Of 30 applicants for a job, 14 had at least 4 years' experience, 18 ha

Question

Of 30 applicants for a job, 14 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree.

(A) 14
(B) 13
(C) 9
(D) 7
(E) 5

Let's discuss.

(A) 14
(B) 13
(C) 9
(D) 7
(E) 5

BLaw22 · Accepted Answer

Step 1: assign variables to each of the data points provided in the question so that they correspond to the OVERLAPPING SETS formula:

30 = Total Applicants = T
14 = Applicants with 4 yrs exp = G1
18 = Applicants with degrees = G2
3 = Applicants with NEITHER 4yrs exp nor degrees = NONE
?? = Applicants with BOTH 4yrs exp AND degrees = BOTH

Step 2: recall the formula for overlapping sets with 2 groups:  Total = G1 + G2 - BOTH + NONE

Step 3: Plug and chug the variables that we just assigned to solve for BOTH:
T = G1 + G2 - BOTH + NONE
30 = 14 + 18 - BOTH + 3
30 = 35 - BOTH
-5 = -BOTH
5 = BOTH

Correct Answer = E

Bunuel · Answer

Probably the easiest way to solve would be to make a matrix: Experience.PNG Note: numbers in black are given and numbers in red are calculated. Answer: E.

SrinathVangala · Answer

https://image.mathcaptain.com/cms/images/45/venn-diagram.JPG

The set of 30 applicants is a square.

Applicants who have less than four years experience and also have no degree are outside both the circles. = 3 applicants.

Left circle denotes the number of applicants with at least 4years experience = A.

Right circle denotes the number of applicants with degrees = B.

Now number of applicants in both the circles should be 30 - 3. ie 27.

This 27 is equal to A + B - A intersection B.

We have to find A intersection B.

27 = 14 + 18 - A intersection B which gives A intersection B as 5

Abhishek009 · Answer

Working same as  Bunuel , still sahring

EMPOWERgmatRichC · Answer

Hi BlueDragon2010,

Each of the responses presents a variation on the solution. Here's one that uses the Tic-Tac-Toe board.

The initial 3x3 grid contains the information given by the prompt.

The second 3x3 grid contains the first set of deductions (the sub-totals, in blue), followed by the sub-groups (in green).

https://postimg.org/image/h4gg5bmu5/

The answer to the question is in the upper-left corner:

Show Spoiler

A

GMAT assassins aren't born, they're made,
Rich

ScottTargetTestPrep · Answer

For this we can setup a table with 2 main categories: years of experience and degrees. These can be broken down further into:

1) Had at least 4 years of experience

2) Had less than 4 years of experience

3) Had a degree

4) Did not have a degree

In addition we are given the following information:

1) There are 30 total applicants

2) 14 applicants had at least 4 years of experience

3) 18 applicants had degrees

4) 3 applicants had less than 4 years of experience and did not have a degree

Let’s fill all this information into a table.

https://i.imgur.com/W1O2yjO.png

We can use the information to fill in the rest of the chart. Remember the “Total” label in each column or row represents the sum of the preceding two cells in each column or row, respectively.

https://i.imgur.com/LUrWLFd.png

We are asked how many of the applicants had at least 4 years' experience and a degree. We can see from our table that the answer is 5.

Answer is E.

dave13 · Answer

can anyone tell me whats wrong with my solution? or is it correct?

?

14+18+3-2x=30 35-2x=30 5 = 2x chetan2u hello,

can please tell me if my solution is correct? it seems like i got 5, but if solve the last part to the end, then i will have x = 2.5

niks18 hello

perhaps you have idea?

niks18 · Answer

Hi  dave13

what is your logic behind "2x"? what is "x" and why "2x" ?

dave13 · Answer

Hi niks18 , thanks for a nice question

i am more than happy to explain

let me explain my logic

total applicants 30 14 at least have 4 years` experience 18 - have degrees 3 - had less than 4 years experience and dont have experinence now question: How many of the applicants had at least 4 years' experience and a degree ? hence let number of applicants who had both at least 4 yrs experience and a degree be 2x (why 2 and not just x because it says both hence x+x = 2x ) please advice

have a fantastic day

niks18 · Answer

x  is a variable here and variable must represent only one particular unknown quantity. For any other unknown quantity you need to define a different variable. Here unknown quantity is number of people who have BOTH a degree and at least 4 years of experience. Same individual will posses both the characteristics.

dave13 · Answer

ok i think now i got it

thank you

# of total applicants = 30 # of apllicants with at least have 4 years` experience = 14 # of applicants with degrees = 18 # of applicants had less than 4 years experience and dont have experinence = 3 # of applicants who had BOTH at least 4 years' experience and a degree = x 14+18-x+3=30 35-x=30 5 = x

msali1983 · Answer

Hi can any one share the solution using venn diagram approach.

BLTN · Answer

Dear msali1983 take it

ArnauG · Answer

To determine the number of applicants who had at least 4 years' experience and a degree, we can use the principle of inclusion-exclusion.

Given:
Total applicants (n) = 30
Applicants with at least 4 years' experience (A) = 14
Applicants with degrees (B) = 18
Applicants with less than 4 years' experience and no degree = 3

To find the number of applicants with at least 4 years' experience and a degree, we can use the formula:

A ∩ B = A + B - (A ∪ B)

Here's the calculation:
A ∪ B = A + B - (A ∩ B) = 14 + 18 - (30 - 3)   = 14 + 18 - 27 = 32 - 27 = 5

Therefore, the number of applicants who had at least 4 years' experience and a degree is (E) 5.

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Of 30 applicants for a job, 14 had at least 4 years' experience, 18 ha

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