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

Question

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.

Kudos for a correct  solution .

AmoyV · Answer

1. 85=17*5
Keep deducting 100 from 1140 and the option look for a unique option which is divisible by 170. 
Ignore the units digit of 0.
114 X--->104 X--->94 X. Notice units digit of 4 is repeated, so look for a multiple of 17 with a units digit of 4.
Now the only solution with 4 in the units place is 34. Add the 0 back to the units place and deduct from 1140.

1140-340=800

So he scored 8 100 points.

This is a unique solution hence Sufficient.

2. Those 12 labs could be made in any way. 1+11, 2+10 etc.

Not Sufficient

Answer: A

Vaibhav21 · Answer

St 1)
Let the number of 100s = x and number of 85s = y
Equation = 100x+85y=1140 or 20x+17y=228 ; x=228-17y/20
X=8 y = 4 Unique solution
St 2) 
René completed a total of twelve labs. so?
Rene scored 100 in 11 labs and 85 in 1 lab or vice-versa

Answer A

peachfuzz · Answer

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

EMPOWERgmatRichC · Answer

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:  A

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

ppac · Answer

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.

Bunuel · Answer

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: efq3a4_img3.png 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.

Celestial09 · Answer

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

Bunuel · Answer

Thank you for noticing this.

Lucky2783 · Answer

(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.

mvictor · Answer

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.

bumpbot · Answer

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

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

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