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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount

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pappal

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09 Jul 2025, 11:34

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let 'x' money on monday
so money on Wednesday=x*(1+m/100)*(1-n/100) which is=x/2
on simplifying n=100*( m-50)/(m+100)
B

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09 Jul 2025, 11:41

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Bunuel

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Let the amount of money with Elena on Monday = x

Tuesday:=x*(1+m/100)
Wednesday= x*(1+m/100)*(1-n/100)

Amount Left = x*(1+m/100)*(1-n/100) = 50%*x

((100+m)/100)*((100-n)/100)=1/2
(100+m)(100-n)=5000
n= 100(100+m-50)/(100+m)

n= 100(m+50)/(100+m)

Answer: (A)

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09 Jul 2025, 11:55

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monday = k dollars

tuesday = k+k*m/100 = t

wednesday = t - t*n/100 = k/2

putting value of t in terms of k

(k+k*m/100) - (k+k*m/100)*(n/100) = k/2

solving we will get n in terms of m

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Choosing Strategy: We can avoid the hard algebra in this question by choosing a Picking numbers approach.

Picking numbers: Let's say that Elena had USD 80, then she increased to 160 (m% = 100%) and then she withdrew 120 (n% = 75% of 160).

Testing alternatives:
A) 75 = 100(150) /200 -> OK

B) 75 = 100(50) / 200 -> not OK

C) 75 = 100(150) / -200 -> not OK

D) 75 = 100(100) / 200 -> not OK

E) 75 = 100(-50) / 0 -> not OK

------------------
On Monday, Elena had a certain amount of money in her savings account. On Tuesday, she increased that amount by m percent. On Wednesday, she withdrew n percent of her Tuesday's closing balance, leaving her with exactly 50 percent of what she had on Monday. What is the value of n in terms of m?

A.
[ltr]100(m+50) / m+100[/ltr]

B.
[ltr]100(m−50) / m+100[/ltr]

C.
[ltr]100(m+50) / 100−m[/ltr]

D.
[ltr]100m / m+100[/ltr]

E.
[ltr]100(50−m) / m−100[/ltr]

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09 Jul 2025, 12:06

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Let the amount of money in her savings account on Monday = a

The Amount of money on Tuesday = a + m%*a

The Amount of money on Wednesday = (a + m%*a) - n%(a + m%*a)

According to given information : 50%*a = (a + m%*a) - n%(a + m%*a)

$\frac{50a}{100} = \frac{(100a+ma)}{100} - (\frac{n}{100})\frac{(100a+ma)}{100} $

$\frac{a}{2} = \frac{(100a+ma)}{100} (1 - \frac{n}{100}) $

$a = \frac{(100a+ma)}{50}(\frac{100−n}{100})$

$\frac{a×50}{(100+m)a} = \frac{100−n}{100}$

$50×100 = (100−n)(100+m)$

$5000 = 10000+100m−100n−nm$

$(100+m)n = 10000−5000+100m$

$n = \frac{5000+100m}{100+m}$

$n = \frac{100(50+m)}{100+m}$

We get Option A as the answer.

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09 Jul 2025, 12:23

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Let amount of money on Monday = x
Amount on Tuesday = (1+m/100)x
Amount on Wednesday = (1-n/100)(1+m/100)x

Given,
(1-n/100)(1+m/100)x = x/2
Solving the above,
=> n = 100(m+50)/(m+100)

Answer is A

Bunuel

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09 Jul 2025, 12:29

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If we assign A to the amount of money on Monday,
On Tuesday, she increased the amount by m percent, so she will have: $A*\frac{100+m}{100}$
On Wednesday, she decreased the new amount by n percent, so she will have: $A*\frac{100+m}{100}*\frac{100-n}{100}$
We know that the result is equal to 50% of A, so we can write:
$A*\frac{100+m}{100}*\frac{100-n}{100}=A*\frac{50}{100}$

If we simplify and solve the equation for n, we will have $ n= \frac{100(m + 50)}{m + 100}$

The answer is A.

Bunuel

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On Monday, Elena had a certain amount of money in her savings account. On Tuesday, she increased that amount by m percent. On Wednesday, she withdrew n percent of her Tuesday's closing balance, leaving her with exactly 50 percent of what she had on Monday. What is the value of n in terms of m?

