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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 09 Jul 2025, 21:05
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Let \(x\) be the amount present on Monday

Forming an equation from the given details we have,
\(x + (mx/100) - nx/100(1 + m/100) = .50x\)
Re-arranging,
\(1 + (m/100) - n/100(1 + m/100) = .5\)
\((1 + m/100)(1 - n/100) = .5\)

Re-arranging and multiplying both sides by \(100\),
\((100 + m)(100 - n) = 5000\)
\((100 - n) = \frac{ 5000 }{ (100 + m) } \)
\(\frac{100 (100 + m) - 5000}{(100 + m)} = n\)
\(\frac{100(m + 50)}{(100 + m)} = n\)

Correct option is Option A
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 09 Jul 2025, 21:42
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We can solve this by taking sample values. Initially suppose we have 100 rs and we increased it by 50% which will get us to 150. Now to get 50% of initiall amount which will be 50, we need to withdraw 200/3% So substituting in options 1st one will get us to 100*100/150=200/3. Option A
Bunuel
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. \(\frac{100(m + 50)}{m + 100}\)

B. \( \frac{100(m - 50)}{m + 100}\)

C. \( \frac{100(m + 50)}{100 - m}\)

D. \( \frac{100m}{m + 100}\)

E. \( \frac{100(50 - m)}{m - 100}\)


 


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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 09 Jul 2025, 22:02
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Let the Monday amount be x.
Tuesday: after m% increase x(1+m/100)
Wednesday: after withdrawing n% x(1+m/100)( 1-n/100)
x(1+m/100)(1-n/100) =x/2

Answer: n=100(m+50)/m+100.
Option A.
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 09 Jul 2025, 22:09
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let money on Monday be = x

so on tuesday, money in account will be: (1+m/100)x

on wednesday, money in account will be: (1-n/100)(1+m/100)x

which is equal to x/2.

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

on solving the equation we get, option A as the correct answer.
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 09 Jul 2025, 22:19
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Let Monday = 100 (a smart, simple choice)
  • Tuesday: Increased by m%, so it becomes ->
    100+m100 + m100+m
  • Wednesday: Withdraw n% of Tuesday’s amount ->
    Left with:(100+m) * (1− (n /100))
But we know this equals 50 (i.e., half of 100):
(100+m)*(1−(n/100)) = 50
Now isolate n:
1− n/100 = 50 / (100+m)
=>
n/100 = 1− (50 / (100+m))
=> (100+m−50)/(100+m) => (50+m) / (100+m)

So:
n= 100 * (50+m)/(100+mn)
(A)

Bunuel
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. \(\frac{100(m + 50)}{m + 100}\)

B. \( \frac{100(m - 50)}{m + 100}\)

C. \( \frac{100(m + 50)}{100 - m}\)

D. \( \frac{100m}{m + 100}\)

E. \( \frac{100(50 - m)}{m - 100}\)


 


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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 09 Jul 2025, 22:39
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Bunuel
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. \(\frac{100(m + 50)}{m + 100}\)

B. \( \frac{100(m - 50)}{m + 100}\)

C. \( \frac{100(m + 50)}{100 - m}\)

D. \( \frac{100m}{m + 100}\)

E. \( \frac{100(50 - m)}{m - 100}\)
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Considering the Monday Amount be = 100.
On Tuesday the new amount will be = 100 + m*100/100= 100+m
On Wednesday, the withdrawal Amount = n/100*(100+m) = n[1+(m/100)]
Amount balance on Tuesday = 100+m - n[1+(m/100)] = 100*50/100
100+m- n[1+(m/100)] = 50
n[1+(m/100)]= m + 50
n= (m + 50 )/ [1+(m/100)] = 100(m+50)/[100+m] A
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 09 Jul 2025, 22:56
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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?

Let's start with a 100 on Monday.
m% increase and then n% decrease on Tue and Wed respectively.
Final amount left is 50 at end of Wed.

We can use the percentage increase formula to find the final increase/decrease as below:

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

Simplifying:

100m - 100n - mn = -50 *100
=> 100m + 50*100 = mn + 100n
=> 100m + 50*100 = n(m+100)
=> 100(m + 50) = n (m +100)
=> n = 100(m+50) / (m +100)


Answer: B
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 09 Jul 2025, 23:38
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Let us assume initial amount on Monday be x units
Given
On Tuesday amount is increased by m%
I.e (x + m% of x) =x * \(((100+m)/100\))

On Wednesday n% of Tuesday's closing balance was withdrawn
I.e Amount withdrawn = n% of x * (\(\frac{(100+m)}{100}\))=(\(\frac{nx}{100}\)) * \((\frac{(100+m)}{100}\))
Remaining amount = x * \((\frac{(100+m)}{100}\)) - (\(\frac{nx}{100}\)) * \((\frac{(100+m)}{100}\)) = x\(\frac{(m+100)}{100}\) * (1-\(\frac{n}{100}\))

Final amount is 50% of Monday's (x) amount
\(\frac{x(m+100)}{100}\) (1-\(\frac{n}{100}\)) = x/2

On solving:
(1-\(\frac{n}{100}\)) = \(\frac{1}{2}\)\(\frac{100}{m+100}\)
==>\(\frac{n}{100}\) = 1 - \(\frac{50}{m+100}\)
==>n = \(\frac{100(m+50)}{m+100}\)

Option A correct
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 09 Jul 2025, 23:58
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Used numbers to solve this.
Suppose on Monday she started with 100 & m= 5
Then on Tuesday, total amount becomes 105
After withdrawing n% of 105, she has 50% of Monday's amount left = 50. Hence she withdrew the remaining 50.

