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Find the average of 7 consecutive even numbers.Statement I. The sum of fourth number and the sixth number is 440.Statement II. The difference of the fifth and fourth number is 8.1. The statement I alone is sufficient to answer the question but, statement II alone is not sufficient.2. The statement II alone is sufficient to answer the question but, statement I alone is not sufficient.3. Both the statements I and II together are needed to answer the question.4. Either statement I alone or statement II alone is sufficient to answer the question.5. Neither statement I nor statement II is sufficient to answer the question. |
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Answer» Correct Answer - Option 1 : The statement I alone is sufficient to answer the question but, statement II alone is not sufficient. Concept: Average = Sum of terms/Number of terms Statement I. Let the 7 consecutive even numbers be (x – 6, x – 4, x – 2, x, x + 2, x + 4, x + 6) Now, x + x + 4 = 440 ⇒ 2x +4 = 440 ⇒ x = 218 Numbers = (218 – 6, 218 – 4, 218 – 2, 218, 218 + 2, 218 + 4, 218 + 6) ⇒ Numbers = 212, 214, 216, 218, 220, 222, 224 Average = Sum of terms/Number of terms ⇒ Average = (212 + 214 + 216 + 218 + 220 + 222 + 224)/7 ⇒ Average = 1526/7 = 218 So, Statement I alone is sufficient to answer the question Statement II. The difference of the fifth and fourth number is 8. (x + 2) – x = 8 Here the variable is cancelled out so, we can't find value of x. So, statement II is not sufficient ∴ The statement I alone is sufficient to answer the question but, statement II alone is not sufficient. |
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