The player of a certain game drew a number of cards from a deck in whi

Question

The player of a certain game drew a number of cards from a deck in which each card was labeled with an integer from 1 to 10. Four more even than odd numbers were drawn. How many times were even numbers drawn?

(1) The player drew 12 cards.

(2) The player received 4 points for each even number and 2 points for each odd number drawn, for a total of 40 points.

Archit3110 · Answer

given 
e=4+0
#1
e+o=12
so 4+2o=12
o=4 and e=8
sufficient
#2
4e+2o=40
or say
16+4o+2o=40
o=4 and e = 8
sufficient
IMO D

Kinshook · Answer

Given:  The player of a certain game drew a number of cards from a deck in which each card was labeled with an integer from 1 to 10. Four more even than odd numbers were drawn.

Asked:  How many times were even numbers drawn?

(1) The player drew 12 cards.
Even = Odd + 4
Even + Odd = 12
Even = 8 ; Odd = 4
SUFFICIENT

(2) The player received 4 points for each even number and 2 points for each odd number drawn, for a total of 40 points.
Even = Odd + 4
4 Even + 2 Odd = 40
16 + 6 Odd = 40 
Odd = 4; Even = 8
SUFFICIENT

IMO D

rishab0507 · Answer

Statement 1: Sufficient: 
even will be 8, odd will be 4

Statement 2 : Sufficient, 
Given that: 
2x+ 4y =40 , where x is odd no card drawn and y is even no drawn
and y= x+ 4 from ques stem
2x + 4 (x+4) = 40 
solving we get x=4, so y=8 : Only 1 solution so its sufficient

Bunuel · Answer

Official Explanation

The wording of this question is potentially confusing because we are counting numbers. For example, if we call E the number of cards drawn that have even numbers, E itself could be odd or even. We'll call the number of odd cards D (to avoid confusion with zero). We are told, therefore, that E = D + 4. Since we have one equation with two variables, one way to get sufficiency would be to get a distinct equation with these variables. On to the statements, separately first.

Statement (1) gives us another equation, namely E + D = 12, so we can solve for E (it's 8). Sufficient.

Statement (2) gives us another equation, namely 4E + 2D = 40, so we can solve for E (it's 8). Sufficient.

The correct answer is (D).

Bunuel · Answer

Video Explanation

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