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For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?
(1) b, c and d are factors of a
(2) a – 2d = b + c
- 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 'D'. Can you explain this answer?
Verified Answer
For any integers x and y, min(x, y) and max(x, y) denote the minimum a...
Steps 1 & 2: Understand Question and Draw Inferences
- min(x, y) → minimum of x and y, where x and y are integers
- max(x, y) → maximum of x and y, where x and y are integers
- a, b, c, d are distinct integers > 0
To Find: Is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?
Step 3: Analyze Statement 1 independently
(1) b, c and d are factors of a
- So, we can write a = bx = cy = dz, where x, y and z are distinct integers > 1
- For example, since 2, 3 and 6 are factors of 36, we can write: 36 = 2x =3y = 6z (in this example, x, y and z will be equal to 18, 12 and 6 respectively)
- Hence, a > {b, c, d}
- Like, in the above example, 36 > {2, 3, 6}
- For solving the expression, we need to start from the innermost bracket. Since we do not know which of c or d is smaller, max(a, max(b, min(c, d))) = max(a, max(b, (c or d)))
- Now, we do not know, which of b, c or d is the greatest, max(a, max(b, (c or d))) = max (a, (b, c or d))
- However, we do know that a > b, c, d. So, we can write max (a, (b, c or d)) = a
- Similarly, we do not know which b or c is smaller, so, max(d, max(a, min(b, c))) = max (d, max (a, (b or c)))
- However, we do know that a > b , c. So, we can write max (d, max (a, (b or c)))= max(d, a)
- Also, as a > d, we can write max (d, a) = a
So, max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))).
Sufficient to answer.
Sufficient to answer.
Step 4: Analyze Statement 2 independently
(2) a – 2d = b + c
- Rearranging the terms: a = b + c + 2d. So, a > b, c and d
- We know that a > b, c, d and for this case we have already evaluated in statement-1 that max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))).
So, max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))).
Sufficient to answer.
Step 5: Analyze Both Statements Together (if needed)
As we have a unique answer from steps 3 and 4, this step is not required.
Answer: D
Most Upvoted Answer
For any integers x and y, min(x, y) and max(x, y) denote the minimum a...
Problem Analysis:
We are given the expressions max(a, max(b, min(c, d))) and max(d, max(a, min(b, c))). We need to determine if these two expressions are equal.
Statement 1: b, c, and d are factors of a.
If b, c, and d are factors of a, it means that a is divisible by b, c, and d. In other words, a should be the multiple of b, c, and d.
Statement 2: a - 2d = b and ca
From this statement, we can deduce that b = a - 2d and c = a - 2d. This implies that b and c are both positive integers.
Combined Analysis:
From Statement 1, we know that a is divisible by b, c, and d. Therefore, a is a multiple of b, c, and d.
From Statement 2, we know that b = a - 2d and c = a - 2d. Substituting these values in the expression max(a, max(b, min(c, d))) gives us:
max(a, max(a - 2d, min(a - 2d, d)))
We can simplify this expression as follows:
1. If a > a - 2d, then max(a - 2d, min(a - 2d, d)) = max(a - 2d, d) = a - 2d
2. If a < a="" -="" 2d,="" then="" max(a="" -="" 2d,="" min(a="" -="" 2d,="" d))="max(a" -="" 2d,="" a="" -="" 2d)="a" -="" />
3. If a = a - 2d, then max(a - 2d, min(a - 2d, d)) = max(a - 2d, d) = a - 2d
Therefore, in all cases, max(a, max(b, min(c, d))) = a - 2d.
Similarly, substituting the values in the expression max(d, max(a, min(b, c))) gives us:
max(d, max(a, min(a - 2d, d)))
We can simplify this expression as follows:
1. If d > a, then max(a, min(a - 2d, d)) = max(a, d) = d
2. If d < a,="" then="" max(a,="" min(a="" -="" 2d,="" d))="max(a," a="" -="" 2d)="" />
3. If d = a, then max(a, min(a - 2d, d)) = max(a, d) = a
Therefore, in all cases, max(d, max(a, min(b, c))) = a - 2d.
Since both expressions simplify to a - 2d, we can conclude that max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))).
Therefore, both statements together are sufficient to answer the question.
Answer: (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.
We are given the expressions max(a, max(b, min(c, d))) and max(d, max(a, min(b, c))). We need to determine if these two expressions are equal.
Statement 1: b, c, and d are factors of a.
If b, c, and d are factors of a, it means that a is divisible by b, c, and d. In other words, a should be the multiple of b, c, and d.
Statement 2: a - 2d = b and ca
From this statement, we can deduce that b = a - 2d and c = a - 2d. This implies that b and c are both positive integers.
Combined Analysis:
From Statement 1, we know that a is divisible by b, c, and d. Therefore, a is a multiple of b, c, and d.
From Statement 2, we know that b = a - 2d and c = a - 2d. Substituting these values in the expression max(a, max(b, min(c, d))) gives us:
max(a, max(a - 2d, min(a - 2d, d)))
We can simplify this expression as follows:
1. If a > a - 2d, then max(a - 2d, min(a - 2d, d)) = max(a - 2d, d) = a - 2d
2. If a < a="" -="" 2d,="" then="" max(a="" -="" 2d,="" min(a="" -="" 2d,="" d))="max(a" -="" 2d,="" a="" -="" 2d)="a" -="" />
3. If a = a - 2d, then max(a - 2d, min(a - 2d, d)) = max(a - 2d, d) = a - 2d
Therefore, in all cases, max(a, max(b, min(c, d))) = a - 2d.
Similarly, substituting the values in the expression max(d, max(a, min(b, c))) gives us:
max(d, max(a, min(a - 2d, d)))
We can simplify this expression as follows:
1. If d > a, then max(a, min(a - 2d, d)) = max(a, d) = d
2. If d < a,="" then="" max(a,="" min(a="" -="" 2d,="" d))="max(a," a="" -="" 2d)="" />
3. If d = a, then max(a, min(a - 2d, d)) = max(a, d) = a
Therefore, in all cases, max(d, max(a, min(b, c))) = a - 2d.
Since both expressions simplify to a - 2d, we can conclude that max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))).
Therefore, both statements together are sufficient to answer the question.
Answer: (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.
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For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?(1) b, c and d are factors of a(2) a – 2d = b + ca)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 '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 For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?(1) b, c and d are factors of a(2) a – 2d = b + ca)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 '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 For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?(1) b, c and d are factors of a(2) a – 2d = b + ca)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 'D'. Can you explain this answer?.
For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?(1) b, c and d are factors of a(2) a – 2d = b + ca)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 '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 For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?(1) b, c and d are factors of a(2) a – 2d = b + ca)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 '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 For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?(1) b, c and d are factors of a(2) a – 2d = b + ca)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 'D'. Can you explain this answer?.
Solutions for For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?(1) b, c and d are factors of a(2) a – 2d = b + ca)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 '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 For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?(1) b, c and d are factors of a(2) a – 2d = b + ca)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 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?(1) b, c and d are factors of a(2) a – 2d = b + ca)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 'D'. Can you explain this answer?, a detailed solution for For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?(1) b, c and d are factors of a(2) a – 2d = b + ca)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 'D'. Can you explain this answer? has been provided alongside types of For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?(1) b, c and d are factors of a(2) a – 2d = b + ca)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 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?(1) b, c and d are factors of a(2) a – 2d = b + ca)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 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
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