Monday = x amount of money
Tuesday = x(1+$\frac{m}{100}$)
Wednesday = (x (1+$\frac{m}{100}$))(1-$\frac{n}{100}$)
Final amount= 0.5x

Now set up the equation
(x (1+$\frac{m}{100}$))(1-$\frac{n}{100}$)=0.5x

(1+$\frac{m}{100}$)(1-$\frac{n}{100}$)=0.5

(1-$\frac{n}{100}$)=$\frac{0.5}{(1+m/100)}$

(1-$\frac{n}{100}$)=$\frac{0.5}{(100/100+m/100)}$

(1-$\frac{n}{100}$)=$\frac{50}{(100+m)}$

$\frac{n}{100}$=1-$\frac{50}{(100+m)}$

$\frac{n}{100}$=$\frac{100+m-50}{(100+m)}$

$\frac{n}{100}$=$\frac{50+m}{(100+m)}$

n= $\frac{100(50+m)}{(100+m)}$

ANSWER A

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09 Jul 2025, 12:58

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On Monday, Elena had a certain amount of money in her savings account. On Tuesday, she increased that amount by m percent. On Wednesday, she withdrew n percent of her Tuesday's closing balance, leaving her with exactly 50 percent of what she had on Monday. What is the value of n in terms of m?

Would love to solve this by assuming values, so lets assume, on Monday she has $$100$ in her account, and on tuesday, it got increased by m%, assuming $m = 10.$

So, her Tuesday's balance is $$100+ $10% of 100$ = $$110.$ [10% of 100 is 10]

Now, she withdraws n% of tuesdays balance, so money withdrawn = $110n/100$ = $11n/10.$

Forming the equation as per the above statements,

Tuesday's balance - Money withdrawn = 50% of Monday's balance.

we get, $110 - 11n/10 = 50%*100.$

$\\
\\
=>11n/10 = 110-50\\
\\
=> 11n/10 = 60\\
\\
=> n = 600/11.\\
\\
$

putting the value of $m = 10$ in the answer choices, we see, only option A gives us, $600/11$. and hence the answer is A

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09 Jul 2025, 13:32

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Topic(s)- Percent Change
Strategy- Algebra
Variable(s)- Monday $ = "a"; Tuesday $ = "b"; Wednesday $ = "c"

Create equations
[1] b = a*(1 + (m/100))
[2] c = b*(1 - (n/100))
[3] c = (50%)*(a) = (1/2)*(a)

Since a is an unknown, use equations to cancel a out
i) Substitute [1] into [2]
c = (a*(1 + m/100))*(1 - (n/100))

ii) Set [2] = [3]
(a*(1 + m/100))*(1 - (n/100)) = (1/2)*(a)
(a*(100+m/100))*(100-n/100) = (1/2)*(a)

iii) Multiply both sides by (100*100/a)
(100+m)*(100-n) = (100*100)/2

iv) Multiply left-hand side out
(100*100) - 100n + 100m - n*m = (100*100)/2

v) Isolate n on the left-hand side
n(-100 - m) = (100*100)/2 - (100*100) - 100*m
n = 100*(50 - 100 - m)/(-m - 100)
n = 100*(-50 - m)/ (-m - 100)
n = 100*(50 + m) / (m + 100)

Answer: A

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Let the amount Elena had on Monday be x.

Tuesday:
She increased it by m%
So, new amount =x(1+(m/100)) => x(100+m)/100

Wednesday:
She withdrew n% of Tuesday’s amount.
Remaining amount after withdrawal =
x(100+m)/100 - nx(100+m)/(100*100)

We are told this final amount equals 50% of Monday’s amount, i.e. x/2
x(100+m)/100 - nx(100+m)/(100*100) =x/2

Simplifying and solve for n:

$n=100(m+50)/(m+100)$

Option A

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Option A is the correct answer.

Before trying to solve the question, first lets understand the information mentioned in it.

So the question starts by telling us that On Monday, Elena had a certain amount in her bank account. Then on Tuesday, she increased that amount by m percent and on Wednesday she withdrew n percent of the amount from her Tuesday's closing balance such that after withdrawing she is left with only 50% of the amount that was in her account on Monday. Now the question asks us to find n in terms of m.

Lets try to solve this question by assuming values so that we can easily do our calculations and find the answer.

So lets take Balance in account on Monday to be 200 and m =100%, so as per the information in the question the amount will Elena added on Tuesday will be 200 and Tuesday's closing balance will be 400 and as per the question the percentage of amount which she withdrew from her account will be 75% respectively.

Lets understand how we get the value of n to be 75%

On Monday Elena's bank balance = 200
Then she added 100% of this amount on Tuesday i.e. 200, So Elena's bank balance on Tuesday = 200+200 => 400
Then she withdrew n percent of amount such that only 50% of the balance which she had on Monday was left i.e. 100 => 400*(n/100) = 300 => n = 75%

Now after understanding how we get to out values lets try to put them in the given options and see check option gets us the required answer i.e. n = 75%.

Option A: (100(m+50))/(m+100) => (100*(100+50))/(100+100) => (100*150)/200 => 75%. This option gets us our desired value so this must be our answer. But lets check other option as well to properly conclude this option as our answer. Selected

Option B: (100*(m-50))/(m+100) => (100*(100-50))/(100+100) => (100*50)/200 => n = 25%. This option does not gives us n = 75% so Eliminated.

