The annual rainfall in a city over the past 50 years is its historical

­HAR is over 50 years, while what is given in the graph is rainfall over 7 consecutive years. Based on the graph, we are asked whether HAR is at least 47mm.

(1) In the seven-year period in City X, the annual rainfall was greater than the HAR in exactly two of the consecutive years.
So we look at the highest rainfall. The question becomes easy as the two highest rainfalls have been in two consecutive years, year 3 and year 4.
This further tells us that the rainfall in year 2, which would otherwise be part of the above mentioned two consecutive years, making two consecutive years as three consecutive years, was not more than the HAR.
Thus, rainfall of 47mm is not more than the HAR or, in other words, HAR is at least 47mm.
Sufficient

(2) In the seven-year period in City X, the annual rainfall was less than the HAR in exactly four of the years.­
The four least rainfall have been in year 1, 5, 6 and 7, so HAR is surely more than 35.
The trap comes now: the next higher rainfall shown is 47, and one could mark this too sufficient.
But HAR need not be one of the rainfalls mentioned on graph, so HAR could be anything greater than 35 but less than 47, inclusive.
Insufficient

A

­Hello chetan2u

I am afraid I can't agree to the solution you provided. The question asks "Is it true that the rounded HAR for City X is 47 mm or greater?". Going by your logic, "But HAR need not be one of the rainfalls mentioned on graph, so HAR could be anything greater than 35 but less than 47, inclusive.", this actually sufficiently points to the fact that the HAR is not more than 47. And thus it actually makes this statement correct.
However, the question asks us whether the HAR is more than or equal to 47. Using the second option, we are unable to determine whether the option equates to less than 47 or equal to 47. Hence, we are unable to conclude and that makes this statement insufficient.
Please let me know your thoughts on this.

 

Is it true that the rounded HAR for City X is 47 mm or greater? Implies Is HAR> or =47? Yes/No Ques

(1) In the seven-year period in City X, the annual rainfall was greater than the HAR in exactly two of the consecutive years.
Annual rainfall was greater than HAR (x) only in 2 periods, that too consecutive. In all other periods it could be less or equal too.
So lets say HAR is 36, so by graph Annual rainfall is greater in 4 consecutive periods (Y1 to 4 hence violating condition)
Lets say HAR is 46, so by graph Annual rainfall is greater in 3 consecutive periods (Y2 to 4 hence violating condition)
Let say HAR is 47, condition is satisified - equal in one year and greater in 2
Lets say HAR is 51/52, so by graph Annual rainfall is greater in only 1 year - year 3
Hence Range of HAR (x) =
47<=HAR<51
Hope this is clear


(2) In the seven-year period in City X, the annual rainfall was less than the HAR in exactly four of the years.­
Lets say HAR is Least value - 23
Years in which Annual rainfall being less than HAR = 0 (Violates condition)
Lets say HAR is 36
Years in which Annual rainfall being less than HAR = 4 ( condition satisfied) but the ans to the Q is No (We are looking for HAR>=47)
Lets say HAR is 46
Years in which Annual rainfall being less than HAR = 4 ( condition satisfied) but the ans to the Q is No (We are looking for HAR>=47)
Lets say HAR is 47
Years in which Annual rainfall being less than HAR = 4 ( condition satisfied) but the ans to the Q is Yes (We are looking for HAR>=47)

We have gotten both Yes and No while complying with the condition - Hence not sufficient

­The annual rainfall in a city over the past 50 years is its historical average rainfall (HAR). The graph above shows the annual rainfall in City X over a seven-year period. All figures are rounded to the nearest integer.

Is it true that the rounded HAR for City X is 47 mm or greater?

(1) In the seven-year period in City X, the annual rainfall was greater than the HAR in exactly two of the consecutive years.

(2) In the seven-year period in City X, the annual rainfall was less than the HAR in exactly four of the years.­