CAT 2001 | Question: 140

Question

On her walk through the park, Hansa collected $50$ coloured leaves, all either maple or oak. She sorted them by category when she got home, and found the following:

• A. The number of red oak leaves with spots is even and positive.
• B. The number of red oak leaves without any spot equals the number of red maple leaves without spots.
• C. All non-red oak leaves have spots, and there are five times as many of them as there are red spotted oak leaves.
• D. There are no spotted maple leaves that are not red.
• E. There are exactly $6$ red spotted maple leaves.
• F. There are exactly $22$ maple leaves that are neither spotted nor red.

How many oak leaves did she collect?

• A. $22$
• B. $17$
• C. $25$
• D. $18$

Answer 1

Oak	Maple
Red and spot is even, = x	Spotted means red
red and w/o spots = red and w/o spots in maple = y	6 red spotted
Non-red implies has spot, = 5x	22 not spotted non red

 

$x + y + 5x + 6 + 22 + y = 50 \\ \implies 3x + y = 11 \\\implies x = 2, y = 5 $

(as $x$ is even). 

So, no. of oak leaves = $6x + y = 17.$

Comments

"There are no spotted maple leaves that are not red."
spot means red , but red leaves may not be spotted always. right?

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yes :) much twisted than usual first order logic questions for GATE :)