Option C: (100*(m+50))/(100-m) => (100*(100+50))/(100-100) from here only we can tell that the denominator for this will be '0' which can never gives us our desired answer. Eliminated

Option D: 100m/(m+100) => 100*100/(100+100) => n = 50%. This option does not gives us n = 75% so Eliminated.

Option E: (100*(50-m))/(m-100) => (100(50-100))/(100-100) from here only we can tell that the denominator for this will be '0' as well as the numerator will also be in negative which can never gives us our desired answer. Eliminated

So after checking and solving all the option now we can properly conclude that only Option A gives us the desired value of n i.e. 75% that's why Option A is our answer.

Bunuel

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Bunuel

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Option A is the answer

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Lets say the amount on monday she had is x
then,
x(100+m/100)(100-n/100)=x/2
=> (100+m)(100-n)=10000/2=5000
=>100-n=5000/100+m
=>n=100-5000/100+m
=>n=10000+100m-5000/100+m
=>n=5000+100m/100+m
=>n=100(50+m)/100+m
IMO:A

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09 Jul 2025, 16:46

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On Monday, Elena had a certain amount of money in her savings account. On Tuesday, she increased that amount by m percent. On Wednesday, she withdrew n percent of her Tuesday's closing balance, leaving her with exactly 50 percent of what she had on Monday. What is the value of n in terms of m?

Monday = X

Tuesday = Monday increased by m percent
Tuesday = X * ( ( 100 + m ) / 100 )

Wednesday = Tuesday decreased by n percent
Tuesday = X * ( ( 100 + m ) / 100 ) * ( ( 100 - n ) / 100 )

Wednesday = 50 percent of Monday

X * ( ( 100 + m ) / 100 ) * ( ( 100 - n ) / 100 ) = 1/2 * ( X )

Divide both sides by X

( ( 100 + m ) / 100 ) * ( ( 100 - n ) / 100 ) = 1/2

Multiply both sides by 100 * 100

( ( 100 + m ) ) * ( ( 100 - n ) ) = 10000 / 2

10000 - 100n + 100m - nm = 5000

Isolate components with "n" to the right side of the equation

10000 - 5000 + 100m = 100n + nm

5000 + 100m = n (100 + m)

( ( 100 * ( 50 + m ) ) / ( 100 + m ) ) = n

Answer = A

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A. $\frac{100(m + 50)}{m + 100}$

X being the initial amount, you have to solve the equation stating halfe of the initial amount equals money on wednesday:
0,5*X = X * (1+m/100) * (1-n/100)
0,5 = (100+m)/100 * (100-n)/100
50/(100+m) = (100-n)/100
100*50/(100+m) = 100-n
n = 100 - 100*50/(100+m)
n = 100 ((100+m)-50) / (100+m)
n = 100 (m+50)/(100+m)

Bunuel

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Correct Answer: Option A (100(m+50)) / (m+100)

Solve this using taking an example
If we keep m= 50 and initial amount = 100, so let’s check this,
Monday= 100
Tuesday= 150 (50% increase)
Wednesday= 50 (50% of Monday)
n= percent change in Wednesday from Tuesday.
n= 66.67%

Now check using options,
Keep m= 50

1) (100(m+50)) / (m+100)
(100 (50+50))/ (50+100)
10000/150= 66.67%= n
Hence we got our answer.
Option A is correct.

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Elena had on Monday $- x$

Increased amount $= \frac{(x+mx)}{100}=\frac{(1+m)}{100}x=\frac{(100+m)}{100}x$

Withdrawn amount $= \frac{(100+m)}{100}x\frac{(100-n)}{100}x$

$= \frac{(100+m)}{100}x\frac{(100-n)}{100}=\frac{50}{100}x$

$100-n=\frac{50*100}{(100+m)}$

$n=100-\frac{50*100}{(100+m)}$

$n=\frac{100(m+50)}{m+100}$

Answer: A

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Bunuel

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On Monday, Elena had a certain amount of money in her savings account.
Monday Amount = A

On Tuesday, she increased that amount by m percent
Tuesday Amount = $\frac{A(100+m)}{100}$

On Wednesday, she withdrew n percent of her Tuesday's closing balance,
Amount left after withdrawal = $\frac{A(100+m) (100-n) }{10000}$

leaving her with exactly 50 percent of what she had on Monday. What is the value of n in terms of m?
Amount left after withdrawal = 50% * Monday Amount

=> $\frac{A(100+m) (100-n) }{10000} $= 50% * A
=> (100-n) = $\frac{10000}{2(100+m)}$
=> (100-n) = $\frac{5000}{(100+m)}$
=> n = $100 - \frac{ 5000}{(100+m)}$
=> n = $\frac{{100(100+m) - 5000}}{(100+m)}$
=> n = $\frac{(10000 + 100m - 5000)}{(100+m)}$
=> n = $\frac{(5000 + 100m)}{(100+m)}$
=> n = $\frac{100(50 + m)}{(100+m)}$

Option A

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