of 'd' is more than 24.
Step 2 of solving this GMAT DS question:
Evaluate Statement (1) ALONE: When 2x is divided by d, the remainder is 23.
Evaluate Statement (1) ALONE: When 2x is divided by d, the remainder is 23.
The question stem states that when x is divided by d, the remainder is 24.
Therefore, when 2x is divided by d, the remainder should be 2 * 24 = 48.
However, from statement (1) we know that the remainder is 23. We can infer the following from the question stem and statement 1:
Therefore, when 2x is divided by d, the remainder should be 2 * 24 = 48.
However, from statement (1) we know that the remainder is 23. We can infer the following from the question stem and statement 1:
- the divisor d is less than 48
- the divisor is at least 25 and
- 48 divided by divisor d should leave a remainder of 23.
i.e., 48 = nd + 23 or nd = 25.
The possible values for d are 1, 5 and 25.
However, as d is at least 25, the divisor cannot be 1 or 5.
So, we can conclude that 25 is the divisor.
The possible values for d are 1, 5 and 25.
However, as d is at least 25, the divisor cannot be 1 or 5.
So, we can conclude that 25 is the divisor.
Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A or D.
Eliminate choices B, C and E. Choices narrow down to A or D.
Step 3 of solving this GMAT DS question:
Evaluate Statement (2) ALONE: When 3x is divided by d, the remainder is 22.
Evaluate Statement (2) ALONE: When 3x is divided by d, the remainder is 22.
If x leaves a remainder of 24 when divided by d, then 3x will leave a remainder of 3 * 24 = 72 when divided by d.
However, the remainder is 22.
This tells us that the divisor is less than 72 and that 72 divided by d leaves a remainder of 22.
However, the remainder is 22.
This tells us that the divisor is less than 72 and that 72 divided by d leaves a remainder of 22.
So, 72 = n * d + 22
Or nd = 72 - 22 = 50
Or nd = 72 - 22 = 50
If nd = 50, d could be 50 or 25 or 10 or 5 or 2.
However, from the question stem we have deduced that the divisor is at least 25. So, d cannot be 10, 5 and 2.
But, d could be 25 or 50.
However, from the question stem we have deduced that the divisor is at least 25. So, d cannot be 10, 5 and 2.
But, d could be 25 or 50.
From statement 2, we are unable to deduce a unique value for d.
Statement 2 ALONE is NOT sufficient.
Eliminate choice D.
Eliminate choice D.
Statement 1 ALONE is sufficient. Choice A is the answer.
Most Upvoted Answer
This data sufficiency problem consists of a question and two statement...
Understanding the Problem
The problem states that when a positive integer \( x \) is divided by a divisor \( d \), the remainder is 24. This means we can express this mathematically as:
\[ x = kd + 24 \]
for some integer \( k \).
We need to find \( d \).
Analyzing Statement 1
Statement 1: When \( 2x \) is divided by \( d \), the remainder is 23.
- We can express \( 2x \) as:
\[ 2x = 2(kd + 24) = 2kd + 48 \]
- According to the statement, the remainder when \( 2x \) is divided by \( d \) is 23. Thus,
\[ 2kd + 48 \equiv 23 \, (\text{mod } d) \]
- Simplifying gives:
\[ 48 \equiv 23 \, (\text{mod } d) \]
- This implies:
\[ 48 - 23 = 25 \equiv 0 \, (\text{mod } d) \]
- Therefore, \( d \) must be a divisor of 25. The possible values for \( d \) are 1, 5, or 25. Since \( x \) must yield a remainder of 24, the only valid value is \( d = 25 \).
Thus, Statement 1 alone is sufficient.
Analyzing Statement 2
Statement 2: When \( 3x \) is divided by \( d \), the remainder is 22.
- We can express \( 3x \) as:
\[ 3x = 3(kd + 24) = 3kd + 72 \]
- According to the statement, the remainder when \( 3x \) is divided by \( d \) is 22. Thus,
\[ 3kd + 72 \equiv 22 \, (\text{mod } d) \]
- Simplifying gives:
\[ 72 \equiv 22 \, (\text{mod } d) \]
- This implies:
\[ 72 - 22 = 50 \equiv 0 \, (\text{mod } d) \]
- Therefore, \( d \) must be a divisor of 50. The possible values for \( d \) are 1, 2, 5, 10, 25, or 50. However, there is no unique value of \( d \) that satisfies both conditions.
Thus, Statement 2 alone is not sufficient.
Conclusion
- Statement 1 alone is sufficient to determine \( d \).
- Statement 2 alone is insufficient to determine \( d \).
Therefore, the correct answer is option 'A'.
The problem states that when a positive integer \( x \) is divided by a divisor \( d \), the remainder is 24. This means we can express this mathematically as:
\[ x = kd + 24 \]
for some integer \( k \).
We need to find \( d \).
Analyzing Statement 1
Statement 1: When \( 2x \) is divided by \( d \), the remainder is 23.
- We can express \( 2x \) as:
\[ 2x = 2(kd + 24) = 2kd + 48 \]
- According to the statement, the remainder when \( 2x \) is divided by \( d \) is 23. Thus,
\[ 2kd + 48 \equiv 23 \, (\text{mod } d) \]
- Simplifying gives:
\[ 48 \equiv 23 \, (\text{mod } d) \]
- This implies:
\[ 48 - 23 = 25 \equiv 0 \, (\text{mod } d) \]
- Therefore, \( d \) must be a divisor of 25. The possible values for \( d \) are 1, 5, or 25. Since \( x \) must yield a remainder of 24, the only valid value is \( d = 25 \).
Thus, Statement 1 alone is sufficient.
Analyzing Statement 2
Statement 2: When \( 3x \) is divided by \( d \), the remainder is 22.
- We can express \( 3x \) as:
\[ 3x = 3(kd + 24) = 3kd + 72 \]
- According to the statement, the remainder when \( 3x \) is divided by \( d \) is 22. Thus,
\[ 3kd + 72 \equiv 22 \, (\text{mod } d) \]
- Simplifying gives:
\[ 72 \equiv 22 \, (\text{mod } d) \]
- This implies:
\[ 72 - 22 = 50 \equiv 0 \, (\text{mod } d) \]
- Therefore, \( d \) must be a divisor of 50. The possible values for \( d \) are 1, 2, 5, 10, 25, or 50. However, there is no unique value of \( d \) that satisfies both conditions.
Thus, Statement 2 alone is not sufficient.
Conclusion
- Statement 1 alone is sufficient to determine \( d \).
- Statement 2 alone is insufficient to determine \( d \).
Therefore, the correct answer is option 'A'.
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This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer?
Question Description
This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem 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 This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem 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 This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer?.
This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem 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 This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem 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 This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer?.
Solutions for This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem 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.
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Here you can find the meaning of This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice This 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 a leap year or the meaning of the word counterclockwise), you must indicate whether -Q.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2.When 3x is divided by d, the remainder is 22a)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.
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