On each lab that René completed he received either 100 points or 85 po

let x = number of tests that are 100
let y =number of tests that are 85

(1) René’s scores for his completed labs totaled 1140 points.
100x+85y=1140
there is only one unique solution where x=8, and y=4
Sufficient

(2) René completed a total of twelve labs.
x+y=12
x and y vary
insufficient

Answer: A

Hi All,

This DS question can be dealt with in a couple of different ways. Many Test Takers would use an Algebraic approach, but the 'scope' of the question is relatively limited, so you can use Number Properties and 'brute force' to get to the answer.

We're told that each lab that René completed gave him either 100 points or 85 points. We're asked on how many labs he scored 100 points.

Fact 1: René’s scores for his completed labs totaled 1140 points.

1140 points is an 'interesting' number. It's small enough that there can't have been that many labs. It also ends in '40', which depends completely on the number of 85-point labs in the total (since you can't get to '40' with multiples of 100).

I'm going to 'map out' the first few multiples of 85 as a reference:
85(1) = 85
85(2) = 170
85(3) = 255
85(4) = 340

Here, we have a possibility: four 85s and eight 100s.

The only question is whether there's another possibility that totals 1140 or not.

From the above pattern, it's clear that to hit a '40', we need an EVEN number of 85s. We can 'map out' those without too much trouble (notice that 85(2) = 170....)
85(2) = 170
85(4) = 340
85(6) = 510
85(8) = 680
85(10) = 850
85(12) = 1020
85(14) = 1190

At this point we can stop; there's no other option that ends in '40', so there's only the one possible answer.
Fact 1 is SUFFICIENT.

Fact 2: René completed a total of twelve labs.

This tells us NOTHING about the number of 100s nor the number of 85s
Fact 2 is INSUFFICIENT

Final Answer:
GMAT assassins aren't born, they're made,
Rich

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.

VERITAS PREP OFFICIAL SOLUTION

When a DS story problem yields a system of distinct linear equations but implicitly requires that solutions be integers, the smart thing to do is to test values. Generally the numbers involved won’t be very large, so the arithmetic won’t be too daunting.

Statement (1): First, stipulate an integer value for y, then calculate 85y, then subtract that product from 1140. If the difference left isn’t a multiple of 100, don’t consider it further:
Since only one integer value for y yields an integer value for x, and since both x and y must be integers, Statement (1) is sufficient. Eliminate B, C, and E.

Statement (2): Any pair of integers that sum to 12 is a possible pair of values for x and y, so Statement (2) is not sufficient. Eliminate D.

The correct answer is A.

Hi,
A small typo :
statement 1 y is showing two yes
where as is should be only one yeas with 340.
In the image
Regards
Celestial




Kudos if it was useful

Thank you for noticing this.

(1) René’s scores for his completed labs totaled 1140 points.
100X + 85Y = 1140
20X + 17Y = 228
Y=68
sufficient
(2) René completed a total of twelve labs.
not sufficient.

1 alone is sufficient.
the only possible way is that he got at 8 labs 100 points, and at 4 labs 85.

2 alone is not sufficient.

A is the answer.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.