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If a, b, c and d are positive consecutive multiples, not necessarily in that order, of a positive integer x greater than 1, is a + b + c + d ≥ 50?
(1) c = 15
(2) The difference between d and b is divisible by only four positive integers, one of which is 10.
- 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 'B'. Can you explain this answer?
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Verified Answer
If a, b, c and d are positive consecutive multiples, not necessarily i...
Steps 1 & 2: Understand Question and Draw Inferences
- x is an integer > 1
- a, b , c, d are integers > 0
- Let the least multiple of x in {a, b, c , d} be xy, where y > 0
- We are taking the least multiple to be xy because we do not know which integer out of a, b, c and d is the least in value. Of course, xy will be equal to one integer out of a, b, c or d.
- So, we can express the other 3 multiples of x in terms of y as: x(y+1), x(y+2), x(y +3)
To Find: Is a + b + c + d ≥ 50?
That is, is xy + x(y+1) +x(y+2) +x(y+3) ≥ 50 ?
Is 4x +6xy ≥ 50 ?
That is, is x(2y + 3) ≥ 25?
So, we need to find a unique answer to the question is x(2y + 3) ≥ 25?
Step 3: Analyze Statement 1 independently
(1) c = 15
As c is a multiple of x, the value of x can be the factors of 15 greater than 1= {3, 5, or 15}. We need to see, if for a value of x, is x(2y+3) ≥ 25?
- If x = 15
- We need to calculate the minimum possible value of y, keeping in mind the constraint that one of the integers, i.e. c = 15
- Minimum possible value of y = 1. For such a case, we will have xy = c = 15. So, minimum possible value of y = 1.
- Minimum value of x(2y+3) = 75 > 25.
- For all values of y, x(2y+3) ≥ 25.
- Is, a + b +c + d ≥ 50> → Yes
- If x = 5
- Minimum Value of y = 1. In this case we will have x(y+2) = c = 15. So, minimum possible value of y = 1
- Minimum value of x(2y+3) = 25 = 25
- For values of y ≥ 1, x(2y+3) ≥ 25
- Is, a +b+c+d ≥ 50> → Yes
- If x = 3
- If we assume here that the minimum possible of y = 1, the maximum possible number out of (a,b,c,d) will be x *(y+3) = 12. So, y = 1 is not the minimum possible value of y.
- For x(y+3) = 15, we need to have a minimum possible value of y + 3 = 5, i.e. y =2
- So, minimum of x(2y+3) = 21 < 25
- For values of y ≥ 3, x(2y+3) ≥ 25
- Is, a +b+c+d ≥ 50> → Yes/No
- If we assume here that the minimum possible of y = 1, the maximum possible number out of (a,b,c,d) will be x *(y+3) = 12. So, y = 1 is not the minimum possible value of y.
As we do not have a unique answer to the question Is, a +b+c+d ≥ 50 , the statement is insufficient to answer.
Step 4: Analyze Statement 2 independently
(2) The difference between d and b is divisible by only four positive integers, one of which is 10.
The possible values of difference between d and b can be ={x, 2x, or 3x}. As we are given that the difference between d and b is divisible by 10, we will try to find , if for all values of x and y, is x(2y+3) ≥ 25?
Also, as 10 has four factors (1,2,5 and 10), a number, which is divisible by 10 will be divisible by all the factors of 10. Since |d-b| is divisible by 10 and has only 4 factors, the only possible value of |d-b| = 10
- Case-I:|d – b| = x, i.e. d and b are consecutive multiples. So, x = 10.
- Minimum value of y = 1
- Minimum value of x(2y+3) = 50 > 25
- For all values of y, x(2y+3) ≥ 25.
- Is, a + b +c + d ≥ 50> → Yes
- Case-II:|d-b| = 2x = 10, i.e. x = 5
- Minimum value of y = 1
- Minimum value of x(2y+3) = 25 = 25
- For values of y ≥ 1, x(2y+3) ≥ 25
- Is, a +b+c+d ≥ 50> → Yes
- Case-III:|d-b| = 3x = 10. Not possible as 10 is not divisible by 3
As we have a unique answer to the question Is, a +b+c+d ≥ 50 , the statement is sufficient to answer.
