From S1:

y ≥ 15 and t = 2.
If y = 15, then remaining is 76-60-6 = 10
If y = 16, then remaining is 76-64-6 = 6
Insufficient.

From S2:

y = 17, then remaining is 76-68 = 8-3t.
If t = 1, remaining is 5
If t = 2, remaining is 2
Insufficient.

Combining both:

y = 17 and t = 2
remaining is 76-68-6 = 2
Sufficient.

C is the answer.

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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from given info y & x are multiple values of 4 &3 respectively
#1
m]y ≥ 15[/m] and t = 2
values of remainder apples can vary
insufficeint
#2
y=17, t not know insufficient
from 1 & 2
y= 17 ; 17 *4 ; 68 so t = 2 ; 74 , remainder 2
IMO C

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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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:

GMAT assassins aren't born, they're made,
Rich
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i know this is an easy question but how long should one take to solve this ?
is 2mins a long time to solve such question ?

Hi hsn81960,

Many GMATers assume that they should spend 2 minutes per Quant question (since the Quant section gives you 62 minutes for 31 questions). Unfortunately, that is NOT good pacing advice. Certain Quant 'gettable' questions actually require far MORE than 2 minutes to solve - and to maximize your Score on Test Day, you will likely have to become comfortable 'dumping' certain questions ON PURPOSE (so that you don't waste time on them). Your goal when dealing with any Quant question that you think you can correctly answer is to approach the prompt in an 'efficient' fashion. Keep in mind that does NOT mean that you have to "work fast" - it means that you have to work through the steps on your note pad in an organized way and not waste time by 'staring' or trying to do work "in your head."

GMAT assassins aren't born, they're made,
Rich
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4y+3t+R=76 question says what is R(remaining) ?
1) y could be several numbers ......clearly not suffice
2) y=17 we do not know "t" ....clearly not suffice
both we can exactly determine. answer is C
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Bearing in mind the law of algebra, you could tell the answer in 30 seconds!
Let's call the apple she kept x
4Y + 3T + X = 76 -----------three variable equation

Since it is a three variable equation, using the law of algebra, it will need three unique equations to solve it.
One equation has already been provided by the question stem as in above.

1 gave us an extra equation with one inequality hence the solution CANOT be a discrete value but a range of values. no need to solve!
NOT SUFFICIENT

2 provided one equation. INSUFFICIENT

BOTH: three unique equation arrives while you can completely ignore the inequality.

you could figure it out without lifting a pen
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Answer: Option C

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