Any approaches to solve these?

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intenseCK: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Wed Feb 01, 2012 9:41 pm

Any approaches to solve these?

by intenseCK » Wed Apr 11, 2012 3:08 am

Q1- Each employee is either a director or a manager. What % of the employees are directors?
A. The avg. salary of managers is 5000$ less then the avg. of employees
B. The avg. salary of directors is $15000 greater then the avg of all employees.

Q2. The ratio of women to children on a tour is 5:2. how many men are there?
A. Ratio of children to women is 5:11
B. There are less then 30 women on the tour.

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Source: Beat The GMAT — Data Sufficiency | Wed Apr 11, 2012 3:08 am

Pharo: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Mon Jan 18, 2010 11:09 pm; Thanked: 8 times

by Pharo » Wed Apr 11, 2012 3:32 am

Q1:

Since we are only given the average values we cannot answer this question. Look at it this way:

Imagine i found that the average salary of managers = 5000 and average salary of directors are 35000. (I can get this information from the statements given by the way). But How can this give me the total number of employees? Maybe i have 1 manager and 1 director. (manager is paid 5k and director is paid 35k hence the averages make out.. ) OR i can have 1 manager with 5k salary and 5 directors with 7k salary..

Hence the solution is E.

Damn.. Made a mistake.. After solving for averages there is a way to get the ratio.. Answer is C

Last edited by Pharo on Wed Apr 11, 2012 3:57 am, edited 1 time in total.

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Pharo: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Mon Jan 18, 2010 11:09 pm; Thanked: 8 times

by Pharo » Wed Apr 11, 2012 3:44 am

Q2:

I am assuming the statement 1 reads as : Ratio of children to men is 5:11
--

Let's write down what we know. We know that for every 5 women there are 2 children.

Statement 1: States that for every 5 children there are 11 men.

Let's try to combine the first statement with the original statement.

5w = 2c && 5c = 11m && c,m,w are all +ve integers. Let's try to put the equations into a line and try to find an equality for xw = ym;

in 5w = 2c we have 2 as a multiplier for c and in 5c = 11m we have 5 as a multiplier. Let's multiply 5w = 2c with 5 and 5c = 11m with 2 (easiest way to equate the c's constants)

25w = 10c && 10c = 22m ; 25w = 10c = 22m ;; Now we have a ratio. For every 25 woman we have 10 children and 22 men. But since this is only a ratio and we do not have an upper bound for one of the numbers, we cannot answer this question. ;;; Statement 1 is insufficient.

Statement 2: Clearly insufficient alone.

Statements 1 & 2 Combined:

now we have 25w = 10c = 22m && an upper bound of 30 for the number of women. hence the problem can be solved. --> There are 25 women, 10 children and 22 men in this group.

Solution is C

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Apr 11, 2012 3:45 am

intenseCK wrote:Q1- Each employee is either a director or a manager. What % of the employees are directors?
A. The avg. salary of managers is 5000$ less then the avg. of employees
B. The avg. salary of directors is $15000 greater then the avg of all employees.

Let the average salary of managers of the task force = S(m), the average salary of the directors on the task force = S(d), and the average salary of all the employee on the task force = S(e).
Let the no. of managers = m and no. of directors = d. We have to find d/(m + d).

(1) S(m) = S(e) - 5000, which ALONE is NOT SUFFICIENT.

(2) S(d) = S(e) + 15000, which ALONE is NOT SUFFICIENT.

Combining (1) and (2), we know that S(e) = {m * S(m) + d * S(d)}/(m + d)
So, S(e) = {m * [S(e) - 5000] + d * [S(e) + 15000]}/(m + d)
m * S(e) + d * S(e) = m * S(e) - 5000m + d * S(e) + 15000d
15000d = 5000m
3d = m
So, d/(m + d) = d/4d = 1/4, which is SUFFICIENT.

The correct answer is C.

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Apr 11, 2012 3:46 am

intenseCK wrote: Q2. The ratio of women to children on a tour is 5:2. how many men are there?
A. Ratio of children to women is 5:11
B. There are less then 30 women on the tour.

Given: w : c = 5 : 2
Let us assume that number of women, w = 5x and number of children, c = 2x for some integer x.
If m = number of males, we have to find the value of m.

(1) c : m = 5 : 11
Let us assume that number of children, c = 5y and number of men, m = 11y, but this is NOT sufficient to find m.

(2) w < 30; NOT sufficient to find m.

Combining (1) and (2), w = 5x and w < 30 implies 5x < 30 or x < 6
c = 5y implies c is a multiple of 5 and c = 2x implies x = 5 (as x < 6)
So, c = 2 * 5 = 10 = 5y implies y = 2
So, m = 11 * 2 = 22; SUFFICIENT.

The correct answer is C.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Wed Apr 11, 2012 7:30 am

intenseCK wrote:Q1- Each employee is either a director or a manager. What % of the employees are directors?
A. The avg. salary of managers is 5000$ less then the avg. of employees
B. The avg. salary of directors is $15000 greater then the avg of all employees.

If we understand the nature of weighted averages, we can solve this problem with almost no math. I posted an explanation here:

https://www.beatthegmat.com/manager-or-d ... 90558.html

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Wed Apr 11, 2012 7:32 am

intenseCK wrote: Q2. The ratio of women to children on a tour is 5:2. how many men are there?
A. Ratio of children to women is 5:11
B. There are less then 30 women on the tour.

For an alternate approach, check here:

https://www.beatthegmat.com/ratio-proportion-t82796.html