In a certain candy store, 22% of the customers are caught sa

Question

In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 12% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?

A) 22%
B) 23%
C) 24%
D) 25%
E) 34%

A) 22%
B) 23%
C) 24%
D) 25%
E) 34%

ricsingh · Accepted Answer

Hi Vikrant,

lets say there are 100 customers in store, out of with x sample the candy
12% of this x was not caught, 88% of this x was caught

this 88% of x = 22% of the total customers (it is given that 22% of the total customers were found sampling)

so x = 22/88 = 0.25

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Bunuel · Answer

Since 12% of the customers who sample the candy  are not  caught, then 88% of the customers who sample the candy  are  caught:

{% of customers who sample candy}*0.88 = 0.22;
{% of customers who sample candy} = 0.25.

Answer: D.

eladavid · Answer

What is the best way to calculate this question? 
I tried to aproximate and i ended up with a wrong answer.

Bunuel · Answer

It's quite easy:

{% of customers who sample candy}*0.88 = 0.22 --> {% of customers who sample candy} = 22/88 = 1/4.

Hope it helps.

vikrantgulia · Answer

I am little bit confused in this question.Would you please elaborate the explanation more clearly.

Lets say we have 100 customer in store. 12% sample the candy but didn't caught. 
So, 88% customer caught sampling the candy. I didn't get after this.

Please explain.

Temurkhon · Answer

One can solve by two equations: 
x-y=22
y=0.12x

we get x-0.12x=22 => 0.88x=22 => x=25

PareshGmat · Answer

Lets say Total = 100 
Sample................................... .............................. Dont Sample
x......................................................................... 100-x

\frac{12x}{100} = Not Caught, means

\frac{88x}{100} = Caught Sampling

Given that 22% of the customers are caught sampling the candy, i.e

\frac{88x}{100} = \frac{22}{100} * 100

x = 25%

Answer = D

iamdp · Answer

Let's say the no of customers who sample candy = S

Now { 0.12 S }+ {22} = S

>> S = 25

EMPOWERgmatRichC · Answer

Hi All,

The presentation in this question is relatively rare on Test Day - the logic most often appears in Overlapping Sets questions (but the wording is a bit more straight-forward). The idea here is essentially about "groups within groups"...

From the prompt we know that there are 3 different types of people....

Those who do NOT sample candy
Those who SAMPLE AND are CAUGHT
Those who SAMPLE but are NOT CAUGHT

The percents that we're given refer to the latter 2 groups....we can TEST VALUES to clarify the logic:

22% of customers are caught sampling candy - this refers to 22% of ALL CUSTOMERS....

IF Total customers = 100
22%(100) = 22 customers SAMPLE AND are CAUGHT.

Next, we're told that 12% of those WHO SAMPLE are NOT CAUGHT. This is NOT 12% of everyone; it's 12% of those who SAMPLE.

TOTAL WHO SAMPLE = X = (those CAUGHT) + (those NOT CAUGHT)

X = 22 + .12(X)

From here, we can combine like terms and solve for X....

.88X = 22
X = 22/.88 = 1/.04 = 25

Thus, 25 out of the original 100 SAMPLE candy. Since that is what the question is focused on, 25% is the answer.

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

mvictor · Answer

i used the total number of clients = 100
now..22 sampling and fined
suppose X is the number of clients who sample
0.12x are not fined.
it means that 22 = 0.88x
now..
x=22*100/88 = 25

so 25 people are sampling.
since we have 100 customers, 25 of them would represent 25%

spetznaz · Answer

Tricky one .. good question ... 25% it is

Divyadisha · Answer

Let 100 be the total number of persons.

22 sample candy and get caught.

Let total number of persons who sample candy be x

12% (.12x) are not caught while 22 (88%) are caught 
.88x= 22
x=25%

TheLostBear · Answer

Good question. I made the mistake of sorting information too mechanically by dividing the customers into Sample/Did not sample and Caught/ Not Caught categories. I completely missed the fact that there was no one who would did not sample but got caught.. Once I saw it, I realized that the "22% of the customers are caught sampling the candy and are charged a small fine" is in fact 22% of total customers.

Because "12% of the customers who sample the candy are not caught", 88% of customers who sample are caught. That 88% is 22% of total customers, so 100% of people who sample is 22%*100%/88%= 25% of total customers.

Because "12% of the customers who sample the candy are not caught", 88% of customers who sample are caught. That 88% is 22% of total customers, so 100% of people who sample is 22%*100%/88%= 25% of total customers.

shashankism · Answer

22% of the overall customers are caught sampling candy and are fined.
12% of the customers who sample candy are not caught.
So, 88% of the customers who sample candy are caught.

So, total percentage of all customers of sample candy = 22/.88 = 22*100/88 = 25 %

Answer D

GMATGuruNY · Answer

22% of the customers are caught sampling the candy. 
Let the total number of customers = 100, implying that the number of samplers who are caught = 22

12% of the customers who sample the candy are not caught. 
Of the total number of samplers, the ratio of caught to not caught = 88:12 =  22:3 
Since 22 samplers are caught, the ratio in blue indicates that 3 samplers are not caught, implying that the total number of samplers = 22+3 = 25

Thus:
 \frac{samplers}{total} = \frac{25}{100} =  25%

D

adewale223 · Answer

Let x be total number of customers and y number who sampled candy.

12% of customers not caught sampling candy. That means 88% were caught.

0.88y = 0.22x

y = 0.22x/0.88

= 0.25x

Percent of customers who sample candy

= 0.25x/x * 100
= 25%

Answer D.

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G-Man · Answer

22% of total customers (T) are 88% of customers who sample candy(x) (Because 12% of people sampling candy were not caught)

Then the percentage of total customers who samples candy is

88% X = 22% T
1% X = 0.25% T
100%X = 25% T

25%

bumpbot · Answer

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In a certain candy store, 22% of the customers are caught sa

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