The table shows partial results of a survey in which consumers were as

Since we aren't told the number of people involved in the survey, let's make things easier on ourselves and assign a "nice" value to the number of people involved in the survey.
Let's say there were 100 people in the survey.

When we apply this to our table, we see that 35 people chose TV ads, 22 people chose coupons, 18 people chose store displays, and 15 people chose samples.

35 + 22 + 18 + 15 = 90
So, the table shows the results for 90 consumers

What fraction indicated either coupons or store displays?
Among the 90 consumers surveyed, 22 chose coupons, and 18 chose store displays
22 + 18 = 40
Fraction = 40/90
= 4/9

Answer: D

Cheers,
Brent
_________________

Solution

Given:

• The table shows partial results of a survey in which consumers were asked to indicate which one of six promotional techniques most influenced their decision to buy a new food product

To find:

• Out of those consumers who indicated one of the four techniques listed, what fraction indicated either coupons or store displays

Approach and Working:
If we assume the total number of consumers who responded is 100, then we can write:

• Total consumers responded to the four mentioned techniques = (35 + 22 + 18 + 15) = 90
• Total consumers responded to either coupons or store displays = (22 + 18) = 40
• Therefore, the required fraction = \(\frac{40}{90} = \frac{4}{9}\)

Hence, the correct answer is option D.

Answer: D
_________________

Notice that you are instructed to use the incomplete table; the percentages add up to only 90%. So first, you will add the percentages for “Coupons” and “Store Displays,” but then you must divide by the total of 90% to get the final answer, as shown here:

(22 + 18)/(35 + 22 + 18 + 15) = 40/90 = 4/9

Answer: D
_________________

When we add all the %'s we get 90 as total value

either coupons or store displays = 40/90

D
_________________

Why we should we add the other 10%?

Could anyone help explain why the stem says "or" "what fraction indicated either coupons or store displays" then we have a sum (22+18)? I think it should be 22/90 or 18/90.

(22+18)/90 --> stem should be "what fraction indicated coupons and store displays"
_________________

This question tries to trick you ! Otherwise the maths is pretty simple
You should solve 40/90 and not 40/100

If you found yourself bewildered why everyone is solving for 90% or why using 100 customers still means you use only the data available and solve for 90:

The question says "of the consumers who indicated one of the four techniques listed...". So, for example, rather than being able to use 22% (out of the usual 100%), the question wants you to use 22% out of the 90% that responded to one of these four options.

Using Brent's example, 100 total consumers, but 90 responded to one of the 4 so that's our denominator.


(Problem Solving Question 129 in GMAT 2021 guide)

Technique	Percent of consumers
Television ads	35%
Coupons	22%
Store displays	18%
Samples	15%
All 4 methods	90%

Given: The table shows partial results of a survey in which consumers were asked to indicate which one of six promotional techniques most influenced their decision to buy a new food product.
Asked: Of those consumers who indicated one of the four techniques listed, what fraction indicated either coupons or store displays?

The fraction indicated either coupons or store displays = (22%+18%)/90% = 40%/90% = 4/9

IMO D
_________________

Coupons + Store displays =22%+18%=40%

Total Survey \(= (35+22+18+15)\)%\(=90\)%

The fraction \(=\frac{40}{90}\)%=\(\frac{4}{9}\)

The answer is \(D\)
_________________

Answer: Option D

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub
_________________

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

_________________

In probability, "or" means "either" or, more technically, the "union" of two events. In this case, the question is asking what fraction indicated "either coupons or store display." In other words, we have to find the number of people who responded with "coupons" and the number of people who responded with "store displays". Coupons amounted to 22% and store display amounted to 18%, so the fraction is equal to 22+18/90 = 4/9.

On the contrary, "and" means "both" or the "intersection" of two events. If the question asked for the fraction that indicated "both coupons and store display," we would need the number of people who made both responses together. In other words, we would have to find the number of people who responded with "coupons and displays." But since the question says " which one of six promotional techniques most influenced," it is clear that each respondent selected only one response, so there is no intersection between the two events, and no one made the two responses at the same time.

I don't understand why we not took into account the missing 10.?

The question clearly states "Of those consumers who indicated one of the four techniques listed".

One needs to consider out of four only and eliminate the 5th one.
So your total will be 90% and not the entire 100%.

joe123x hope this helps.

Posted from my mobile device
_________________

Hi Bunuel,

If the question is framed as such - what fraction indicated the coupons & store displays?, then will we still be adding up the output from Coupon and Store Display to form the fraction?

Sorry I am trying to understand the difference between the below 2 statements to get some more clarity.

what fraction indicated the coupons & store displays

what fraction indicated either coupons or store displays

Thank you!

Hello Traj201090


You have raised an interesting question. I will answer this in two main parts – (1) For this question (actual version vs your version) and (2) General.

THIS QUESTION

Let’s read through the question one more time and understand what all we are exactly given. I will highlight what I want you to most focus on:

“The table shows partial results of a survey in which consumers were asked to indicate which one of six promotional techniques most influenced their decision to buy a new food product. Of those consumers who indicated one of the four techniques listed, what fraction indicated either coupons or store displays?"

We shall list down every piece of information from the question:

• The table has partial data.
  
  • There were 6 promotional techniques that influence the decision to buy a new food product; we have data about only 4.
• Each consumer voted for “ONE of six” promotional techniques.
• Of the people who had voted for one of the shown 4 techniques, we are asked the fraction that voted for “either coupons or store displays”.

EITHER-OR: (Actual question)

We needed the fraction of people who voted for “either coupons or store displays”. Since every consumer voted for only ONE technique, we got the required number of customers by taking the sum of:

1. Consumers who voted for coupons
2. Consumers who voted for store displays.

Why is directly taking the sum okay? Because there anyway is NO overlap between the two categories. (As I said, each customer chose only one technique.)


AND: (Your Version)

Okay, so you want to find the fraction of students who voted for “coupons AND store displays”. \
This is the group of consumers who voted for BOTH coupons and store displays. But we already know from the given question that a consumer can vote for only one technique. So, does that mean we cannot answer?
Well, no. We can answer, but it’s interesting.
Since there are no consumers who could have voted (indicated) for coupons and store displays both, the required fraction is 0/90 = 0!

Hope you clearly understand this difference between ‘OR’ and ‘AND’ in this question. Now, it’s time to see what generally the difference is between ‘OR’ and ‘AND’ – this will be when overlap is possible.

GENERAL

To understand the general meaning, let’s consider two sets, A and B. Then:

A or B

In Math, “or” is inclusive. That is, A or B means either only A, or only B, or both A and B. To find the number of elements in A or B, we will use the following formula:
#(A or B) = #(A) + #(B) - #(A and B).
Why the subtraction, you ask? Well, this is to remove the elements that belong in both sets A and B (because these would be counted twice – once with A and once with B - when we add the number of elements of A and those of B)
In the question above, this part was 0 since no one could have voted for more than one technique. And so, only addition was enough there!


• A and B
  
  A and B simply means both A and B. This is more direct.
  Here, the number of elements that are in both A and B simultaneously are considered. So, the number of such elements, #(A and B), will be calculated by counting all the elements that are common to both A and B.

Hope this gives you perfect clarity!

Best Regards,
Ashish
Quant Expert, e-GMAT
_________________