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12 Days of Christmas GMAT Competition - Day 4: Currently, on a certain

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Bunuel

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12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

Currently, on a certain website, out of all online users, 2,400 are registered users, and 1,000 are male. How many users are currently online?

(1) The number of online female users is twice the number of online unregistered users.

(2) Among the online users, 800 are registered males.

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Bunuel

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Bunuel

12 Days of Christmas 2024 - 2025 Competition with $30,000 of Prizes

Currently, on a certain website, out of all online users, 2,400 are registered users, and 1,000 are male. How many users are currently online?

(1) The number of online female users is twice the number of online unregistered users.

(2) Among the online users, 800 are registered males.

GMAT Club's Official Explanation:

Currently, on a certain website, out of all online users, 2,400 are registered users, and 1,000 are male. How many users are currently online?

Let T represent the total number of online users. The breakdown is as follows:

	Registered	Un-registered	TOTAL
Male			1,000
Female			T - 1,000
TOTAL	2,400	T - 2,400	T

(1) The number of online female users is twice the number of online unregistered users.

This implies that T - 1,000 = 2(T - 2,400), which gives T = 3,800. Sufficient.

(2) Among the online users, 800 are registered males.

This gives the following breakdown:

	Registered	Un-registered	TOTAL
Male	800	200	1,000
Female	1,600		T - 1,000
TOTAL	2,400	T - 2,400	T

From this, we still do not have enough information to determine the total number of online users, T. Not sufficient.

Answer: A.

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Statement 1 is insufficient as we dont have any information on M(UR) and M(R) as well as F(R)
Statement 2 is insufficient too as we dont have relations between them
Both combining we have two equations
2400=M(R)+F(R)
x= M(UR)+F(UR)
F(UR)+F(R) =2x
Solving these three equations with numbers in statements ,we can solve the question . So C

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Number of male users: 1000
Number of registered users: 2400

Let R be registered user, UR be unregistered user, M be male users and F be female users.

Statement 1:

	R	UR	T
M			1000
F			2x
T	2400	x	y

2400 + x = 1000 + 2x
x = 1400
y = 2400 + x = 3800

This statement is sufficient.

Statement 2:

	R	UR	T
M	800	200	1000
F	1600
T	2400		y

Cannot calculate the value of y here, so this statement is insufficient.

Answer: A

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---

Step 1: Define Variables
Let:
- R: Number of registered users = 2400.
- M: Number of male users = 1000.
- F: Number of female users.
- U: Total number of online users.

From the problem:

U = R + {unregistered users}.

We need more information to determine U.

---

Step 2: Analyze the Statements

Statement (1):
- "The number of online female users is twice the number of online unregistered users."

F = 2 ({unregistered users}).

We know R = 2400, so the unregistered users are U - 2400. Substituting this:

F = 2 (U - 2400).

We also know U = M + F , and M = 1000. Substituting F = 2 (U - 2400):

U = 1000 + 2 (U - 2400).

Expanding and simplifying:

U = 1000 + 2U - 4800 implies U - 2U = -3800 implies U = 3800.

Thus, Statement (1) is sufficient.

---
Statement (2):
- "Among the online users, 800 are registered males."

{Registered males} = 800.

This tells us only part of the breakdown of the registered users R = 2400 but does not provide information about unregistered users or females. Without additional information, we cannot determine.
Statement (2) is insufficient.

