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guddo
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A company has a total of 1,650 employees, some of whom are office work 24 Jan 2024, 02:13
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55% (hard)

Question Stats:

73% (02:23) correct 27% (02:01) wrong based on 909 sessions

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A company has a total of 1,650 employees, some of whom are office workers. How many of the employees are enrolled in Medical Plan X ?

(1) The number of employees not enrolled in the plan is 75 more than the number of office workers enrolled in the plan.
(2) The number of employees enrolled in the plan is twice the number of office workers enrolled in the plan.

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A company has a total of 1,650 employees, some of whom are office work 13 May 2024, 13:05
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guddo
A company has a total of 1,650 employees, some of whom are office workers. How many of the employees are enrolled in Medical Plan X ?

(1) The number of employees not enrolled in the plan is 75 more than the number of office workers enrolled in the plan.
(2) The number of employees enrolled in the plan is twice the number of office workers enrolled in the plan.
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We can solve this question using a 2 * 2 matrix 

A company has a total of 1,650 employees, some of whom are office workers. How many of the employees are enrolled in Medical Plan X

 ­
Attachment:
1.png
1.png [ 30.01 KiB | Viewed 12856 times ]

\(OW\) ⇒ Office Workers
\(MP_x\) ⇒ Enrolled in Medical Plan X­

Statement 1

(1) The number of employees not enrolled in the plan is 75 more than the number of office workers enrolled in the plan.

Let the number of office workers enrolled in the plan = x

The number of employees not enrolled in the plan = x + 75

However, as we do not know the values of the other cells, we cannot find the value of x. The statement alone is not sufficient and we can eliminate A, and D.

Attachment:
2.png
2.png [ 34.34 KiB | Viewed 12207 times ]

Statement 2

(2) The number of employees enrolled in the plan is twice the number of office workers enrolled in the plan

Let the number of office workers enrolled in the plan = y

The number of employees enrolled in the plan = 2y

However, as we do not know the values of the other cells, we cannot find the value of y. The statement alone is not sufficient. Eliminate B.

Attachment:
3.png
3.png [ 33.08 KiB | Viewed 11940 times ]

Combined

Using both statements, we can conclude that x = y

Hence, we can represent the combined information as shown below.

Attachment:
4.png
4.png [ 37.12 KiB | Viewed 11847 times ]

2x + x + 75 = 1650

3x = 1575

x = 525

Hence, 2x = 1050

The statements combined are sufficient.

Option C

 ­
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A company has a total of 1,650 employees, some of whom are office work 26 Jan 2024, 16:22
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guddo
A company has a total of 1,650 employees, some of whom are office workers. How many of the employees are enrolled in Medical Plan X ?

(1) The number of employees not enrolled in the plan is 75 more than the number of office workers enrolled in the plan.
(2) The number of employees enrolled in the plan is twice the number of office workers enrolled in the plan.

Show Spoiler
Attachment:
2024-01-24_13-10-46.png
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\(1650 = O_e+O_{ne}+P_e+P_{ne}\)...(i)

\(O_e\) = office enrolled
\(O_{ne}\) = office NOT enrolled.

\(P_e\) = NOT office, enrolled.
\(P_{ne}\) = NOT office, NOT enrolled.

We need \(O_e\)+\(P_e\) = i.e. Those that are enrolled from office and those that are enrolled from outside office.

\(O_e\)+\(P_e = 1650 - (O_{ne} +P_{ne})\)...(ii) \(\hspace{4mm}\)from ...(i)

(1) The number of employees not enrolled in the plan is 75 more than the number of office workers enrolled in the plan.

\(O_{ne} +P_{ne} - O_e=75 \)

Using (ii) and statement (1) we finally get :

\(2O_e + P_e = 1575\)

INSUFF.

(2) The number of employees enrolled in the plan is twice the number of office workers enrolled in the plan

\(O_e + P_e = 2O_e\)

\(P_e = O_e\)

INSUFF.

1+2

\(3O_e = 1575\)

\(O_e = 525\)

Since \( O_e=P_e \)

Total enrolled from office and outside office is \(525+525 =1050\)

SUFF.

Hope it helped.
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A company has a total of 1,650 employees, some of whom are office work 16 May 2024, 11:20
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­A company has a total of 1,650 employees, some of whom are office workers. How many of the employees are enrolled in Medical Plan X?

Let's use the following:

Employees Enrolled = EE

Employees Not Enrolled = EN

Office Workers Enrolled = OE

Office Workers Not Enrolled = ON

(1) The number of employees not enrolled in the plan is 75 more than the number of office workers enrolled in the plan.

EN = OE + 75

Many values work in this case since we have 1,650 employees to work with.

So, OE could be anything from 0 to (1,650 - 75)/2, making EE anything from (1,650 - 75)/2 to 1,650 - 75.

Insufficient.

(2) The number of employees enrolled in the plan is twice the number of office workers enrolled in the plan.

EE = 2 * OE

In this case, EE and OE could be anything from 0 and 0 to 1650 and 1650/2 respectively.

Insufficient.

(1) and (2) combined

EN = OE + 75

EE = 2 * OE

Since EN = 1,650 - EE, we see that we can put everyting in terms of EE in the following equation:

1650 - EE = EE/2 + 75

We could solve that equation to determine EE.

Sufficient.

Correct answer: C
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A company has a total of 1,650 employees, some of whom are office work 14 Apr 2026, 07:42
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Total = 1650
Let
Office Workers = x , Office Workers in PLAN = y
Not Office Workers = (1650 - x), NOT Office Workers in PLAN = z

To FIND : ( y + z ) = ?

I. The number of employees not enrolled in the plan is 75 more than the number of office workers enrolled in the plan

(x - y) + (1650 - x - z) = y +75
=> 1575 = 2y +z

II. The number of employees enrolled in the plan is twice the number of office workers enrolled in the plan.

(y + z) = 2y
=> y = z

I + II
=> 2 Equation , 2 Variables , Therfore Answer - C
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A company has a total of 1,650 employees, some of whom are office work 18 Aug 2026, 22:26
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We can solve this by the 2x2 matrix
1) The number of employees not enrolled in the plan is 75 more than the number of office workers enrolled in the plan.
enroll no enroll total
office a ?
no office a+75
total 1650

We still can not solve ? --> Not sufficient

2) The number of employees enrolled in the plan is twice the number of office workers enrolled in the plan.

enroll no enroll total
office b 2b
no office
total 1650

We have ? = 2b, but still can't find the exact number , hence insufficient

(1) +(2) : a = b , since they both are the box of both enroll and office

enroll no enroll total
office b 2b
no office b + 75
total 1650

3b + 75 = 1650 => b= 525 => 2b = 1050
C is OA
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