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

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A report consisting of 2,600 words is divided into 23 [#permalink]

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06 Sep 2006, 20:45
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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 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-report-consisting-of-2-600-words-is-divided-into-23-paragr-144340.html
[Reveal] Spoiler: OA
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Re: A report consisting of 2,600 words is divided into 23 [#permalink]

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06 Sep 2006, 21:12
haas_mba07 wrote:
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 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.

In order for the average number of words per paragraph for all 25 paragraphs to be less than 120, the total number of words (2,600 + two paragraph preface) must be less than 3000 words (25x120).

(1) isn't sufficient b/c the average number of words per paragraph could be less than 120 or more than 120. For example, if each paragraph of the preface had 300 words each then the total number of words = 2,600 + 600 = 3,200. We know from earlier that if the total number of words is greater than 3,000 then the average number of words per paragraph for all 25 paragraphs will be greater than 120.
On the other hand, if each paragraph of the preface had 120 words each then the toal number of words = 2,600 + 240 = 2,840 so the average number of words per paragraph for all 25 paragraphs will be less then 120.

(2) is sufficient b/c the total number of words per paragraph for all 25 paragraphs will be less than 3,000 even if the preface had 150 words per paragraph. As long as the two paragraph preface is less then 400 words, the total number of words will be less than 3,000 which will in turn maintain that the average number of words per for all 25 paragraphs will be less than 120.
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Re: A report consisting of 2,600 words is divided into 23 [#permalink]

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06 Sep 2006, 23:09
Got B also...

From 1, we cannot determine the average since the 2 additional paragraphs could be 500 words each

INSUFF

From 2, the upper bound on all paragraphs is 150. Hene 23 paragraphs are 2600 words and the other 2 could be 149 + 149

the average in this case is <120. Hence SUFF
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Re: A report consisting of 2,600 words is divided into 23 [#permalink]

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06 Sep 2006, 23:18
yeah B. 25*120= 3000

2600 + 2*150 = 2900 at most.

Hence, B is enough
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Re: A report consisting of 2,600 words is divided into 23 [#permalink]

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07 Sep 2006, 01:54
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average number of words per paragraph for all 25 paragraphs less than 120

ie : 2600+additional wards from the additional preface (say it is represented by Y)/25<120

thus the question asks whether Y<400 OR NOT

From one it could b yes or no.....insuff
from two and if we assumed worst case scenario y = 300 thus

sure y<400

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Re: A report consisting of 2,600 words is divided into 23 [#permalink]

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11 Nov 2012, 03:14
Hi Bunuel,
It took a crazy 3:19 mins to solve this Question by pluggin in the values.. chose 101 for (1) and 149 for (2)

Is these any faster way to solve this Question ?
Regards,
Sachin
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Re: A report consisting of 2,600 words is divided into 23 [#permalink]

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11 Nov 2012, 03:25
haas_mba07 wrote:
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 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.

Consider (1) -> If each preface paragraph has more than 100 words, then
i) each preface paragraph can have 1,000,000 words. Clearly, average number of words for all 25 paragraphs will be more than 120.

ii) each preface paragraph can have just 3 words. $$\frac{(2600+3+3)}{25}<120$$

Therefore, (1) alone is insufficient.

Consider (2) -> If each preface paragraph has less than 150 words, then
worst case - both paragraphs will have 149 words. $$\frac{(2600+149+149)}{25}=\frac{2898}{25}<120$$
Therefore, (2) is sufficient.

Hence, B is the answer. I don't think any substitution beyond this is necessary here.
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Re: A report consisting of 2,600 words is divided into 23 [#permalink]

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11 Nov 2012, 03:52
th03 wrote:
haas_mba07 wrote:
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 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.

Consider (1) -> If each preface paragraph has more than 100 words, then
i) each preface paragraph can have 1,000,000 words. Clearly, average number of words for all 25 paragraphs will be more than 120.

ii) each preface paragraph can have just 3 words. $$\frac{(2600+3+3)}{25}<120$$

Therefore, (1) alone is insufficient.

Consider (2) -> If each preface paragraph has less than 150 words, then
worst case - both paragraphs will have 149 words. $$\frac{(2600+149+149)}{25}=\frac{2898}{25}<120$$
Therefore, (2) is sufficient.

Hence, B is the answer. I don't think any substitution beyond this is necessary here.

you still need to consider 101 and then calculate the average .. and you cannot say you have 3 words per paragraph as its clearly mentioned that it has to be more than 100..

The prob with this question is it tests how quickly we can divide.. and that sucks :D
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Re: A report consisting of 2,600 words is divided into 23 [#permalink]

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11 Nov 2012, 04:57
Sachin9 wrote:
th03 wrote:
haas_mba07 wrote:
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 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.

Consider (1) -> If each preface paragraph has more than 100 words, then
i) each preface paragraph can have 1,000,000 words. Clearly, average number of words for all 25 paragraphs will be more than 120.

ii) each preface paragraph can have just 3 words. $$\frac{(2600+3+3)}{25}<120$$

Therefore, (1) alone is insufficient.

Consider (2) -> If each preface paragraph has less than 150 words, then
worst case - both paragraphs will have 149 words. $$\frac{(2600+149+149)}{25}=\frac{2898}{25}<120$$
Therefore, (2) is sufficient.

Hence, B is the answer. I don't think any substitution beyond this is necessary here.

you still need to consider 101 and then calculate the average .. and you cannot say you have 3 words per paragraph as its clearly mentioned that it has to be more than 100..

The prob with this question is it tests how quickly we can divide.. and that sucks :D

Not really. The question tests how can u interpret same information in differnt ways. If you can, question becomes simpler and less time consuming.

Lets see. Question says, 23 para -2600 words. after addition of 2 more paras is average less than 120. OR is total word count for 25 paras less than 3000?

Stem 1: Each new para has more than 100 words. it could be only 101 or 500 each. So total word count may or may not be less than 3000.
Not suff
Stem 2: Each new para has less than 150 word. So max addition could have been something less than 300. So total has to be less than 2900.

Hence B it is.
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Re: A report consisting of 2,600 words is divided into 23 [#permalink]

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11 Nov 2012, 08:02
agreed.. didn;t reallyhave to calculate /divide in case 2.. since its a DS Question..
just knowing that we can answer the prompt should be sufficient..
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Re: A report consisting of 2,600 words is divided into 23 [#permalink]

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Re: A report consisting of 2,600 words is divided into 23 [#permalink]

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30 Jul 2015, 07:22
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haas_mba07 wrote:
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 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.

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 ?

The question asks whether the average number of words per paragraph for all 25 paragraphs is less than 120, or whether the total number of words for all 25 paragraphs is less than 25*120=3,000. Thus, the question basically asks whether the total number of words for 2-paragraph preface is less than 3,000-2,600=400.

(1) Each paragraph of the preface has more than 100 words. This implies that the total number of words for 2-paragraph preface is more than 200. Not sufficient.

(2) Each paragraph of the preface has fewer than 150 words. This implies that the total number of words for 2-paragraph preface is less than 300. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-report-consisting-of-2-600-words-is-divided-into-23-paragr-144340.html
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Re: A report consisting of 2,600 words is divided into 23   [#permalink] 30 Jul 2015, 07:22
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# A report consisting of 2,600 words is divided into 23

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