Data Sufficiency

AAPL wrote:On each lab that René completed he received either 100 points or 85 points. On how many labs did he score 100 points?

(1) René's scores for his completed labs totaled 1140 points.
(2) René completed a total of twelve labs.

The OA is A.

Let the number of labs for 100 points be x and the number of labs for 85 points be y. Therefore the equation is 100x+85y.

St1: 100x+85y=1140. ---> 20x+17y=228. We need the last digit as 8 in 228. (try 17*4=68) 228-68=160. 160/20=8. Therefore x=8 labs. Sufficient.
ST2: x+y=12. x and y can have multiple values. Insufficient.

Has anyone another strategic approach to solving this DS question? Regards!

You have done all correct.

My take: Picking from the linear equation, 20x + 17y = 228

Though this is a linear equation, implying no unique solutions, we must not forget that two conditions are hidden in it.

1. x & y > 0 and
2. x & y are integers.

From 20x + 17y = 228, we have x = (228 - 17y)/20 = (220 + 8 - 17y)/20 = 220/20 + (8 - 17y)/20 = 11 + (8 - 17y)/20

So, we have x = 11 + (8 - 17y)/20

Since x is a positive integer, (8 - 17y) must be a multiple of 20. Since a multiple of 20 must have 0 in its unit digit, (8 - 17y) must have 0 in its unit digit. This is possible if 17y has its unit digit as 8. In the table of 7, we have 7*4 = _8; 7*14 = _8; 7*24 = _ _8; etc.

Or, y can be 4, 14, 24, etc.

At y = 4, we have x = 11 + (8 - 17*4)/20 = 11 - 60/20 = 11 - 3 = 8
At y = 14, we have x = 11 + (8 - 17*14)/20 = 11 - 230/20 = 11 - 11.5 = -0.5 (Not valid as x is not an integer and negative)

We need not find out the probable values of x as at higher values of y, x will be negative. Thus, the unique value of x is 8. Sufficient.

Hope this helps!

-Jay
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Hi All,

We're told that on each lab that René completed, he received either 100 points or 85 points. We're asked for the number of labs did on which he scored 100 points.

1) René's scores for his completed labs totaled 1140 points.

At first glance, you might instinctively think that Fact 1 is insufficient. However, 1140 is a relatively small number (especially since the labs are worth either 100 or 85 points each), so it's possible that there's only one way to get to that total. If that's the case, then Fact 1 is actually sufficient - so we have to do enough work to PROVE whether there's just one answer or multiple answers...

Since the first type of score will always give us a multiple of 100, we have to focus on the multiples of 85 (we're looking for a multiple that will 'end' in '....40', so we have to look at just the EVEN multiples of 85)....
Even Multiples of 85 = 0, 170, 340, 510, 680, 850, 1020, 1190

Notice how we have JUST ONE option that ends in "40": 340. This means that the ONLY way to get a sum of 1140 is if we have four 85s and eight 100s
Fact 1 is SUFFICIENT

2) René completed a total of twelve labs.

Fact 2 tells us the MAXIMUM possible answer (re: 12), but we don't know enough to determine the exact number of labs on which Rene scored 100.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich