AbeNeedsAnswers wrote:Jack picked 76 apples. Of these, he sold 4y apples to Juanita and 3t apples to Sylvia. If he kept the remaining apples, how many apples did he keep? (t and y are positive integers.)
(1) y ≥ 15 and t = 2
(2) y = 17
C
Source: Official Guide 2020
Say Jack is left with x apples. We have to get the unique value of x.
So, we have
x = 76 - 4y - 3t; given that x, t and y are positive integers
Let's take each statement one by one.
(1) y ≥ 15 and t = 2
Case 1: Say y = 15 and t = 2
We have x = 76 - 4y - 3t => x = 76 - 4*15 - 3*2 => 10
Case 2: Say y = 16 and t = 2
We have x = 76 - 4y - 3t => x = 76 - 4*16 - 3*2 => 6
Case 3: Say y = 17 and t = 2
We have x = 76 - 4y - 3t => x = 76 - 4*17 - 3*2 => 2
y cannot be 18, else x would then be negative, not a possible value of x.
No unique value of x. Insufficient.
(2) y = 17
We have x = 76 - 4y - 3t => x = 76 - 4*17 - 3t => x = 8 - 3t
Case 1: t = 1
x= 8 - 3*1 = 5
Case 2: t = 2
x= 8 - 3*2 = 2
t cannot be 3, else x would then be negative, not a possible value of x.
No unique value of x. Insufficient.
(1) and (2) together
Case 3 of Statement 1 is applicable. Thus, we have x = 2. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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