Suppose that Dog-o-Rama provides day care for 30 dogs and regular groo

Question

Data Insights (DI) Quiz-II 2023       Click here for Details ]

Suppose that Dog-o-Rama provides day care for 30 dogs and regular grooming for 24 dogs.

In the table, select two numbers that are consistent with the information given. In the first column, select the row that displays the largest number of dogs at Dog-o-Rama that are receiving either day care or regular grooming, and in the second column, select the row that displays the largest number of dogs at Dog-o-Rama that are receiving both day care and regular grooming. Select only one option in each column.

pintukr · Answer

Suppose that Dog-o-Rama provides day care for 30 dogs and regular grooming for 24 dogs.

In the table, select two numbers that are consistent with the information given. In the first column, select the row that displays the largest number of dogs at Dog-o-Rama that are receiving either day care or regular grooming, and in the second column, select the row that displays the largest number of dogs at Dog-o-Rama that are receiving both day care and regular grooming. Select only one option in each column.

A. Receiving either day care or grooming

Total count of facilities availed = 30 + 24 = 54

So, Receiving either day care or grooming <= 54

Amongst the given values , Max value for Receiving either day care or grooming = 48 
(possible for Receiving day care only = 27
 Receiving grooming only = 21 
 Receiving both day care and regular grooming = 3)

Hence, Receiving either day care or grooming (max) = 48

B. Receiving both day care or grooming.

The value is <= since, regular grooming for 24 dogs.

The only consistent value is 17.

Hence, amongst the given values, Receiving both day care or grooming (max) =17

Hence, Receiving both day care or grooming (max) = 17

Elite097 · Answer

Receiving either day care or grooming= 48 since max people will be 30+24 and 48 is the closest number below
Receiving both day care and grooming =17 since the overlap can max be 24 and 17 is the largest number below 24

p456 · Answer

48 and 17

This one got my head spinning as none of the combinations were working. Then i thought to try this with inequality. I assume this solution is correct, but not sure.

Given:
day_care = 30 dogs
regular_grooming = 24 dogs

either_day_care_or_grooming = day_care + regular_grooming - both_day_care_and_grooming

either_day_care_or_grooming = 54 - both_day_care_and_grooming

at this point i assume everyone would have come. but no matter what value you pick for 2 unknown variables, equality will not be measured. let's try inequality.

with some logical thinking, we can assume, both_day_care_and_grooming < min(30,24) or can we write this as,

both_day_care_and_grooming < 24
here options in table may help us. we can narrow down value for this variable to 17.
=> both_day_care_and_grooming = 17

Now, coming back to our equation
either_day_care_or_grooming = 54 - 17 = 37

37 not there in table, i can feel you. Let's apply some logic again
either_day_care_or_grooming > max(37,24)
=> either_day_care_or_grooming must be greater than 37, AND either_day_care_or_grooming must be less than or equal to 54(calculated above)
only one option in table, 48.

This was tough for me. Please correct the solution if i am wrong.

pudu · Answer

the maximum 24+30=54 can receive either services. The maximum value we can choose from the option is 48.The maximum number of dogs that can receive both the services is 24. 17 is the maximum available from the option. So (d,a) is the answer

hallfootball · Answer

Let a be the number of dogs who received only day care.
Let b be the number of dogs who received only regular grooming.
Let c be the number of dogs who received both day care and regular grooming.
Here a, b and c will be non negative integers.

Dog-o-Rama provides day care for 30 dogs and regular grooming for 24 dogs.
This can be translated as a + b = 30 let's call this equation 1, and b + c = 24, let's call this equation 2.

Column 1: Select the row that displays the largest number of dogs at Dog-o-Rama that are receiving either day care or regular grooming.

We need to maximize the value of a + c in order to answer column 1.

Adding equation 1 and 2 we get a + 2b + c = 54.
Therefore, a + c = 54 - 2b. Let's call this equation 3.

To maximize equation 3 we need to reduce the value of 2b. i.e. reduce the value of b.
The minimum value b can take is 0. Therefore, the maximum value a + c can take is 54. Hence we can eliminate two options 56 and 60.

We also, see that 54 is not one of the options, hence we also need some other constraint to get the answer.
If we close look at equation 3, we see that 54 is an even number and 2b is also an even number. Recalling Even / Odd concepts Even - Even = Even.
Therefore, out of the 4 remaining options we need to eliminate odd numbers. Post POE we see that the only option remains which is 48.

Hence, the largest number of dogs at Dog-o-Rama that are receiving either day care or regular grooming from the given option choices is 48.

Therefore, there are 48 dogs at Dog-o-Rama that are receiving either day care or regular grooming and 3 dogs at Dog-o-Rama that are receiving both day care and regular grooming.

Column 2: Select the row that displays the largest number of dogs at Dog-o-Rama that are receiving both day care and regular grooming.

We need to maximize the value of b.

From equation 3 we get b = (54 - a - c)/2.
This can be simplified as b = 27 - (a+c)/2.

To maximize the value of b we need to reduce the value of a + c.
The minimum value a + c can take is 0. Hence the maximum value b can take is 27. Which is one of the options.
However, looking closely at equation 2, we see that b + c = 24 and both b and c are non negative. Hence the maximum value b can take is 24 which is not an option. However, there is only one option which is lesser than 24 i.e. row 1 (17).

Hence the largest number of dogs at Dog-o-Rama that are receiving both day care and regular grooming from the given option choices is 17.

Therefore, there are 17 dogs at Dog-o-Rama that are receiving both day care and regular grooming and 20 dogs at Dog-o-Rama that are receiving either day care or regular grooming.

Sajjad1994 · Answer

Official Explanation

The correct answers are 48 dogs receiving either day care or grooming and 17 dogs receiving both day care and grooming.

Altogether, 54 dogs are receiving day care and grooming services (30 day care and 24 grooming). The number 54 is not given in the table, and 56 is too large. The number 48 is the next largest number, so 48 is correct.

The largest number of dogs that could possibly be receiving both day care and regular grooming is 24. This would be the case if all 24 dogs receiving grooming were also receiving day care. However, the number 24 is not included in the table. The number 17 is the next largest number, so 17 is correct.

Suppose that Dog-o-Rama provides day care for 30 dogs and regular groo

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Receiving either day care or grooming	Receiving both day care and grooming	Number of dogs
		17
		27
		31
		48
		56
		60

GMAT Two-part Analysis (TPA) Questions

Suppose that Dog-o-Rama provides day care for 30 dogs and regular groo

Prep Toolkit

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

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