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Math Expert V
Joined: 02 Sep 2009
Posts: 55172
A stenographer is tasked with typing a certain letter. How many words  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 60% (01:35) correct 40% (01:43) wrong based on 454 sessions

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A stenographer is tasked with typing a certain letter. How many words long is the letter?

(1) It will take two minutes less time to type the letter at an average speed of 80 words per minute than at an average speed of 60 words per minute.
(2) It will take 6 minutes to type the first half of the letter at an average speed of 40 words per minute.

Kudos for a correct solution.

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Re: A stenographer is tasked with typing a certain letter. How many words  [#permalink]

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Bunuel wrote:
A stenographer is tasked with typing a certain letter. How many words long is the letter?

(1) It will take two minutes less time to type the letter at an average speed of 80 words per minute than at an average speed of 60 words per minute.
(2) It will take 6 minutes to type the first half of the letter at an average speed of 40 words per minute.

Kudos for a correct solution.

(1) It will take two minutes less time to type the letter at an average speed of 80 words per minute than at an average speed of 60 words per minute.

80(t-2) = 60t => t => the number of words long => SUFFICIENT
2) It will take 6 minutes to type the first half of the letter at an average speed of 40 words per minute.
Typing the letter will spend 12 mins => the number words: 40*12 => SUFFICIENT

Ans: D
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A stenographer is tasked with typing a certain letter. How many words  [#permalink]

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St1: 60*x=80*(x-2) -> x=8 480 Words Sufficient
St2: Half of the letter = 6*40 = 240 Wholw= 480

Answer (D)
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Re: A stenographer is tasked with typing a certain letter. How many words  [#permalink]

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1
Let N be the number of words in the letter.
We need to find N

Statement 1:

Speed of typing =Total Words / Time taken

Using this we can write

(N/60 ) - (N/80) = 2
We can find N from this equation.
Sufficient

Statement 2
(N/2) = 6 * 40
Therefore N = 480
Sufficient

Answer = D
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Re: A stenographer is tasked with typing a certain letter. How many words  [#permalink]

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camlan1990 wrote:
Bunuel wrote:
A stenographer is tasked with typing a certain letter. How many words long is the letter?

(1) It will take two minutes less time to type the letter at an average speed of 80 words per minute than at an average speed of 60 words per minute.
(2) It will take 6 minutes to type the first half of the letter at an average speed of 40 words per minute.

Kudos for a correct solution.

(1) It will take two minutes less time to type the letter at an average speed of 80 words per minute than at an average speed of 60 words per minute.

80(t-2) = 60t => t => the number of words long => SUFFICIENT
2) It will take 6 minutes to type the first half of the letter at an average speed of 40 words per minute.
Typing the letter will spend 12 mins => the number words: 40*12 => SUFFICIENT

Ans: D

I agree with the solution. But should we consider the probability that the half of letter can be half of the pages or half of the lines than just assuming that it means half of the words.?
Math Expert V
Joined: 02 Sep 2009
Posts: 55172
Re: A stenographer is tasked with typing a certain letter. How many words  [#permalink]

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1
Bunuel wrote:
A stenographer is tasked with typing a certain letter. How many words long is the letter?

(1) It will take two minutes less time to type the letter at an average speed of 80 words per minute than at an average speed of 60 words per minute.
(2) It will take 6 minutes to type the first half of the letter at an average speed of 40 words per minute.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Question Type: What Is the Value? This question asks for a specific number indicating the length—in words—of the letter.

Statement 1: This statement can be translated into the following equation: “(t – 2) 80 = t (60)” where t is the number of minutes it takes to type the letter at a rate of 60 words per minute. This equation then simplifies to “80t – 160 = 60t.” Subtract 60t from both sides and add 160 to each, and the equation becomes “20t = 160” and “t = 8.” Therefore 8 • 60 gives a total of 480 words. Of course the equation did not have to be solved. As soon as you got (t – 2) 80 = 60t you should see that this is a linear equation with just one variable and it can be solved for a single value. This is sufficient. The answer is either A or D.

