Two integers are in the ratio of 1 to 4. If 12 is added to the smaller number, the ratio becomes 1 to 2. Find the larger integer.
Choose the correct choice from the following:
A) 8
B) 16
C) 32
D) 48
E) 54

Rationale: one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 4 , then 4 x = y , where x is the smaller integer . if adding 12 to the smaller integer makes the ratio 1 to 2 , then 2 ( x + 12 ) = y . substituting y = 4 x into the second equation yields 2 x + 24 = 4 x . so , x = 12 ( smaller integer ) and , y = 4 x = 48 ( larger integer ) so d is the correct answer . another option is to test the answer choices . a ) the larger number is 8 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 2 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 2 ) , we get 14 . so , the new ratio is 14 to 8 which is the same as 7 to 4 . no good . we want a resulting ratio of 1 to 2 eliminate a b ) the larger number is 16 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 4 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 4 ) , we get 16 so , the new ratio is 16 to 16 which is 1 to 1 . no good . we want a resulting ratio of 1 to 2 eliminate b c ) the larger number is 32 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 8 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 8 ) , we get 20 so , the new ratio is 20 to 32 which is 5 to 8 . no good . we want a resulting ratio of 1 to 2 eliminate c d ) the larger number is 48 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 12 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 12 ) , we get 24 so , the new ratio is 24 to 48 . this is the same as the ratio of 1 to 2 therefore ( d ) is correct e ) the larger number is 54 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 13.5 ( which is not an integer ) since both numbers are integers , the larger number can not be 54 . eliminate e therefore d is the only correct choice .
Answer: D