---

Step 3: Combine Statements
Since Statement (1) is sufficient on its own, there is no need to combine the statements.
Answer : A

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19 Dec 2024, 09:44

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IMO A

Statement (1):
can be double by 2X2 matrix easily

R UR Total
M 1000
F 2x
Total 2400 X

Now 2400 + X = 1000+2X

hence X= 3800

sufficient

Statement 2: We still don't know unregistered Female hence can't determine the total

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19 Dec 2024, 09:46

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Let x = total online users
We know registered users = 2,400
We know male users = 1,000
Let's say unregistered users = u
Female users = x - 1,000

From the given information:
x = 2,400 + u (registered + unregistered = total)

Statement 1:
Female users = 2(unregistered users)
(x - 1,000) = 2u
From step 2: 2,400 + u - 1,000 = 2u
1,400 = u
Therefore x = 2,400 + 1,400 = 3,800

Therefore, Statement 1 alone is sufficient

Statement 2:
800 registered males
From total males = 1,000:
200 males are unregistered
From total registered = 2,400:
1,600 users are registered females
We still don't know number of unregistered females => Cannot determine total users

Statement 2 alone is insufficient

The answer is A: Statement 1 alone is sufficient.

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Using S1+S2 only we get all variables and its sum
C)

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Registered users = 2400
Male registered users= 1000
Female registered users= 1400
The question asks us to find current online users
(1) The number of online female users is twice the number of online unregistered users.
Registered +Unregistered female users= 2*online unregistered users
INSUFFICIENT

(2) Among the online users, 800 are registered males.
This says nothing about current online users.
INSUFFICIENT
(1)&(2) together are also insufficient as neither gives information about current online users.

Answer: E

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19 Dec 2024, 09:53

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Bunuel

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Given :
[*]U: Total number of online users (what we want to find).
[*]R: Number of registered users =2400
[*]M: Number of online male users =1000
[*]F: Number of online female users.
[*]Un: Number of online unregistered users.
[*]

So U = Un+2400. and U=1000+F.

(1) The number of online female users is twice the number of online unregistered users.

From this f = 2Un, So using both the above equations

U - 1000 = 2(U-2400) => U=3800.

Hence Stmt 1 is sufficient

(2) Among the online users, 800 are registered males.

We cannot get the U using this info as 3 variables, 2 equations are given.

Hence Stmt 2 is not sufficient.

IMO A

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Given Information:
Registered users: 2,400.
Male users: 1,000.

Statement (1):
The number of online female users is twice the number of online unregistered users.

Let:
T = Total online users.
R = Registered users (R=2,400).

U = Unregistered users (U=T−R).
M = Male users (M=1,000).
F = Female users (F=T−M).
From the statement, we know:
F=2×U.

Substituting
F=T−M and U=T−R:

T−M=2×(T−R).

This equation relates T,M, and R,
but M and R are given constants. However, it still involves two unknowns (T and M) and cannot be solved uniquely.

Statement (1) is insufficient.

Statement (2):
Among the online users, 800 are registered males.

Let:
RM = Registered males (RM=800).
RF = Registered females (RF=R−RM=2,400−800=1,600).
UM = Unregistered males (UM=M−RM=1,000−800=200).
UF = Unregistered females (UF=U−UM).

This provides information about the distribution of male and registered users but does not give a direct relationship to T or the total number of unregistered users.

Statement (2) is insufficient.

Combining Statements (1) and (2):
From Statement (2), we know:
RM=800, so
RF=1,600 and UM=200.
From Statement (1),
F=2×U.
Substitute F=RF+UF and U=UM+UF into the equation:

RF+UF=2×(UM+UF).

Substitute known values (RF=1,600 and UM=200):

1,600+UF=2×(200+UF).

Simplify:
1,600+UF=400+2UF.
Rearrange: 1,200=UF.

Thus:
U=UM+UF=200+1,200=1,400.

T=R+U=2,400+1,400=3,800.
Statements (1) and (2) together are sufficient.

Final Answer: (C)
Both statements together are sufficient, but neither alone is sufficient.

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19 Dec 2024, 09:57

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Currently, on a certain website, out of all online users, 2,400 are registered users, and 1,000 are male. How many users are currently online?

Online users	Male	Female	Total
Registered			2400
Unregistered
Total	1000		x=?

(1) The number of online female users is twice the number of online unregistered users.

Online users	Male	Female	Total
Registered			2400
Unregistered			y
Total	1000	2y	x=2400+y=1000+2y

x = 2400+y = 1000+2y
y = 1400
x = 2400+1400 = 3800
3800 users are currently online
SUFFICIENT

(2) Among the online users, 800 are registered males.

