CAT 1994 — QA Question 11
Answer the next 3 questions based on the information given below:
Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighospur, Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; in his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighospur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighospur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighospur are 32 and 117 respectively.
If the harmonic mean between two positive numbers is to their geometric mean as 12 : 13; then the numbers could be in the ratio
Answer & solution
- A
12 : 13
- B
1/12 : 1/13
4 : 9
- D
2 : 3
The harmonic mean of two numbers x and y is and the geometric mean is
∴ =
⇒ =
Although this can be simplified to get the answer, the best way to proceed from here would be to look out for the answer choices and figure out which pair of x & y satisfies the above equation.
Option (c) satisfies the above expression
Alternately,
Please note that this sum is a classic example of how you could have gone for intelligent guess work. Since we know that the denominator of the ratio is the geometric mean, which is , the two numbers should be in such a ratio that their product should be a perfect square.
The only pair from the answer choices that supports this is 4 & 9, as = = 6
Hence, option (c).