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A report consisting of 2,600 words is divided into 23 [#permalink]
06 Sep 2006, 19:45

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

65% (02:21) correct
35% (01:24) wrong based on 49 sessions

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 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.

The answer is (B).

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.

Re: A report consisting of 2,600 words is divided into 23 [#permalink]
11 Nov 2012, 02:25

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.

Re: A report consisting of 2,600 words is divided into 23 [#permalink]
11 Nov 2012, 02:52

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

_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Re: A report consisting of 2,600 words is divided into 23 [#permalink]
11 Nov 2012, 03:57

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. Sufficient to answer.

Re: A report consisting of 2,600 words is divided into 23 [#permalink]
11 Nov 2012, 07:02

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..

_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.