If There are 78 People Working at an Office, How Many of Them are Women Older than 40?

Question: If there are 78 people working at an office, how many of them are women older than 40?

1. There are twice as many men working at the office than women.
2. The number of men and women under the age of 40 is the same.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“If there are 78 people working at an office, how many of them are women older than 40?" is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer:

Approach 1

Firstly, consider the statement (1), we have:

There are twice as many men working at the office than women.

This statement is insufficient in itself because it is only given that there are 26 women and 53 men.

Now, we will consider statement (2), we have:

The number of men and women under the age of 40 is same.

This statement is insufficient in itself because this only tells that there are the same number of men and women under the age of 40.

So, we have observed that both statement (1) and (2) combined are insufficient.

Correct option: E

Approach 2

let us consider that men and women older than 40 years be M and W.
From question data, there are total of 78 people working at an office. The value of W has to be found out.

Firstly, consider the statement (1), we have:
There are twice as many men working at the office than women.
This means: Total number of men = 2 (Total number of women)
But it is insufficient to find out the exact value of W since this can only tell us the vale of the total number of women.
So, by observing this, we can say that options A and D can be eliminated.

Now considering statement(2), we have:
The number of men and women under the age of 40 is same.
This means, m = w
This statement is also insufficient to find out the exact value of w.
So, we can say that option B can also be eliminated.

Combining the statement (1) and (2), we will have:
From statement (1), total number of men = 52 and total number of women = 26
From statement (2), m = w
But we don’t have any information about how many of the 26 women are under 40 and how many ae older than 40, more importantly, there is no information about how many people are exactly 40 years old.
The combination of the above two statements is insufficient.

So, Option C can also be eliminated.

Correct option: E

Suggested GMAT Quant Questions

• p, r, s, t, u An Arithmetic Sequence is a Sequence in Which each Term After the First Term is Equal to the Sum of the Preceding Term and a Constant
• Last Year 26 Members of a Certain Club Traveled to England, 26 Members Traveled to France, and 32 Members Traveled to Italy.
• Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
• Excluding Stoppages, The Speed of a Bus is 54km/hr and Including Stoppage, It is 45km/hr
• If x is a positive integer, what is the value of x?
• If 75 Percent of a Class Answered the First Question on a Certain Test Correctly
• Running at the Same Constant Rate, 6 Identical Machines can Produce a Total of 270 Bottles Per Minute.
• What is the Value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2
• The Kinetic Energy K, in Joules, Provided by the Mass of a Particle m, in Kilograms, With a Velocity of v Meters Per Seconds
• Juan Bought Some Paperback Books That Cost $8 Each and Some Hardcover Books That Cost $25 Each
• Of the 150 houses in a certain development, 60 percent have air-conditioning, 50 percent have a sunporch, and 30 percent have a swimming pool
• Company C Sells a Line of 25 Products with an Average Retail Price of $1,200
• Six Bells Commence Tolling Together and Toll at Intervals of 2, 4, 6, 8 10 and 12 seconds Respectively
• The Set S of Numbers has the following Properties
• If 10, 12 and ‘x’ are Sides of an Acute Angled Triangle, How Many Integer Values of ‘x’ are Possible?
• How Many Five Digit Numbers Can be Formed Using Digits 0, 1, 2, 3, 4, 5, Which Are Divisible By 3
• X is Older Than Y, Z Is Younger Than W And V is Older Than Y. Is Z Younger Than X?
• A is twice as good a workman as B and together they finish a piece of work in 16 days.
• A Merchant has 1000 kg of Sugar Part of Which He Sells at 8% Profit and The Rest at 18% Profit
• The Average Age of Chief Executive Officers (CEO’s) in a Large Sample of Companies is 57