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# A report consisting of 2,600 words is divided into 23 paragr

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Re: A report consisting of 2,600 words is divided into 23 paragr [#permalink]
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If the average is 120 words per paragraph, then for 25 paragraphs, there will be a total of 25*120=3000 words. So any total less than 3000 words will give an average less than 120.

(1) Each paragraph of the preface has more than 100 words.
The total number of words may or may not exceed 3000. Insufficient

(2) Each paragraph of the preface has fewer than 150 words.
The total number of words cannot exceed 2750 so average is less than 120. SUFFICIENT

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A report consisting of 2,600 words is divided into 23 paragr [#permalink]
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Question. I tried 2 ways. First way worked, second way didn't. Could someone have a look and let me know where I went wrong with the 2nd method?

FIRST WAY (CORRECT):

Background info:
Y/N question
23 paragraphs, 2,600 words
Added 2 preface paragraphs. Let x be total of new words added.
Thus question is: (2,600+x)/25<120? OR, simply, is x<400?

Stem (1): Each preface paragraph has 100+ words.
If each preface paragraph has 101 words then x= 2*(101) = 202 words. This would make x<400
Alternatively if each preface paragraph has 250 words then x=2*(202) = 404 words. This would mean x>400. Stem 1 is Insufficient.

Stem (2) Each preface paragraph has less than 150 words. This means x is AT MOST 2*(149) = 298 words. I.e. x MUST BE <400. Stem 1 is Sufficient.

WAY TWO (INCORRECT)

I worked out the average word count for the current 23 paragraphs: 2,600/23= approx 113 words
I then thought, if the new average (inclusive of 2 preface paragraphs) is 120 then the difference b/w the 2 averages is 7 words.
The total number of words added due to preface paragraphs would then = 7*25 = 175 words
The answer stem has to tell me if the 2 new paragraphs has less or more than 175 words.

Stem (1): Each preface paragraph has 100+ words. Total must be more than 175 words. Sufficient
Stem (2): Each preface paragraph has less than 150 words. So could be 100 words, 200 words, 298 words. NOT sufficient

Thanks guys!
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Re: A report consisting of 2,600 words is divided into 23 paragr [#permalink]
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Hi ColdSushi,

There's nothing wrong with the second approach that you took (although the "rounding" that did could be a problem in certain questions that require specifics/accuracy).

The "7 word difference" you calculated IS correct, but you also have to account for the 120 words that would need to appear in EACH of the 2 preface paragraphs. Your calculation didn't do that.

Using your approximation, your calculation should have been (7)(25) + 2(120) = 415 words

Using this value, you would have gotten the correct answer.

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Re: A report consisting of 2,600 words is divided into 23 paragr [#permalink]
EMPOWERgmatRichC wrote:
Hi ColdSushi,

There's nothing wrong with the second approach that you took (although the "rounding" that did could be a problem in certain questions that require specifics/accuracy).

The "7 word difference" you calculated IS correct, but you also have to account for the 120 words that would need to appear in EACH of the 2 preface paragraphs. Your calculation didn't do that.

Using your approximation, your calculation should have been (7)(25) + 2(120) = 415 words

Using this value, you would have gotten the correct answer.

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

Thanks very much Rich. Appreciate your help and it makes sense now!
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Re: A report consisting of 2,600 words is divided into 23 paragr [#permalink]
ColdSushi wrote:
EMPOWERgmatRichC wrote:
Hi ColdSushi,

There's nothing wrong with the second approach that you took (although the "rounding" that did could be a problem in certain questions that require specifics/accuracy).

The "7 word difference" you calculated IS correct, but you also have to account for the 120 words that would need to appear in EACH of the 2 preface paragraphs. Your calculation didn't do that.

Using your approximation, your calculation should have been (7)(25) + 2(120) = 415 words

Using this value, you would have gotten the correct answer.

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

Thanks very much Rich. Appreciate your help and it makes sense now!

Hey,
I too did the same way as you did in the second method .
however I still didnt get the point - "account for the 120 words that would need to appear in EACH of the 2 preface paragraphs."
what I thought was :
consider avg to be 120 , so difference in avg is 7 , that means 7 words per para is extra . to find out what extra was divided equally -->> 7*25= 175 extra words was divided equally among 25 to increase the avg to 120.
this 125 extra words came from 2 paras combined so each para approx 87.5 words
so basically q is asking does each para less than 87.5 words?

OMG! while typing this and reviewing it, I found out what was wrong in my analysis, I will still continue to write since it will help those who thought this same thing as mentioned before..
125 words are EXTRA words...again " EXTRA" words.. that means those 2 paras to fit into the avg of 113 it should first satisfy its requirement i.e. 120 words/para
so 2 paras have 120*2 words and then extra 25*7 to increase the avg to 120
therefore those 2 paras have -->> 2*120+25*7 = 415 words ... that means 207.5 each para
tht means Q is asking " if each para < 207.5 then avg is <120 "
I hope this is correct.
thanks
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Re: A report consisting of 2,600 words is divided into 23 paragr [#permalink]
A report consisting of 2,600 words is divided into 23 paragraphs. A 2-paragraph preface is then added to the report. Is the average (arithmetic mean) number of words per paragraph for all 25 paragraphs less than 120 ?

(1) Each paragraph of the preface has more than 100 words.
(2) Each paragraph of the preface has fewer than 150 words.

Information Given:-
1) 2 paragraphs are added to existing 23 paragraphs, making total paragraphs to be 25
2) Number of words in existing 23 paragraphs= 2600

Average number of words <120

Inference:-
Total number of words <120*25
T<3000

Initially words were 2600, so if newly added words are less then 400 then we can answer the question.

