Price increased by M% from 1991 to 1992 and by N% from 1992

Question

Price increased by  m\%  from 1991 to 1992 and by  n\%  from 1992 to 1993. What was the percentage increase in price from 1991 to 1993?

(1)  mn = 300

(2)  100m + 100n + mn = 4300

M24-19

Bunuel · Accepted Answer

Price increased by  m\%  from 1991 to 1992 and by  n\%  from 1992 to 1993. What was the percentage increase in price from 1991 to 1993? 
 
Increasing some value by  x\%  is the same as multiplying by  1 + \frac{x}{100} . For example, if you increase something by 10% you multiply by  1 + \frac{10}{100}= 1.1 . Hence, after the increase by  m\%  and then by  n\% , the price would become  (1 + \frac{m}{100})(1 + \frac{n}{100}) = 1 + \frac{m}{100} + \frac{n}{100} + \frac{mn}{10,000}  times the original price. 
 
(1)  mn = 300 .
 
From the above, we cannot deduce the value of  (1 + \frac{m}{100})(1 + \frac{n}{100})  . Not sufficient.
 
(2)  100m + 100n + mn = 4300 .
 
Dividing the above by 10,000 gives  \frac{m}{100} + \frac{n}{100} + \frac{mn}{10,000}=0.43 . Adding 1 to both sides gives  1 + \frac{m}{100} + \frac{n}{100} + \frac{mn}{10,000}=1.43 . Therefore, the price increased by 43%. Sufficient.

Answer: B

vjsharma25 · Answer

1991------------------1992-------------------1993
x ------------------ x(1+M/100)------------------x(1+M/100)(1+N/100)

% Increase from 1991 to 1993

(x(1+M/100)(1+N/100) - X) * 100
--------------------------------------- = N+M+MN/100 = (100N+100N+MN)/100 = 4300/100 = 43 %
 x

So only B is needed.

jlgdr · Answer

Hi, would you mind explaining what exactly is DS guessing theory? Could you kindly elaborate more on this?

rohit8865 · Answer

Let price on 1991 be P
in 1992=P(1+m/100)
1993=P(1+m/100)(1+n/100)
%increase= change(1993)-original(1991)/original(1991)
=P(1+m/100)(1+n/100)-P/P
P cancels out.
(1+m/100)(1+n/100)-1
(10^4+100m+100n+mn-10^4)/10^4
(100m+100n+mn)/10^4------(a)
Given in (2) 100m+100n+mn=4300-------->m+n+mn/100=43----(b)
taking 100 out common from (a)
(m+n+mn/100)/10^2
substituting from(b) we get
43/100
43%
Ans B

Bambi2021 · Answer

There is a formula for cumulative percentage changes:

a + b + ab/100 = total percentage change 
a = first period change
b = second period change.

In statement (2) we are simply given this formula, multiplied by 100.

100M + 100N + MN = 4300

equals

M + N + MN/100 = 43

The cumulative increase is 43 %.

ohhno · Answer

Let's solve this as  GMAT Data Sufficiency .
Let the price in 1991 be  100 .
Step 1: Apply the percentage increases
From 1991 → 1992, price becomes:
100(1+m100)100\left(1+\frac m{100}ight)
From 1992 → 1993, it increases by n%n\%:
100(1+m100)(1+n100)100\left(1+\frac m{100}ight)\left(1+\frac n{100}ight)
Expand:
=100+m+n+mn100=100+ m+n+\frac{mn}{100}
Therefore, the  total percentage increase  from 1991 → 1993 is:
m+n+mn100\boxed{m+n+\frac{mn}{100}}
So we need to determine m+n+mn100m+n+\frac{mn}{100}.
 
Statement (1)
mn=300mn=300
We know the product, but  not m+nm+n .
For example:
 
 m=10,n=30m=10,n=30 → m+n=40m+n=40 
 m=15,n=20m=15,n=20 → m+n=35m+n=35  
Both have mn=300mn=300, but give different total increases.
❌  Statement (1) alone is NOT sufficient. 
 
Statement (2)
100m+100n+mn=4300100m+100n+mn=4300
Divide everything by 100:
m+n+mn100=43m+n+\frac{mn}{100}=43
But that's  exactly the total percentage increase !
Therefore:
43%\boxed{43\%}
So statement (2) alone is sufficient.
✅  Statement (2) is sufficient. 
 
Answer:  B 
 Statement (2) alone is sufficient. 
The shortcut to remember
For two successive percentage increases:
Total increase=m+n+mn100\boxed{	ext{Total increase}=m+n+\frac{mn}{100}}
So when you see:
100m+100n+mn100m+100n+mn
you should immediately recognize:
100×Total increase100	imes	ext{Total increase}
Here:
4300100=43%\frac{4300}{100}=\boxed{43\%}

Price increased by M% from 1991 to 1992 and by N% from 1992

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Price increased by M% from 1991 to 1992 and by N% from 1992

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards