amanvermagmat wrote:
A number of people are standing in rows for a group photograph in a unique way. After the front row, each row has 4 more people than the row in front of it. If the total number of rows in which people are standing is N, what is the value of N?
(1) Total number of people standing for the group photograph in all N rows combined are 72.
(2) N is divisible by 3.
Approach - counter exampleStatement 1:Total number of people standing for the group photograph in all N rows combined is 72.
Example 1: N can be as low as 2. When N is 2, the front row will have 34 people and the one behind it will have 38 people.
Example 2: N can be 3. Note that the number of people in each row forms an AP with a common difference of 4.
So, to find number in each row, divide 72 by 3. Average is 24. 4 less than 24 = 20 (number in the front row), 24 (number in second row), 28 number in 3rd row.
More than one value exists for N. So, statement 1 alone is not sufficient.
Statement 2: N is divisible by 3
We can eliminate this statement as more than one value is possible.
Statement together: Total number of people 72. N is divisible by 3.
We know N = 3 is possible. We checked that possibility in statement 1.
Let us try N = 6. Even number of rows. So, the average number will be the number between the 3rd and the 4th row. Divide 72 by 6 to get 12 as the average.
3rd row will have 10 and 4th row will have 14.
1st row will have 2, second row will have 6, 5th row will have 18 and the last one will have 22 people adding up to 72.
More than one value exists for N. Statements together not sufficient. Choice E.
What if? Had the second statement said, N is divisible by 6, the two statements together would have been sufficient. N = 12 or values greater than that are not possible because one or more terms of the sequence will become negative.