Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

The workforce of a certain company comprised exactly 10,500 [#permalink]

Show Tags

09 Sep 2005, 06:32

2

This post received KUDOS

13

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

49% (05:07) correct
51% (03:41) wrong based on 281 sessions

HideShow timer Statistics

The workforce of a certain company comprised exactly 10,500 employees after a four-year period during which it increased every year. During this four-year period, the ratio of the number of workers from one year to the next was always an integer. The ratio of the number of workers after the fourth year to the number of workers after the the second year is 6 to 1. The ratio of the number of workers after the third year to the number of workers after the first year is 14 to 1. The ratio of the number of workers after the third year to the number of workers before the four-year period began is 70 to 1. How many employees did the company have after the first year?

10,500/6 = 1,750 = number of workers after the second year

Now we need a number of workers after the third year. Let it = X. We have some clues to get to X:
- 10,500/X is an integer greater than 1.
-X/1,750 is an integer greater than 1.

We note that 10,500/1750 = 6. So we need two integer factors of 6, and neither factor can be 1. This means that the factors are 2 and 3.

Therefore we have two possibilities: either X is 3,500 or X is 5,250.

But we know that the ratio of the number of workers after the third year to the number of workers after the first year is 14 to 1.

3,500/14 = 250
5,250/14 = 375

So the number of workers after the first year is either 250 or 375. But this has to be an integer ratio with the number of workers after the second year, which is 1,750. Of the two possibilities, only 250 satisfies the condition, because 1,750/250 = 7 and 1,750/375 = 4 2/3.

Therefore the number of workers after the first year is 250. Answer C.

Re: The workforce of a certain company comprised exactly 10,500 [#permalink]

Show Tags

24 Sep 2014, 03:37

jlgdr wrote:

Any alternative approach to solve this backsolving?

Thanks much! Cheers! J

make a table according to ratios

x 5x 1750 70x 10500

now put options in place of 5x (i.e. multiply each option by 14) you can eliminate A & B just by looking C gives 3500 D gives 490 E gives 10500 (Eliminated) D will not give an integer ratio It will take less than 90 seconds

Re: The workforce of a certain company comprised exactly 10,500 [#permalink]

Show Tags

08 Nov 2014, 01:34

sanket1991 wrote:

jlgdr wrote:

Any alternative approach to solve this backsolving?

Thanks much! Cheers! J

make a table according to ratios

x 5x 1750 70x 10500

now put options in place of 5x (i.e. multiply each option by 14) you can eliminate A & B just by looking C gives 3500 D gives 490 E gives 10500 (Eliminated) D will not give an integer ratio It will take less than 90 seconds

I didn't get it ? checking each option w.r.t to 5x, will give x=10 for option A. This will satisfy all the ratios. May be I am not getting it? Can any one explain this. Thanks

Re: The workforce of a certain company comprised exactly 10,500 [#permalink]

Show Tags

09 Nov 2014, 17:20

solitaryreaper wrote:

sanket1991 wrote:

jlgdr wrote:

Any alternative approach to solve this backsolving?

Thanks much! Cheers! J

make a table according to ratios

x 5x 1750 70x 10500

now put options in place of 5x (i.e. multiply each option by 14) you can eliminate A & B just by looking C gives 3500 D gives 490 E gives 10500 (Eliminated) D will not give an integer ratio It will take less than 90 seconds

I didn't get it ? checking each option w.r.t to 5x, will give x=10 for option A. This will satisfy all the ratios. May be I am not getting it? Can any one explain this. Thanks

Well 5x is the number of first year students (as x is number before first year) What I meant was , Options are given for first year, and I have take first year as 5x multiply by 14 will give you number of third year students A and B are so low that they wont reach to 10500 when multiplied by these numbers. I hope you understand...

The workforce of a certain company comprised exactly 10,500 [#permalink]

Show Tags

14 Jul 2016, 23:15

Is this Question Correct? Question says " the ratio of the number of workers from one year to the next was always an integer." i.e. (After 2nd Year): (After 3rd year):: (integer):1

This statement should be " the ratio of the number of workers from one year to the PREVIOUS was always an integer."

The workforce of a certain company comprised exactly 10,500 [#permalink]

Show Tags

03 Aug 2016, 23:21

1

This post was BOOKMARKED

FN wrote:

The workforce of a certain company comprised exactly 10,500 employees after a four-year period during which it increased every year. During this four-year period, the ratio of the number of workers from one year to the next was always an integer. The ratio of the number of workers after the fourth year to the number of workers after the the second year is 6 to 1. The ratio of the number of workers after the third year to the number of workers after the first year is 14 to 1. The ratio of the number of workers after the third year to the number of workers before the four-year period began is 70 to 1. How many employees did the company have after the first year?

A very trickily-worded question. I'll use the notation \(Y_n \to Y_k = R\) to signify the ratio increase from year \(n\) to year \(k\), where \(R\) is an integer \(> 1\) (the number of workers increased every year and is an integral ratio).

Determine the number of workers on year 2: \(Y_2 = \frac{Y_4}{Y_2 \to Y_4} = \frac{10500}{6} = 1750\)

Since \(Y_2 \to Y_4 = 6\) is a 2-year gap, there must be two intermediate ratios, the product of which is 6. Therefore each ratio is a combination of the prime factors of 6. We do not currently know this combination. \(Y_2 \to Y_3 \,\bigg\vert\, Y_3 \to Y_4 = \{2,3\}\).

Since \(Y_1 \to Y_3 = 14\) is a 2-year gap, there must be two intermediate ratios, the product of which is 14. \(Y_1 \to Y_2 \,\bigg\vert\, Y_2 \to Y_3 = \{2,7\}\).

From the intersection of the above two statements, we can see that: \(Y_2 \to Y_3 = 2\). From this, we can conclude: \(Y_1 \to Y_2 = 7\\ Y_3 \to Y_4 = 3\)

Since we know \(Y_2\) from above, we can obtain \(Y_1\) as follows: \(Y1 = \frac{Y_2}{Y_1 \to Y_2} = \frac{1750}{7} = 250\)

Re: The workforce of a certain company comprised exactly 10,500 [#permalink]

Show Tags

11 Jan 2017, 06:38

x --> x1--> x2 --> x3 --> x4

x4 is 10,500 & x4:x2=6:1 i.e. x2=1750 x3:x1=14:1 x3:x=70:1

since the question states that the ratio between any two years is always an integer, we know that 1,750 must be a multiple of the number of workers after the first year. Since only 70 and 250 are factors of 1750, we know the answer must be either choice B or choice C. If we assume that the number of workers after the first year is 70, however, we can see that this must cannot work. The number of workers always increases from year to year, but if 70 is the number of workers after the first year and if the number of workers after the third year is 14 times greater than that, the number of workers after the third year would be 14 x 70 = 980, which is less than the number of workers after the second year. So choice B is eliminated and the answer must be choice C. I started with choice c. x1=250

50--> 250 --> 1750 --> 3500 --> 10,500

Chocie A returns x3=700 which is less than x2=1750, so it has to be ruled out and Choice B can also be ruled out.

No other answer choice returns an integer ratio.
_________________

Thanks & Regards, Anaira Mitch

gmatclubot

Re: The workforce of a certain company comprised exactly 10,500
[#permalink]
11 Jan 2017, 06:38

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...