Newaz111 wrote:The sum of positive integers x and y is 77. What is the value of xy?
(1) x = y + 1
(2) x and y have the same tens digit.

Statement 1:
Since x+y = 77 and x-y = 1, we have two variables and two distinct linear equations, allowing us to solve for x and y.
Thus, the value of xy can be determined.
SUFFICIENT.

Statement 2:
Since 29+29 = 48 and 39+39 = 78 -- and the sum of x and y is BETWEEN 48 and 78 -- the tens digit for x and y must be 3.
Since 39+39 = 78, and the desired sum for x and y is ONE LESS than 78, either x or y must be ONE LESS THAN 39.
If x=38 and y=39, then xy = 38*39.
If x=39 and y=38, then xy = 39*38.
Since the product is the same in each case, SUFFICIENT.

The correct answer is D.

x + y = 77

1) x = y+1
when 2 numbers differ by 1 the numbers are consecutive numbers

to find the consecutive numbers that add up to 77, we divide 77 by 2, a round up 1 number and round down 1 number

77/2 = 38.5
one number = 38
one number = 39
can we find the product of these 2 numbers? yes
statement is sufficent

2)x and y have the same tens digit
19 + 19 = 38 , not equal to and less than 77
29 + 29 = 58 , not equal to and less than 77
39 + 39 = 78 , not equal to and greater than 77 by one
if we decrease one of the numbers, we have...
38 + 39 = 77 , equal to 77
can we find the product of 38 and 39? yes
statement is sufficent

answer = d