Statement 2: This statement can be translated into an equation using the formula w = rt (work = rate • time). The work is 1/2 of the letter. The rate is 40 words per minute and the time is 6 minutes. The equation is “ 1/2*w = 40*6” or “1/2*w = 240” and “w = 480.” This statement is sufficient as well; the answer is D.
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GMAT 1: 620 Q47 V30 Re: A stenographer is tasked with typing a certain letter. How many words  [#permalink]

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Question, how many words? Let the number of words be X
St 1: Time (80 wpm) = Time (60 wpm) - 2
--> x/80 = x/60 - 2. X can be easily calculated. So, St 1 is sufficient. Possible Ans - A and D
St 2 : first half means x/2. for X/2 words it takes 6 minutes with the rate of 40 wpm.
--> x/2 = 6*40. again X can easily be calculated. so, St2 is also sufficient. Ans D
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Re: A stenographer is tasked with typing a certain letter. How many words  [#permalink]

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pushpitkc niks18 Hatakekakashi
amanvermagmat VeritasPrepKarishma

Quote:
A stenographer is tasked with typing a certain letter. How many words long is the letter?

How many TOTAL words in the letter she writes?

Quote:
(1) It will take two minutes less time to type the letter at an average speed of 80 words per minute than at an average speed of 60 words per minute.

How to interpret this as : Avg = Sum of words / No of words and take it forward
Quote:
(2) It will take 6 minutes to type the first half of the letter at an average speed of 40 words per minute.

Why do we assume that RATE will NOT CHANGE in the second half?
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Re: A stenographer is tasked with typing a certain letter. How many words  [#permalink]

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adkikani wrote:
pushpitkc niks18 Hatakekakashi
amanvermagmat VeritasPrepKarishma

Quote:
A stenographer is tasked with typing a certain letter. How many words long is the letter?

How many TOTAL words in the letter she writes?

Quote:
(1) It will take two minutes less time to type the letter at an average speed of 80 words per minute than at an average speed of 60 words per minute.

How to interpret this as : Avg = Sum of words / No of words and take it forward
Quote:
(2) It will take 6 minutes to type the first half of the letter at an average speed of 40 words per minute.

Why do we assume that RATE will NOT CHANGE in the second half?

Hi adkikani

Quote:
(1) It will take two minutes less time to type the letter at an average speed of 80 words per minute than at an average speed of 60 words per minute.

How to interpret this as : Avg = Sum of words / No of words and take it forward

Note here we are given average speed of words typed i.e. total words typed/total time taken to type. Now you are given two scenarios and two average speed. You can frame an equation using the relationship and solve to get total number of words.

Quote:
(2) It will take 6 minutes to type the first half of the letter at an average speed of 40 words per minute.

Why do we assume that RATE will NOT CHANGE in the second half?

Here you are given Average Speed which will again imply that $$\frac{total words typed}{total time taken}$$. So there will not be multiple average speeds for the same document. Average speed implies that it has taken care of all the intermittent speeds.
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Re: A stenographer is tasked with typing a certain letter. How many words  [#permalink]

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Bunuel wrote:
Bunuel wrote:
A stenographer is tasked with typing a certain letter. How many words long is the letter?

(1) It will take two minutes less time to type the letter at an average speed of 80 words per minute than at an average speed of 60 words per minute.
(2) It will take 6 minutes to type the first half of the letter at an average speed of 40 words per minute.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Question Type: What Is the Value? This question asks for a specific number indicating the length—in words—of the letter.

Statement 1: This statement can be translated into the following equation: “(t – 2) 80 = t (60)” where t is the number of minutes it takes to type the letter at a rate of 60 words per minute. This equation then simplifies to “80t – 160 = 60t.” Subtract 60t from both sides and add 160 to each, and the equation becomes “20t = 160” and “t = 8.” Therefore 8 • 60 gives a total of 480 words. Of course the equation did not have to be solved. As soon as you got (t – 2) 80 = 60t you should see that this is a linear equation with just one variable and it can be solved for a single value. This is sufficient. The answer is either A or D.

Statement 2: This statement can be translated into an equation using the formula w = rt (work = rate • time). The work is 1/2 of the letter. The rate is 40 words per minute and the time is 6 minutes. The equation is “ 1/2*w = 40*6” or “1/2*w = 240” and “w = 480.” This statement is sufficient as well; the answer is D.

From the wording of Statement 2, it is not clear that the average speed of 40 words per minute is for the whole document. I considered the average speed of 40 words per minute only for the first half. Re: A stenographer is tasked with typing a certain letter. How many words   [#permalink] 03 Jan 2019, 07:51
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