ustureci wrote:
Here is the data sufficiency problem from GMATPrep;
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.
I answered the question as A becuase i thought the statement (1) alone was sufficient. GMATPrep on the other hand said that it is a D -each statement alone is sufficient.
Here is my problem, if we do not know the statement (1), how can we decide these numbers? They of course should be with a tens digit of 3, but all those pairs as (30,37), (31,36), (32,35), (33,34) can maintain the sum of 77, with difference results when they are multiplied. It is because i did not think statement 2 is sufficient, can anyone make it clear, if the GMATPrep's answer is correct? Thanks.
Welcome to GMAT Club. Hope below solution clears your doubts.
The sum of positive integers x and y is 77, what is the value of xy?Given: x+y=77. Question: xy=?
(1) x=y+1 --> together with x+y=77 we have two distinct linear equations, hence we can solve the for variables and obtain the value of xy. Sufficient.
(2) x and y have the same tens digit --> x and y cannot have the tens digit of 2 or 4 (as 29+29<77 and 40+40>77) --> the units digit is 3 --> now, if x=y then x=y=77/2=38.5 --> as both are integers then x and y are 38 and 39 or vise versa (neither of them can be less than 38 as in this case the sum will be less than 77: 37+39=76). Therefore xy=38*39. Sufficient.
Answer: D.
The problem with your solution is that (30,37), (31,36), (32,35), (33,34) add up to 67 not 77.
Hope it's clear.
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