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Directions: The following question is accompanied by statements A, B and C. You have to determine which statement(s) is/are sufficient to answer the question.
Q. If product of two positive numbers m and n is 80, then what are the values of m and n, respectively?
A. m is 25% more than n.
B. n + 2m : n + m = 14 : 9
C. m + n = 18
  • a)
    Only A alone is sufficient
  • b)
    Only B alone is sufficient
  • c)
    Only C alone is sufficient
  • d)
    Either A alone or B alone is sufficient
  • e)
    Each of statements A, B and C alone is sufficient
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Directions:The following question is accompanied by statements A, B an...
To find the values of m and n, we need to consider all the statements together.

Statement A: m is 25% more than n.
Statement B: n/(2m) : n/m = 14 : 9
Statement C: mn = 18

Let's analyze each statement separately:

Statement A: m is 25% more than n.
This statement alone is not sufficient to determine the values of m and n. We don't have any specific values or equations to solve for m and n.

Statement B: n/(2m) : n/m = 14 : 9
This statement alone is not sufficient to determine the values of m and n. It only gives us a ratio between n/(2m) and n/m, but we still need more information to find the actual values of m and n.

Statement C: mn = 18
This statement alone is not sufficient to determine the values of m and n. We know that the product of m and n is 18, but we don't have any information about the relationship between m and n.

Now, let's consider the combinations of two statements:

Combining Statements A and B:
From statement A, we know that m is 25% more than n. Let's represent n as x. Then m = x + (25/100)x = (125/100)x = (5/4)x.
From statement B, we have the ratio n/(2m) : n/m = 14 : 9.
Substituting the values of m and n, we get (x/(2*(5/4)x)) : (x/(5/4)x) = 14 : 9.
Simplifying, we get (4/10) : (4/5) = 14 : 9.
This simplifies to 2 : 2 = 14 : 9, which is not true.
Therefore, combining statements A and B does not give us a unique solution for m and n.

Combining Statements A and C:
From statement A, we know that m is 25% more than n. Let's represent n as x. Then m = x + (25/100)x = (125/100)x = (5/4)x.
From statement C, we have mn = 18.
Substituting the values of m and n, we get (5/4)x * x = 18.
This simplifies to (5x^2)/4 = 18.
Solving for x, we get x = 4.
Substituting this value back into m = (5/4)x, we get m = (5/4)*4 = 5.
Therefore, combining statements A and C gives us the values of m = 5 and n = 4.

Combining Statements B and C:
From statement B, we have the ratio n/(2m) : n/m = 14 : 9.
From statement C, we have mn = 18.
We can solve these two equations simultaneously to find the values of m and n.
Let's represent n as x and m as y.
From the ratio in statement B, we have x/(2y) : x/y = 14 : 9.
Simplifying, we get 9x = 28y.
From statement C, we have xy = 18.
Now, we have two equations:
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Directions:The following question is accompanied by statements A, B and C. You have to determine which statement(s) is/are sufficient to answer the question.Q. If product of two positive numbers m and n is 80, then what are the values of m and n, respectively?A. m is 25% more than n.B. n + 2m : n + m = 14 : 9C. m + n = 18a)Only A alone is sufficientb)Only B alone is sufficientc)Only C alone is sufficientd)Either A alone or B alone is sufficiente)Each of statements A, B and C alone is sufficientCorrect answer is option 'D'. Can you explain this answer?
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Directions:The following question is accompanied by statements A, B and C. You have to determine which statement(s) is/are sufficient to answer the question.Q. If product of two positive numbers m and n is 80, then what are the values of m and n, respectively?A. m is 25% more than n.B. n + 2m : n + m = 14 : 9C. m + n = 18a)Only A alone is sufficientb)Only B alone is sufficientc)Only C alone is sufficientd)Either A alone or B alone is sufficiente)Each of statements A, B and C alone is sufficientCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions:The following question is accompanied by statements A, B and C. You have to determine which statement(s) is/are sufficient to answer the question.Q. If product of two positive numbers m and n is 80, then what are the values of m and n, respectively?A. m is 25% more than n.B. n + 2m : n + m = 14 : 9C. m + n = 18a)Only A alone is sufficientb)Only B alone is sufficientc)Only C alone is sufficientd)Either A alone or B alone is sufficiente)Each of statements A, B and C alone is sufficientCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions:The following question is accompanied by statements A, B and C. You have to determine which statement(s) is/are sufficient to answer the question.Q. If product of two positive numbers m and n is 80, then what are the values of m and n, respectively?A. m is 25% more than n.B. n + 2m : n + m = 14 : 9C. m + n = 18a)Only A alone is sufficientb)Only B alone is sufficientc)Only C alone is sufficientd)Either A alone or B alone is sufficiente)Each of statements A, B and C alone is sufficientCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Directions:The following question is accompanied by statements A, B and C. You have to determine which statement(s) is/are sufficient to answer the question.Q. If product of two positive numbers m and n is 80, then what are the values of m and n, respectively?A. m is 25% more than n.B. n + 2m : n + m = 14 : 9C. m + n = 18a)Only A alone is sufficientb)Only B alone is sufficientc)Only C alone is sufficientd)Either A alone or B alone is sufficiente)Each of statements A, B and C alone is sufficientCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
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