Online users	Male	Female	Total
Registered	800	2400-800=1600	2400
Unregistered	1000-800=200	y	200+y
Total	1000	1600+y	x=2600+y

Since the value of y is unknown
NOT SUFFICIENT

IMO A

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Correct ans is option A

In such question is better to identify all the categories and their relations first.
Given some 'registered' user the other category would be 'unregistered'. These two are MECE.
basically Total = 'reg' + 'un-reg'

We also have Total = 'male' + 'female'

St 1) female=2*(unreg)
Total = 'reg' + 'un-reg' = 'male' + 'female'
2400 + unreg = 1000 + 2*unreg
=> unreg = 1400
Hence total =3800 which is the required answer => SUFFICIENT

St 2) Clearly NOT SUFFICIENT, because I have no idea of total

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Bunuel

This question was provided by GMAT Club
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R = registered users = 2400
M = male users = 1000
U = total online users
F = female users
UR = unregistered users
We need to find U.

Statement (1): F = 2 * UR
We can't directly find U from this information. Insufficient.

Statement (2): Registered Male = 800 Again, we can't directly find U.
Insufficient.

Combining both:
F = 2 * UR Registered Male + Registered Female = 2400 800 + Registered Female = 2400
Registered Female = 1600
Total Female = Registered Female + Unregistered Female
Total Female = 1600 + UR Total Male = Registered Male + Unregistered Male
Total Male = 800 + (U - R - UR)
Total Male + Total Female = U 800 + (U - R - UR) + 1600 + UR = U 2400 + U - R = U 2400 - R = 0
Since R = 2400, the equation is true. we still don't have a specific value for U. both statements together are insufficient.

IMO D

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Let, T: Total online users
R: No. of online registered users => 2400
U: No. of online unregistered users => T - 2400
M: No. of male online users => 1000
F: No. of female online users => T - 1000

We need to find T

Statement 1

F = 2U
T - 1000 = 2(T - 2400)
T = 3800 SUFFICIENT

Statement 2

If RM = 800, then UM = 200, we have RF = 1600, but we don't know UF to calculate total online users. NOT SUFFICIENT

Answer A.

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Here I have solved it by Table Method

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(I)

	Male	Female	Total
Registered			2400
Unregistered			x
Total	1000	2x

we can say
2400 + x = 1000 + 2x
Solve for x and put in any 1 equation

sufficient

(II)

	Male	Female	Total
Registered	800	1600	2400
Unregistered	200	x
Total	1000

Not sufficient

Bunuel

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Q: To determine the total number of users currently online.

Statement (1): The number of online female users is twice the number of online unregistered users. This provides a relationship, but lacks specific details to determine the total number of online users. Insufficient.
Statement (2): Among online users, 800 are registered males. This gives partial information but doesn’t provide the number of unregistered or female users. Insufficient.
Combining (1) and (2): While we know the number of registered males and the relationship between female and unregistered users, the exact numbers of each group are not clear enough to solve for the total.

Thus, both statements together are still insufficient to answer the question.
The answer is E.

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19 Dec 2024, 10:27

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A alone is sufficient.

Registered users =2400 , Male users = 1000, Female users= ? T=total online users

T=M+F = Registered + Unregistered

T= R+U = M+2U => 2400+U = 1000 + 2U
2400-1000 = U
T=3800

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19 Dec 2024, 10:28

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Quote:

Currently, on a certain website, out of all online users, 2,400 are registered users, and 1,000 are male. How many users are currently online?

(1) The number of online female users is twice the number of online unregistered users.

(2) Among the online users, 800 are registered males.

Using 1) We dont know the number of online unregistered users nor the number of female users hence this statement is of no use on its own

Using 2) If 800 are registered males, then 200 online males are unregistered. and 1600 females are registered.

We still dont know the total females that are online.

IMO (E) is the answer