(1) Each paragraph of the preface has more than 100 words.
If the words added are 101 with each paragraph then 'yes'. But if 300 words are added with each paragraph then 'No'

(2) Each paragraph of the preface has fewer than 150 words.
Basically, this statement tells that fewer than 300 words are added. And this was the information we were looking for

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Re: A report consisting of 2,600 words is divided into 23 paragr [#permalink]
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A report consisting of 2,600 words is divided into 23 paragraphs. A 2-paragraph preface is then added to the report. Is the average (arithmetic mean) number of words per paragraph for all 25 paragraphs less than 120 ?

(1) Each paragraph of the preface has more than 100 words.
(2) Each paragraph of the preface has fewer than 150 words.

Target question: Is the average (arithmetic mean) number of words per paragraph for all 25 paragraphs less than 120?

When it comes to averages, we know that average value = (sum of n values)/n
We can rewrite this into a useful formula: sum of n values = (average value)(n)

So, if 25 paragraphs were to have an average EQUAL TO 120 words, then the TOTAL number of words = (120)(25) = 3000

We want to determine whether or not the average is LESS THAN 120. This will occur when the total number of words is LESS THAN 3000

So, we could rephrase the target question as follows...
REPHRASED target question: Is the total number of words less than 3000?

IMPORTANT: When I scan ahead, I see that the two statements tell us about the number of words in the PREFACE. So, let's rephrase the target question so that it pertains to the preface only.
Since the report (without the preface) contains 2600 words, the preface must have FEWER THAN 400 words in order to keep the entire word count under 3000 words. So, we can RE-REPHRASE the target question as follows:

RE-REPHRASED target question: Does the preface contain fewer than 400 words?

Now that we've rewritten the target question to suit the statements, the rest of the question is a breeze.

Statement 1: Each paragraph of the preface has more than 100 words
In other words, the preface contains more than 200 words. There are several possibilities. Here are two:
Case a: the preface contains 220 words, in which case the preface contains fewer than 400 words
Case b: the preface contains 450 words, in which case the preface DOES NOT contain fewer than 400 words
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Each paragraph of the preface has fewer than 150 words
In other words, the preface contains fewer than 300 words.
If the preface contains FEWER than 300 words, then we can be certain that the preface contains fewer than 400 words
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Re: A report consisting of 2,600 words is divided into 23 paragr [#permalink]
A report consisting of 2,600 words is divided into 23 paragraphs. A 2-paragraph preface is then added to the report. Is the average (arithmetic mean) number of words per paragraph for all 25 paragraphs less than 120 ?

(1) Each paragraph of the preface has more than 100 words.
(2) Each paragraph of the preface has fewer than 150 words.

(1) Each paragraph of the preface has more than 100 words.

each para can hypothetically have 20k words as no upper limit is given
insufficient

(2) Each paragraph of the preface has fewer than 150 words
let each para has 149 words
both combined = 398

total words 2600+398 = 2898
max avg = 2898/25 = ~117 words

sufficient.

B
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Re: A report consisting of 2,600 words is divided into 23 paragr [#permalink]
A report consisting of 2,600 words is divided into 23 paragraphs. A 2-paragraph preface is then added to the report. Is the average (arithmetic mean) number of words per paragraph for all 25 paragraphs less than 120 ?

(1) Each paragraph of the preface has more than 100 words.
(2) Each paragraph of the preface has fewer than 150 words.

THIS IS A YES /NO TYPE DS
Original scenario
23 paragraphs 2600 words
average words per paragraph = 2600/23 = 113

Revised scenario
Added Preface (2 more paragraphs)
AIM :- IS average word per paragraph <120

(1) Each paragraph of the preface has more than 100 words.
The new preface paragraphs may have 30 words or 300 words.
Answer can be BOTH.
YES <120 or NO >120
INSUFFICIENT

(2) Each paragraph of the preface has fewer than 150 words.
Now either we will get a either only a YES or NO
SUFFICIENT

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Re: A report consisting of 2,600 words is divided into 23 paragr [#permalink]
Step 1: Analyse Question Stem

Total number of words in the 23 paragraphs = 2600
Number of paragraphs in preface = 2
Let total number of words in the preface = x

Average number of words per paragraph = $$\frac{Total words }{ Number of paragraphs}$$

Therefore, for all 25 paragraphs,

Average number of words per paragraph = $$\frac{{2600 + x} }{ 25}$$

The question can now be rephrased as, “Is $$\frac{{2600 + x} }{ 25}$$ < 120?”, which can further be rephrased as,

“Is 2600 + x < 120 * 25?” or,

“Is 2600 + x < 3000?” or,

“Is x < 400?”
Now, this is the question we have to answer.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: Each paragraph of the preface has more than 100 words.

If each paragraph has 101 words, then total number of words in these two paragraphs = 2 * 101 = 202 words. IN this case, x = 202 and x < 400.
If each paragraph has 1000 words, then total number of words in these two paragraphs = 2 * 1000 = 2000 words. IN this case, x = 2000 and x > 400.

The data in statement 1 is insufficient to find if x < 400.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2: Each paragraph of the preface has fewer than 150 words.

If each paragraph has fewer than 150 words, then total number of words in these two paragraphs = 2 * 150 = 300. Therefore, x < 400.

The data in statement 2 is sufficient to answer the question “Is x < 400?” with a definite YES.
Statement 2 alone is sufficient. Answer options C and E can be eliminated.

The correct answer option is B.
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Re: A report consisting of 2,600 words is divided into 23 paragr [#permalink]
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Re: A report consisting of 2,600 words is divided into 23 paragr [#permalink]
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