12 Days of Christmas GMAT Competition 2025 - Day 3: On January 1 of

On January 1 of 2025, Website Nexus had 1,000 registered users, and Website Echo had 1,600 registered users. Each site gained a constant number of new users every month, and by May 1, 2025, Website Nexus had 250% more registered users than Website Echo.

In the table, select for Nexus the number of registered users it gained per month and select for Echo the number of registered users it gained per month that would be jointly consistent with the given information. Make only two selections, one in each column.

Vaishbab

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18 Dec 2025, 01:56

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Nexus on Jan 1: 1000
Echo on Jan 1: 1600

Nexus's growth/month = x
Echo's growth/month=y

On May 1 (4 months later), Nexus has 250% more members than Echo

That means, 1000 + 4x = 3.5(1600 + 4y)

Simplifying the equation, we get 2x-7y = 2300

The values that satisfy this equation are x=3600 & y=700

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18 Dec 2025, 02:02

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Bunuel

if we take 700 as Echo increment ( because as can be inferred from question that Echo increment will be less than that of Nexus)

So 700 * 4 =2,800

2800 + 1600 =4,400

4400 * 3.5 =15,400 ( as percent increase is 250 %)

15400 - 1000 =14,400 ( As 1000 are already registered users)

14400/4 =3,600

Yup we have 3600 in option

So answer will be 700 & 3600

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18 Dec 2025, 02:25

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From Jan 1 to May 1 = 4 months of Growth .
Let Nexus Monthly Gain = N
Echo Monthly Gain = E
250 % more than echo means
Nexus has 100% + 250 %
N= 3.5 (E)
Write totals after 4 months
Nexus = 1000+ 4N
Echo = 1000+ 4E
1000+4N = 3.5(1000+4E)
N= 1150 + 3.5 E
Using answer choices from the list
E = 700
N= 1150 +2450 = 3600.

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18 Dec 2025, 02:30

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WN= 1000 + 4x on may 1
WE= 1600 + 4y on may 1

where x and y are constants that are added each month.

we know WN = WE * 3.5

therefore by solving we will get an equation 2x - 7y= 2300

lets start plugging values y = 700 and x = 3600

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18 Dec 2025, 03:07

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What we know is from Jan 1 to May 1, we see 4 months of growth

Let us assume that Nexus gains x users per month and Echo gains y users per month
So we can assume that on May 1
Nexus users = 1000 + 4x
Echo users = 1600 + 4y

We also know that Nexus had 250% more registered users than Echo
=> Nexus = Echo + 2.5Echo = 3.5Echo
So,

1000+4x = 3.5(1600 + 4y)
x = 1150+3.5y

Now, from the given values in the table we substitute and find that,
x = 3600, y = 700

=>
Echo = 700 users per month
Nexus = 3600 users per month

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18 Dec 2025, 03:57

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N = 1000 + 4n = 2.5E
E = 1600 + 4e

=> 1000 +4n = 2.5*(1600 + 4e)

=> 2n - 5e = 1500

n = 1500, e = 300

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18 Dec 2025, 05:01

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Nexus=1000
Echo=1600
May 1, 4 months
Nexus 250%more than Echo

nexus monthly gain=n
Echo monthly gain=e
4 months= Nexus 1000+4n
Echo =1600=4e
Nexus 250% more than Echo
1000+4n=(1+2.5)(1600+4e)=3.5(1600+4e)
1000+4n=3.5x1600+3.5x4e
1000+4n=5600+14e

4n=4600+14e
n=1150+3.5e
IF e=200
n=1150+3.5(200)=1150+700=1850 (no)
if e=300
n=1150+1050=2200(no)
if e=700
n=1150+2450=3600 (yes)
if e=1500
n=1150+5250=6400(no)

echo=700, nexus=3600

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18 Dec 2025, 05:02

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I would put this question in the naughty list, for how much of my time it consumed

But either way, in retrospect a few tricks could've helped me quicken the base. I'll try my best to mention those here.

---
So, Nexus has 1,000 users; Echo has 1,600 on Jan 1.

On May 1, however, Nexus's user base grew to 250% more than Echo.

Straight off the bat, this means a 3.5x gain, which is easy to miss when directly converting percentage increases.

This also means that Nexus grew a lot faster than Echo in the 4 MONTHS between Jan 1 and May 1. Again, let's be clear here: Jan 1 to Feb 1 is a month passed, to March 1 is two, April is three, and May 1 is fourth. Another bait for miscalculation, avoided by being observant.

Now, among the options, I would like to first see how the lowest values go; this will help set an estimate for the answer. I'd take 200 gained for Echo, which in four months is a gain of 800, or 1,600 + 800 = 2,400.

Now, 3.5x this number is 8,400, which is what we need Nexus to be for the value to hold true. Things started at 1,000 - which means a gain of 7,400. For the monthly gain, which the question is asking about, will be 7,400 / 4 = 1,850. Not quite there in the answers, isn't it?

We at least know that Nexus will be either 2,100 or 3,600. I'd go the other end of the spectrum to further narrow things down, and this time I might want to calculate Nexus first.

