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


DS86502.01
OG2020 NEW QUESTION
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Remaining apples = 76-4y-3t
So, we require to know the value of y and t

1.\(y ≥ 15\) and t = 2
Substituting t=2 in 76-4y-3t, we get 76-4y-3*2=76-4y-6=70-4y.
Now, 70-4y ≥0.....70 ≥4y.....17.5 ≥y
Thus y can be 15, 16 and 17, and accordingly remaining will be 70-4*15=10 or 70-4*16=6 or 70-4*17=2
Insuff

2. y = 17
so Remaining apples = 76-4y-3t=76-4*17-3t=76-68-3t=8-3t
Now, 8-3t ≥0.....8 ≥3t.....2.66 ≥t
Thus t can be 1 and 2, and accordingly remaining will be 8-3*1=5 or 8-3*2=2
Insuff

Combined..
I gives 2, 6 or 10, while II gives 2 and 5..
Only 2 is common and the answer

C
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We need to determine the value of 76 - 4y - 3t.

Statement One Alone:

y ≥ 15 and t = 2

We do not have enough information to determine 76 - 4y - 3t.

If y = 15 and t = 2, then we have:

76 - 60 - 6 = 10 apples left for Jack to keep

If y = 16 and t = 2, then we have:

76 - 64 - 6 = 6 apples left for Jack to keep

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

y = 17

Since we know nothing about t, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the statements together we see that y = 17 and t = 2, so we have enough information to answer the question.

Answer: C
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