Exactly 18 months ago management in a certain retail electronics store

Question

Exactly 18 months ago management in a certain retail electronics store began making monthly observations of the percentage of shoppers who appear to be showrooming—examining a product while in the store and then buying the product online from another store. The results of the observations were that the percentage of customers who appeared to be showrooming increased by 0.5% each month. If p is the percent of customers who appeared to be showrooming in their store x months after the monthly observations began and 10 months ago p was equal to 10.5%, which of the following equations most accurately models the findings of the management team for the past 18 months?

A. p = 0.5x

B. p = 0.5x + 5.5

C. p = 0.5x + 6.5

D. p = 0.5x + 10.5

E. p = 0.5x + 18

Source: Skills Insight

A.​ p = 0.5x​
B.​ p = 0.5x + 5.5​
C. ​p = 0.5x + 6.5​
D.​ p = 0.5x + 10.5​
E. ​p = 0.5x + 18

Source: Skills Insight

stne · Accepted Answer

It's an A.P. problem in slight disguise.

Value of nth term of A.P  = a + (n-1)d  ...(i)

a  is the first term

Common difference  d = 0.5

If  10  months ago p  = 10.5\% , it means  8  months from the beginning p  = 10.5

10.5 = a + 7(0.5)  ->using ...(i) where  n = 8 ,

10.5 = a +3.5

a= 10.5 -3.5 =7  ...(First term).

Hence p after  x   months

= 7+(x-1)0.5 ... using (i) where  n =x, a=7   and  d= 0.5

=7+0.5x -0.5

=6.5 +0.5x

Ans C

avggmatstudent23 · Answer

% of shoppers increase by 0.5% every month
10 month earlier, p=10.5%
This means, 8 months earlier (at the beginning), p=10.5 - 0.5(8) = 6.5
Model = 6.5 + 0.5x
 Answer is C

Bunuel  does this make sense?

sninja · Answer

Bunuel - when working with percent increase we usually take the rate + rate*(%increase). (for example if the interest rate is increased by 5% we dont simply add 5% to it). Why can we use the linear equation here. The language to me seems to indicate that we should take the original rate*(1.005)^n where n is the number of months from the origination of the pattern.

Thanks!

Thanks!

GMATCoachBen · Answer

sninja Interesting question. Note that on the actual test, you want to get in the habit of immediately glancing at the answer choices and noticing that all of them are linear, and not spend time or energy asking yourself questions like this. (I often see students asking themselves similar questions on SC, wondering whether something that "sounds off" is correct, but all of the answer choices have the same issue so it doesn't matter.) The wording here is "The PERCENTAGE (of customers who appeared to be showrooming) increased by 0.5% each month." This wording, in which the subject is "percentage" and verb is "increased", means we are ADDING to the percentage value itself; it's not compound exponential growth. Alternatively, if the wording said "The NUMBER of customers increased by 50% each month", it would mean compound exponential growth. Here are two other good official examples, one that uses addition, and one that uses compound exponential growth: https://gmatclub.com/forum/each-year-fo ... l#p1102575 https://gmatclub.com/forum/when-a-certa ... ml#p811565

Paras10 · Answer

The question is very easy , once you understand it .
But the language here is wrong ,

"The results of the observations were that the percentage of customers who appeared to be showrooming increased by 0.5% each month."

Should be

"The results of the observations were that the percentage of customers who appeared to be showrooming increased by 0.5 each month."

That % sign makes it Geometric progression question rather than Arithmetic progression question....

tbd · Answer

I agree, this question is poorly worded.

Anonymous · Answer

Hello  GMATCoachBen  !

I concluded with B, following this line of thought. Please help me identify the mistake. We know that the showrooming percentage increases by 0.5% per month. This can be represented as 0.5x, where x is the number of months. We also know that 10 months ago (x = 10), the showrooming percentage was 10.5%. So, we need to add a constant value (y) to 0.5x to get 10.5 when x = 10.

p = 0.5x + y

Now, we can plug in the values we know:
 
 p = 10.5 
 x = 10  
10.5 = 0.5(10) + y => 10.5 = 5 + y => y = 5.5

Shradaze · Answer

There’s no proper solution

Bunuel  can you help?

Kinshook · Answer

Exactly 18 months ago management in a certain retail electronics store began making monthly observations of the percentage of shoppers who appear to be showrooming—examining a product while in the store and then buying the product online from another store. The results of the observations were that the percentage of customers who appeared to be showrooming increased by 0.5% each month. If p is the percent of customers who appeared to be showrooming in their store x months after the monthly observations began and 10 months ago p was equal to 10.5%, which of the following equations most accurately models the findings of the management team for the past 18 months?

A. p = 0.5x

B. p = 0.5x + 5.5

C. p = 0.5x + 6.5

D. p = 0.5x + 10.5

E. p = 0.5x + 18

Source: Skills Insight

Let p0 be percentage of customers who appear to be  showrooming at the time of observations

p = p0 + .5x

10.5 = p0 + .5*(18-10) = p0 + 4 
 p0 = 10.5-4 = 6.5

p = 6.5 + .5x

IMO C

KarishmaB · Answer

There are certain issues in the question though the options clarify what we are required to do. Observations started 18 months ago. Every month, p increases by 0.5% (it should be given as 'p increases by 0.5 percentage points' for more clarity) 10 months ago (which means 8 months after observations started), p = 10.5%. In the 8 months, p increased 8 times by 0.5% i.e. it increased by 4% points. Hence at the start, p must have been 10.5% - 4% = 6.5% Hence, general form for p = 6.5% + 0.5%*x The % sign is missing from the options, but it is missing from all the options so ignore. Answer (C) Here is another question on sequences: https://anaprep.com/algebra-a-difficult ... sequences/

yazlal25 · Answer

Thanks  avggmatstudent23 . This is a really simple explanation.

asingh91 · Answer

Thanks karishma,

I am trying to understand why in this attached  question  we DIDNT apply (n-1) to the formula when it was increased by a constant amount. but are applying the same in this question. Thankyou in advance.

SudsMeister · Answer

Just to append, this question too seems to be of a similar type:

https://gmatclub.com/forum/when-a-certain-rubber-ball-is-dropped-it-rebounds-75-percent-as-high-420055.html#p3413355

Exactly 18 months ago management in a certain retail electronics store

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