Taking 3,600 first;

3,600*4 = 14,400, or 15,400 included the 1,000 things started off as, would be the value this would result in.

Now, 15,400 is 3.5x of what number? That's 15,400 / 3.5 or 4,400. What's the difference between 4,400 and 1,600 - which is what Echo was on January 1 - that is 2,800. So a gain of 2,800 over 4 months or a monthly gain of 700.

We see that somewhere in the answer don't we? 700.

So 3,600 for Nexus and 700 for Echo are the answers.

Hopefully I can be a bit quicker with a question like this in the actual exam!

Bunuel

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18 Dec 2025, 05:09

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Based on the information given,

Jan 1, 2025
Nexus = 1,000
Echo = 1,600

Time = 4 months (Jan → May)

By May 1:
Nexus has 250% more users than Echo
→ Nexus = 3.5 × Echo

Let

Nexus monthly increase = x
Echo monthly increase = y

After 4 months:

Nexus = 1000 + 4x
Echo = 1600 + 4y

Equation: 1000 + 4x = 3.5(1600 + 4y)

Simplify: 1000 + 4x = 5600 + 14y
4x = 4600 + 14y
2x = 2300 + 7y

Test options

If y = 700: 2x = 2300 + 4900 = 7200
x = 3600

Check: Nexus = 1000 + 4(3600) = 15,400
Echo = 1600 + 4(700) = 4,400
15,400 = 3.5 × 4,400

Answer

Nexus: 3,600 per month
Echo: 700 per month

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18 Dec 2025, 05:29

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From 1-Jan-2025 to 1-May-2025 we get 4 increments of users. Let's say increment per month for Nexus = n and for echo = e
1000 + 4n = 2.5(1600+4e)
On simplifying we get the following Linear Diophantine equation
2n + (-5e) = 1500

We know n > e because Nexus has to grow at a faster rate than Echo to have more customers.
Finding the easiest solution to the equation => n = 750 and e = 0.
To get more solution, add 2 to the e value and subtract -5 from the n value.
Let's take n = 1500, that is subtracting 150 -5s to n, and so we need to add 150 2s to e
Therefore, n = 1500 and e = 300

Column 1 = 1500 and Column 2 = 300.

Bunuel

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18 Dec 2025, 05:29

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Logic behind: Constant increment & equation formation.

	Nexus	Echo
Jan 25	1000	1600
Feb 25	1000+a	1600+b
Mar 25	1000+2a	1600+2b
Apr 25	1000+3a	1600+3b
May 25	1000+4a	1600+4b

Nexus is 250% more than Echo in May 25, which means nexus is 3.5x of echo.

1000+4a = 3.5 (1600+4b)

Solving this, we arrive at: 2a -7b = 2300

Now, it's substitution,

Answer: a=3600 & b=700.

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18 Dec 2025, 05:30

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On January 1 of 2025, Website Nexus had 1,000 registered users, and Website Echo had 1,600 registered users. Each site gained a constant number of new users every month, and by May 1, 2025, Website Nexus had 250% more registered users than Website Echo.

Let, Nexus has N user increase per month
Echo has E user increase per month
1 Jan, N= 1000 users & E=1600 users
1 Jan to 1 may are 4 months
On 1 may, N has 250% more users than Echo
Nexus users = 3.50* Echo Users
1000+4N= 3.5*(1600+4E)
1000+4N = 5600+14 E
N=1150+3.5E
Try different choices from the given options
E= 700, N=1150+3.5(700)= 3600
Both are available in choices

Nexus = 3600 AND Echo= 700

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18 Dec 2025, 06:07

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Jan 01
Nexus registered users = 1000
echo registered users = 1600

Let 'a and b' be the number of new users gained constantly every month by Nexus and Echo.

Total number of users gained by nexus website over Feb, March and April = a+a+a = 3a

Total number of users gained by echo = b+b+b = 3b

May 01
registered users of nexus= 250% more users than echo.

3a = 250% +3b
3a = 3b x 350/100
2a=7b

Looking at the options, only 200 and 700 fit into the above formula.
Therefore,
Echo is 200
Nexus is 700

Bunuel

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18 Dec 2025, 06:15

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x=nexus
y=echo
250% more -> multiply by 1+2.5=3.5

1000+4x=3.5(1600+4y)=5600+14y
4x-14y=4600
2x-7y=2300

Only works with x=3600 and y=700

Nexus=3600
Echo=700

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18 Dec 2025, 06:28

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On Jan 1,
Nexus = 1000
Echo = 1600

On May 1,
Nexus = 1000 + 4x
Echo = 1600 + 4y

We have to find values of 'x' and 'y'

As per the stem
1000 + 4x = (1 + 250/100)(1600+ 4y)
=> 1000 + 4x = 3.5(1600+4y)
=> 1000 + 4x = 5600 + 14y
=> 4x - 14y = 4600
=> 2x - 7y = 2300

Going by numbers we get
y = 200, then x = 1/2 * (2300 + 1400) = (3700)/2 X Not matching
y = 300, then x = (2300 + 2100)/2 X Not matching
y = 700, then x = (2300 + 4900)/2 = 7200/2 = 3600 Yes Matching

y = 700
x = 3600

Bunuel