Read the information given below carefully and answer the question that follows:
(A) The mean of 20 observations is 17. On checking, it was found that two observations were wrongly copied as 3 and 6. If the wrong observations are replaced by correct values 8 and 9, then the correct mean will be 16.4.
(B) The ratio of \(4^{3.5} : 2^5\) is same as 4 : 1
(C) The ratio of 1.5 : 2.5 can also be written as 3 : 5
(D) If: 2A = 3B = 4C, then, A : B : C is equal to 6 : 4 : 3
Choose the correct option:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) is incorrect but (B), (C) and (D) are correct
(A) The mean of 20 observations is 17. On checking, it was found that two observations were wrongly copied as 3 and 6. If the wrong observations are replaced by correct values 8 and 9, then the correct mean will be 16.4. Incorrect.
The mean is total ÷ number of observations, so correct the total first:
Total used \(=20\times17=340\)
Correct total \(=340-(3+6)+(8+9)=340-9+17=348\)
Correct mean \(=348\div20=17.4\), not 16.4; the correct values are larger, so the mean must rise above 17
(B) The ratio of \(4^{3.5} : 2^5\) is same as 4 : 1 Correct.
Writing both with base 2: \(4^{3.5}=(2^{2})^{3.5}=2^{7}=128\) and \(2^{5}=32\)
Ratio \(=128:32=4:1\)
(C) The ratio of 1.5 : 2.5 can also be written as 3 : 5 Correct.
A ratio does not change when both terms are multiplied by the same number; multiplying by 2 gives \(3:5\)
(D) If: 2A = 3B = 4C, then, A : B : C is equal to 6 : 4 : 3 Correct.
Assuming \(2A=3B=4C=12\): \(A=6\), \(B=4\), \(C=3\)
So \(A:B:C=6:4:3\)