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# A math teacher has 30 cards, each of which is in the shape

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A math teacher has 30 cards, each of which is in the shape [#permalink]

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24 Jul 2012, 05:01
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A math teacher has 30 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.

A. 9
B. 10
C. 11
D. 12
E. 13
[Reveal] Spoiler: OA

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Last edited by Bunuel on 25 Jul 2012, 07:33, edited 1 time in total.
Edited the question.
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Re: A math teacher has 30 cards, each of which [#permalink]

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24 Jul 2012, 06:15
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imhimanshu wrote:
Hi

A math teacher has 30 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.

a) 9
b) 10
c) 11
d) 12
e)13

Squares are both rectangles and rhombuses. Circles are neither rectangles, nor rhombuses.
There are 15 rectangles and 10 rhombuses.
Using a Venn diagram or a 2 X 2 table, we can deduce that the maximum number of cards that re circles is 30 - (15 + 10 - 8) = 13.

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Re: A math teacher has 30 cards, each of which [#permalink]

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24 Jul 2012, 06:16
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Remember:
a square is a special kind of rhombus (sides are perpendicular)
a square is a special kind of rectangles (sides with same length)

Among the 30 cards with have:
15 rectangles
10 rhombus
8 squares

Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.
Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.
We have 8 squares.
So the minimum different cards that represent a square, a rhombus or a rectangle is 2 + 7 + 8 = 17
Which means that the maximum number of circles that you could have is 30 - 17 = 13

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Re: A math teacher has 30 cards, each of which is in the shape [#permalink]

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02 May 2013, 16:06
can anyone actually get me 13 non-rectangular AND non-rhombus shape cards out of 30 cards with the specifications clearly stated half of the 30 cards (15 cards) are rectangular (including some square cards) and one third of the 30 cards (10 cards) are rhombus (including some square cards)??????

clearly the question stem stated there are 25 cards that is the combination of rectangular shape and rhombus shape.. there are 8 cards within the 25 cards so 25-8=13 cards are non square but still either rectangular or rhombus.. so the non-rectangular AND non-rhombus shape only has 5 spots left in a hand of 30 cards..

i know van-diagram or matrix is what the test or the study of the test want people to go with.. but that is not reasoning and in fact in real life that can never happen.. if anyone disagrees and can make me a hand of 30 cards with exactly what the question stem asked and have 13 circle (non-rectangular AND non-rhombus) cards in real life, let me know!
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Re: A math teacher has 30 cards, each of which is in the shape [#permalink]

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17 Nov 2013, 16:57
Ellexuxin GMAT does not tests real world practicality; rather it tests practicality within the constraints given in the problem.
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Re: A math teacher has 30 cards, each of which is in the shape [#permalink]

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10 Jun 2015, 03:17
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Re: A math teacher has 30 cards, each of which is in the shape [#permalink]

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17 Jan 2017, 11:56
Hello from the GMAT Club BumpBot!

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Re: A math teacher has 30 cards, each of which is in the shape [#permalink]

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20 Jan 2017, 01:36
Key to remember here is that square is also a rhombus. After that its plug-n-play, 15 rectangles , all squares are also rhombus ==> only 2 rhombuses are not square.

Total 17 items so far, thus, max 13 circles are possible.

Ans. E
Re: A math teacher has 30 cards, each of which is in the shape   [#permalink] 20 Jan 2017, 01:36
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# A math teacher has 30 cards, each of which is in the shape

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