Hence n% of 105 = 50
n = 5000/105

Now putting m = 5 in options to find which gives this value of n.

(D) 100m/(m+100) = 5000/105 hence correct option is (D)

You can put m=5 in other options as well to check, only D gives the value of n.

Ans D
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 10 Jul 2025, 00:39
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suppose she has x on Monday

Tuesday it increased by m% = x+(m/100)*x = (100+m)*x/100 ----- eq (1)
Wednesday she spend n% of the Tuesday balance = (100-n)*(100+m)*x/100*100 ----eq(2)

remaining balance = 50*x/100 ----eq(3)

As per the equation eq(2) and eq(3) are same
(100-n)*(100+m)*x/100*100 = 50*x/100

on simplifying
n = 100*(50+m)/(100+m)
Option A
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 10 Jul 2025, 00:51
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Let Monday's balance= M

Tuesday's balance = M *(1+(m/100))

Wednesday balance

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

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

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

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

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

n= 100 ((2-1+m/100))/(2+m/100)
n=100(1+m/100)/(2+m/100)
n= 100+m/(2+m/100)
n=100(100+m)/100(2+m)
n=100(100+m)/(m +200)
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 10 Jul 2025, 01:34
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montuewed
Elenalet, x x*(100+m/100)
after m% increment		x*(100+m/100)*(100-n/100),
after n% decrement
so finally,
x*(100+m/100)*(100-n/100) =x*50%= x/2
after solving we will get n=100(m+50)/100+m
option A
Bunuel
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. \(\frac{100(m + 50)}{m + 100}\)

B. \( \frac{100(m - 50)}{m + 100}\)

C. \( \frac{100(m + 50)}{100 - m}\)

D. \( \frac{100m}{m + 100}\)

E. \( \frac{100(50 - m)}{m - 100}\)


 


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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 10 Jul 2025, 01:59
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Bunuel
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. \(\frac{100(m + 50)}{m + 100}\)

B. \( \frac{100(m - 50)}{m + 100}\)

C. \( \frac{100(m + 50)}{100 - m}\)

D. \( \frac{100m}{m + 100}\)

E. \( \frac{100(50 - m)}{m - 100}\)

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We can sole this with fair assumption.
Lets take Monday Amt be $100 -- increased by 50% (m) --> $150 ---- Now we need to decrease to get $50 so n = 60%.

Now we know if we take m = 50 ; then n= 60%, plug m value to check which option give n- 60% its A
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 10 Jul 2025, 04:14
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So best way to solve this is by choosing smart numbers

On Monday lets assume she deposit 100 in bank
on Tuesday she increased m% we can assume this to be 50%. So now the bank has 150.

We know on wednesday, after withdrawing her money was exactly 50% so she will have 50 in her account.
Money withdrew on wednesday is 150-50=100.
So, N will be \frac{100}{150}=\frac{2}{3}or \frac{200}{3}%

m=50 n=200/3

So lets see the answers:
1. \frac{100(50+50)}{(50+100)}=\frac{100(100)}{150}=\frac{200}{3 }

Yes this is the answer

Answer A


Bunuel
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. \(\frac{100(m + 50)}{m + 100}\)

B. \( \frac{100(m - 50)}{m + 100}\)

C. \( \frac{100(m + 50)}{100 - m}\)

D. \( \frac{100m}{m + 100}\)

E. \( \frac{100(50 - m)}{m - 100}\)


 


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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 10 Jul 2025, 04:15
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increase by m percent -> Money is (1+m/100) greater
withdraw n percent -> Money is (1-n/100) less

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

Answer A
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 10 Jul 2025, 04:22
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Given,
Monday, Elena has money in her account = x
Tuesday, after adding m %, the money in the account will become
= x + xm/100
Wednesday, after withdrawing n%, the money in the account will become
= x + xm/100 – (x + xm/100)*n/100
In other words, = x/2
To find
the value of n in terms of m?

Solve:
x + xm/100 – (x + xm/100)*n/100 = x/2
taking x common & cancelling from both sides
1+ m/100 – n/100 – mn/10000 = 1/2
1⁄2 + (m – n)/100 = mn/10000

Multiplying 100 on both sides,

100/2 + m = n + mn/100
50 + m = n (100 +m)/100
n = 100(m+50)/(m+100)

Ans: A


Bunuel
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. \(\frac{100(m + 50)}{m + 100}\)

B. \( \frac{100(m - 50)}{m + 100}\)

C. \( \frac{100(m + 50)}{100 - m}\)

D. \( \frac{100m}{m + 100}\)

E. \( \frac{100(50 - m)}{m - 100}\)


 


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a = amount

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

IMO A
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 10 Jul 2025, 04:42
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Successive percent calculation : if a % increase then b% decrease = (a - b - (ab/100))%

Using this, m - n - (mn/100) = 50

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

B
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GMAT Club Olympics 2025 (Day 8): On Monday, Elena had a certain amount 10 Jul 2025, 04:43
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let amount of money on Monday be = \(A\)

On Tuesday, amount increases to =\( A(1 + \frac{m} {100} )\)

On Wednesday, amount decreases to = \( A(1 + \frac{m} {100} )(1 - \frac {n} {100})\) = 50% of amount on Monday =\( \frac{50}{100}A\)

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

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

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

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

Answer is A : \(\frac{100(m + 50)}{m + 100}\)
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