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Kushchokhani
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Kushchokhani
Bad habit Number of toddlers
Drooling 55
Nose-picking 48
Biting people 58

A group of parents were surveyed about their toddlers' bad habits, and the results are shown in the table above. No toddlers had only one bad habit, 15 toddlers drooled and picked their nose, 25 toddlers drooled and bit people, and 18 toddlers bit people and picked their nose. How many toddlers had all three bad habits?

A) 0
B) 5
C) 10
D) 15
E) 45


(Source: GMAT Ninja)

Please refer to the attached fig
Attachment:
Toddlers 1 GMAT.png
We can use any one of the bad habits to arrive at \(x.\)

Drooled \(= 15-x+25-x+x=55\)
\(x=15\)

or

NP \(= 15 -x +x +18-x= 48\)
\(x=15\)

Similarly we can use biting to arrive at the same value of \(x.\)

Ans D

RajatGMAT777 Hope it's clear.

stne

x=-15 as per calculation. Is venn diagram full proof approach? I have learnt that when there are 3 different activities, Table method or formula approach is the best.
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stne
Kushchokhani
Bad habit Number of toddlers
Drooling 55
Nose-picking 48
Biting people 58

A group of parents were surveyed about their toddlers' bad habits, and the results are shown in the table above. No toddlers had only one bad habit, 15 toddlers drooled and picked their nose, 25 toddlers drooled and bit people, and 18 toddlers bit people and picked their nose. How many toddlers had all three bad habits?

A) 0
B) 5
C) 10
D) 15
E) 45


(Source: GMAT Ninja)

Please refer to the attached fig
Attachment:
Toddlers 1 GMAT.png
We can use any one of the bad habits to arrive at \(x.\)

Drooled \(= 15-x+25-x+x=55\)
\(x=15\)

or

NP \(= 15 -x +x +18-x= 48\)
\(x=15\)

Similarly we can use biting to arrive at the same value of \(x.\)

Ans D

RajatGMAT777 Hope it's clear.

stne

x=-15 as per calculation. Is venn diagram full proof approach? I have learnt that when there are 3 different activities, Table method or formula approach is the best.

HI Kushchokhani,

You are correct, about the value of \(x\), though couldn't find anything to change in my soln.

Regarding table vs Venn Diagram, choose whatever helps you arrive at the answer , I would prefer not to have a rigid approach and favor only one method, rather having all the weapons of a trade is a better strategy.

Hope it helps !

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