Data Sufficiency

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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Hi All,

We're told that Jack picked 76 apples - and of these, he sold 4Y apples to Juanita and 3T apples to Sylvia (and T and Y are positive integers.) and kept the remaining apples. We're asked for the number of apples that he kept. To answer this question, we'll need to know the values of T and Y. This question can be solved with Arithmetic and TESTing VALUS.

(1) Y ≥ 15 and T = 2

IF....
Y=15 and T = 2, then Jack sold (4)(15) + (3)(2) = 66 applies, so the answer to the question is 76 - 66 = 10
Y=16 and T = 2, then Jack sold (4)(16) + (3)(2) = 70 applies, so the answer to the question is 76 - 70 = 6
Fact 1 is INSUFFICIENT

(2) Y = 17

Fact 2 clearly tells us nothing about the value of T....
IF....
Y=17 and T = 1, then Jack sold (4)(17) + (3)(1) = 71 applies, so the answer to the question is 76 - 71 = 5
Y=17 and T = 2, then Jack sold (4)(17) + (3)(2) = 74 applies, so the answer to the question is 76 - 74 = 2
Fact 2 is INSUFFICIENT

Combined, we know...
Y ≥ 15 and T = 2
Y = 17

By combining the information in both Facts, we know the exact values of Y and T, so we can answer the question that's asked.
Y=17 and T = 2, so Jack sold (4)(17) + (3)(2) = 74 applies, so the answer to the question is 76 - 74 = 2
Combined, SUFFICIENT

Final Answer: C

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