Venn Diagram (confused on this idea)

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Mark has 60 blue marbles, half of which are checked, 50 checked marbles, half of which are oval, and 40 oval marbles, half of which are blue. If 10 marbles Mark has are blue, checked and oval and all the marbles he has are either blue, checked or oval, then how many total marbles Mark has?

[GMATGuruNY]

Mark has 60 blue marbles, half of which are checked, 50 checked marbles, half of which are oval, and 40 oval marbles, half of which are blue. If 10 marbles Mark has are blue, checked and oval and all the marbles he has are either blue, checked or oval, then how many total marbles Mark has?

Draw a VENN DIAGRAM representing the following:
Mark has 60 blue marbles, 50 checked marbles, and 40 oval marbles.


Complete the Venn diagram by working from the INSIDE OUT.

10 marbles Mark has are blue, checked and oval.


60 blue marbles, half of which are checked = 30 blue and checked.
50 checked marbles, half of which are oval = 25 checked and oval.
40 oval marbles, half of which are blue = 20 oval and blue.
Subtracting from 30, 25 and 20 the 10 marbles that are in all 3 groups, we get:


Subtracting the values in the diagram from B=60, C=50, and O=40, we get:


How many total marbles does Mark have?
Adding together the values in the Venn Diagram, we get:
T = 20+20+5+10+10+15+5 = 85.

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Hi akshat.pant3,

Is this question from a GMAT resource or a 'math' resource? I ask because if it's meant to be a GMAT question, then there should be 5 answer choices. Having those answers would provide us with various options (other than just 'doing math') that we might use to answer this question.

If you find a question to be 'too hard', it might be because you're approaching the prompt in a difficult way.

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

[Brent@GMATPrepNow]

Here's a free video that explains Mitch's technique: https://www.gmatprepnow.com/module/gmat- ... /video/921

After watching the video, try this practice question: https://www.gmatprepnow.com/module/gmat- ... /video/922

Cheers,
Brent

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Thank you all ... it was very helpful.

And, yes, this is a GMAT question. I just missed to write the answer choices.