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Before the summer holidays, Bill got 100 mathematics exercises for hom

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Before the summer holidays, Bill got 100 mathematics exercises for hom  [#permalink]

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New post 27 Jun 2015, 03:50
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Question Stats:

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Before the summer holidays, Bill got 100 mathematics exercises for homework. During the first week of his vacation, Bill worked out exercises number 1 to 5, 35 to 40, and 76 to 100. If Bill finished working out all his homework on the second week of the vacation, how many exercises did he complete on the second week?

A. 66
B. 65
C. 64
D. 36
E. 34

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Re: Before the summer holidays, Bill got 100 mathematics exercises for hom  [#permalink]

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New post 27 Jun 2015, 04:15
I got it right, but was wondering Whether this question can be 600-700 level question. This question is primarily testing addition and subtraction.

reto wrote:
Before the summer holidays, Bill got 100 mathematics exercises for homework. During the first week of his vacation, Bill worked out exercises number 1 to 5, 35 to 40, and 76 to 100. If Bill finished working out all his homework on the second week of the vacation, how many exercises did he complete on the second week?

A. 66
B. 65
C. 64
D. 36
E. 34

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Re: Before the summer holidays, Bill got 100 mathematics exercises for hom  [#permalink]

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New post 27 Jun 2015, 04:26
shriramvelamuri wrote:
I got it right, but was wondering Whether this question can be 600-700 level question. This question is primarily testing addition and subtraction.

reto wrote:
Before the summer holidays, Bill got 100 mathematics exercises for homework. During the first week of his vacation, Bill worked out exercises number 1 to 5, 35 to 40, and 76 to 100. If Bill finished working out all his homework on the second week of the vacation, how many exercises did he complete on the second week?

A. 66
B. 65
C. 64
D. 36
E. 34


Agree. I have no offical level for that question.
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Before the summer holidays, Bill got 100 mathematics exercises for hom  [#permalink]

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New post 30 Jul 2018, 11:00
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reto wrote:
Before the summer holidays, Bill got 100 mathematics exercises for homework. During the first week of his vacation, Bill worked out exercises number 1 to 5, 35 to 40, and 76 to 100. If Bill finished working out all his homework on the second week of the vacation, how many exercises did he complete on the second week?

A. 66
B. 65
C. 64
D. 36
E. 34

The issue is inclusive counting.

Of his 100 problems, Bill "worked out exercises number 1 to 5."

The real question in this case: "What is the number of problems from problem #1 to problem #5?"

Bill finished problems numbered (labeled) 1, 2, 3, 4, and 5. Easy: count the integers in that list. He finished 5 problems.

But if we simply subtract, the number of problems finished is incorrect: (5-1) = 4

We need inclusive counting to find out the number of problems he finished.

"Add one before you are done," (Manhattan Prep, I think?) is a corny but effective way to remember that in a given set of numbers, subtraction alone yields the distance between numbers, NOT the number (quantity) of numbers.

Another way to remember: fenceposts with rope in between them.

|____|____|____|____|
1____2____3____4____5

We are being asked to COUNT THE FENCE POSTS, not intervals of rope.

Unless we see the word "between" (or a strict inequality), we are almost always being asked to count the number of fence posts. Hence we can use
(Highest - Smallest) + 1

The first week, Bill finished
A) ((#5 - #1) = 4) + 1 = 5
B) (40 - 35 = 5) + 1 = 6
C) (100 - 76) = 24 + 1 = 25

Bill finished (5 + 6 + 25) = 36 problems.
In the second week, during which he finishes all the problems, he works out
(100 - 36) = 64 problems

Answer C

What about inclusive counting the "second" time, i.e., when we are calculating number of problems that he finished and the number that remain?

No inclusive counting. Imagine "finished" as knocking over a fence post. How many posts are left to knock over?

In essence, if we say that he finished THREE problems, we are giving the number of numbers he finished. We subtract that quantity from the total number of numbers.

Test small numbers every time this issue presents trouble.

Bill had 5 problems. He finished 3.
How many problems remain for him to do?
Finished = X
Remain to do = O

1 - 2 - 3 - 4 - 5
X - X - X - O - O

Total number of problems (total number of numbers): 5
Number of problems finished (number of numbers finished): 3

(5 - 3) = 2 left to finish

mikemcgarry addresses this issue in Inclusive Counting on the GMAT, here
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Before the summer holidays, Bill got 100 mathematics exercises for hom &nbs [#permalink] 30 Jul 2018, 11:00
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