sachin_yadav wrote:Last Friday each of the pets at a certain veterinary clinic was given either 1 treat or 2 treats. What was the total number of treats given to pets at the clinic last Friday?
(1) The total number of pets at the clinic last Friday was 90.
(2) 2/3 of the pets at the clinic last Friday were given 2 treats each.
Target question: What was the total number of treats given to pets at the clinic last Friday?
Let x = NUMBER of pets given ONE treat
Let y = NUMBER of pets given TWO treats
So,
x + 2y = TOTAL number of treats given. Let's REPHRASE the target question....
REPHRASED target question: What is the value of x + 2y?
Aside: We have a free video with tips on REPHRASING the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Statement 1: The total number of pets at the clinic last Friday was 90.
In other words, x + y = 90
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 10 and y = 80, in which case
x + 2y = 170
Case b: x = 20 and y = 70, in which case
x + 2y = 160
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 2/3 of the pets at the clinic last Friday were given 2 treats each.
In other words: (number of pets given 2 treats) = 2/3(TOTAL number of pets)
So, we can write: y = 2/3(x + y)
Multiply both sides by 3 get: 3y = 2(x + y)
Expand: 3y = 2x + 2y
Simplify: y = 2x
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 10 and y = 20, in which case
x + 2y = 50
Case b: x = 20 and y = 40, in which case
x + 2y = 100
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that x + y = 90
Statement 2 tells us that y = 2x
Since we COULD solve this system of equations for x and y,
we COULD definitely determine the value of x + 2y
Since we can answer the
REPHRASED target question with
certainty, the combined statements are SUFFICIENT
Answer =
C
Aside: if we solve the system of equations, we get x = 30 and y = 60, which means
x + 2y = 150.
In other words,
150 treats were given last Friday.
Cheers,
Brent
