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Mark has 60 blue marbles, half of which are checked, 50 checked marble 25 Sep 2018, 07:18
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35% (medium)

Question Stats:

77% (02:50) correct 23% (02:48) wrong based on 209 sessions

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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, & oval, and all marbles he has either blue, checked or oval, then how many total marbles Mark has?

A 45
B 75
C 50
D 85
E 60
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D
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Schools: IIM (A) ISB '24
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Mark has 60 blue marbles, half of which are checked, 50 checked marble 25 Sep 2018, 08:28
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shard87
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, & oval, and all marbles he has either blue, checked or oval, then how many total marbles Mark has?

A 45
B 75
C 50
D 85
E 60
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Answer Option D

Check the solution as attached.

The black values are given information

Blue values are derived values
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Mark has 60 blue marbles, half of which are checked, 50 checked marble 25 Sep 2018, 16:15
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shard87
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, & oval, and all marbles he has are either blue, checked or oval, then how many total marbles Mark has?

A 45
B 75
C 50
D 85
E 60
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\(? = T\)

Based on the Venn diagram presented above, let´s apply the simplifier immediately:

\(? = 60 + 40 + 50 - \left[ {\left( {20 - 10} \right) + \left( {25 - 10} \right) + \left( {30 - 10} \right)} \right] - 2 \cdot 10 = 85\)


Regards,
Fabio.
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Mark has 60 blue marbles, half of which are checked, 50 checked marble 14 Nov 2024, 22:23
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fskilnik I m not able to understand y u did "-(2x10)". I have solved it in this way, (30+25+20)+10=85.
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Mark has 60 blue marbles, half of which are checked, 50 checked marble 15 Nov 2024, 00:03
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Rikhraj1

fskilnik
shard87
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, & oval, and all marbles he has are either blue, checked or oval, then how many total marbles Mark has?

A 45
B 75
C 50
D 85
E 60




\(? = T\)

Based on the Venn diagram presented above, let ́s apply the simplifier immediately:

\(? = 60 + 40 + 50 - \left[ {\left( {20 - 10} \right) + \left( {25 - 10} \right) + \left( {30 - 10} \right)} \right] - 2 \cdot 10 = 85\)


Regards,
Fabio.

fskilnik I m not able to understand y u did "-(2x10)". I have solved it in this way, (30+25+20)+10=85.
Show more

That solution uses the formula explained here: ADVANCED OVERLAPPING SETS PROBLEMS.

\(Total = A + B + C - (sum \ of \ EXACTLY \ 2-group \ overlaps) - 2*(all \ three) + Neither\).

You see, \((20 - 10) + (25 - 10) + (30 - 10)\) represents the sum of marbles with exactly two features: only blue and checked, only checked and oval, and only oval and blue.

Hope this helps.
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