Step 5: Analyze Both Statements Together (if needed)
As we have a unique answer from step 4, this step is not required
Answer: B
Most Upvoted Answer
If a, b, c and d are positive consecutive multiples, not necessarily i...
Statement Analysis:
Statement 1: c = 15
This statement provides the value of c, but it does not give information about the other variables. Without additional information, we cannot determine whether a + b + c + d equals 50.
Statement 2: The difference between d and b is divisible by only four positive integers, one of which is 10.
This statement provides a restriction on the difference between d and b. However, it does not provide information about the specific values of a, b, c, or d. Therefore, we cannot determine if the sum of a + b + c + d equals 50 based solely on this statement.
Combined Analysis:
When we combine both statements, we know that c = 15 and the difference between d and b is divisible by only four positive integers, one of which is 10. This information is not sufficient to uniquely determine the values of a, b, c, and d, and therefore we cannot definitively conclude whether a + b + c + d equals 50.
Therefore, the correct answer is option B as neither statement alone is sufficient to answer the question.
Statement 1: c = 15
This statement provides the value of c, but it does not give information about the other variables. Without additional information, we cannot determine whether a + b + c + d equals 50.
Statement 2: The difference between d and b is divisible by only four positive integers, one of which is 10.
This statement provides a restriction on the difference between d and b. However, it does not provide information about the specific values of a, b, c, or d. Therefore, we cannot determine if the sum of a + b + c + d equals 50 based solely on this statement.
Combined Analysis:
When we combine both statements, we know that c = 15 and the difference between d and b is divisible by only four positive integers, one of which is 10. This information is not sufficient to uniquely determine the values of a, b, c, and d, and therefore we cannot definitively conclude whether a + b + c + d equals 50.
Therefore, the correct answer is option B as neither statement alone is sufficient to answer the question.
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If a, b, c and d are positive consecutive multiples, not necessarily in that order, of a positive integer x greater than 1, is a + b + c + d ≥ 50?(1) c = 15(2) The difference between d and b is divisible by only four positive integers, one of which is 10.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 'B'. Can you explain this answer?
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If a, b, c and d are positive consecutive multiples, not necessarily in that order, of a positive integer x greater than 1, is a + b + c + d ≥ 50?(1) c = 15(2) The difference between d and b is divisible by only four positive integers, one of which is 10.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 'B'. 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 a, b, c and d are positive consecutive multiples, not necessarily in that order, of a positive integer x greater than 1, is a + b + c + d ≥ 50?(1) c = 15(2) The difference between d and b is divisible by only four positive integers, one of which is 10.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 'B'. 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 a, b, c and d are positive consecutive multiples, not necessarily in that order, of a positive integer x greater than 1, is a + b + c + d ≥ 50?(1) c = 15(2) The difference between d and b is divisible by only four positive integers, one of which is 10.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 'B'. Can you explain this answer?.
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If a, b, c and d are positive consecutive multiples, not necessarily in that order, of a positive integer x greater than 1, is a + b + c + d ≥ 50?(1) c = 15(2) The difference between d and b is divisible by only four positive integers, one of which is 10.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 'B'. Can you explain this answer?, a detailed solution for If a, b, c and d are positive consecutive multiples, not necessarily in that order, of a positive integer x greater than 1, is a + b + c + d ≥ 50?(1) c = 15(2) The difference between d and b is divisible by only four positive integers, one of which is 10.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 'B'. Can you explain this answer? has been provided alongside types of If a, b, c and d are positive consecutive multiples, not necessarily in that order, of a positive integer x greater than 1, is a + b + c + d ≥ 50?(1) c = 15(2) The difference between d and b is divisible by only four positive integers, one of which is 10.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 'B'. Can you explain this answer? theory, EduRev gives you an
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