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Four cards are chosen from a standard deck: two aces (one of

by fskilnik@GMATH » Wed Feb 20, 2019 7:17 am

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GMATH practice exercise (Quant Class 19)

Four cards are chosen from a standard deck: two aces (one of Spades, another of Hearts) and two kings (one of Spades, another of Hearts). The aces are considered as -1 (Spades) and 1 (Hearts), while the kings are considered as -2 (Spades) and 2 (Hearts). If two different cards among these four are randomly chosen, and their corresponding numerical values are multiplied together, which of the following is closest to the probability that the product obtained is negative or odd (or both)?

(A) 17%
(B) 50%
(C) 56%
(D) 67%
(E) 75%

Answer: [spoiler] ____(D)__[/spoiler]
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by GMATGuruNY » Wed Feb 20, 2019 8:03 am
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 19)

Four cards are chosen from a standard deck: two aces (one of Spades, another of Hearts) and two kings (one of Spades, another of Hearts). The aces are considered as -1 (Spades) and 1 (Hearts), while the kings are considered as -2 (Spades) and 2 (Hearts). If two different cards among these four are randomly chosen, and their corresponding numerical values are multiplied together, which of the following is closest to the probability that the product obtained is negative or odd (or both)?

(A) 17%
(B) 50%
(C) 56%
(D) 67%
(E) 75%
The following cases are possible:
(-1)(1) = -1
(-1)(-2) = 2
(-1)(2) = -2
(1)(-2) = -2
(1)(2) = 2
(-2)(2) = -4
Of the 6 cases above, the 4 in blue each yield a product that is negative, odd or both:
4/6 = 2/3 ≈ 67%.

The correct answer is D.
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by fskilnik@GMATH » Wed Feb 20, 2019 10:47 am
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 19)

Four cards are chosen from a standard deck: two aces (one of Spades, another of Hearts) and two kings (one of Spades, another of Hearts). The aces are considered as -1 (Spades) and 1 (Hearts), while the kings are considered as -2 (Spades) and 2 (Hearts). If two different cards among these four are randomly chosen, and their corresponding numerical values are multiplied together, which of the following is closest to the probability that the product obtained is negative or odd (or both)?

(A) 17%
(B) 50%
(C) 56%
(D) 67%
(E) 75%
$$\left\{ { - 2, - 1,1,2} \right\}\,\, \to \,\,{\rm{two}}\,{\rm{different}}\,\,{\rm{chosen}}$$
$$? = P\left( {{\rm{odd}}\,\,{\rm{or}}\,\,{\rm{negative}}\,\,{\rm{product}}} \right)$$
$${\rm{6}}\,\,{\rm{equiprobable}}\,\,{\rm{outcomes}}\,\,:\,\,\,\left\{ \matrix{
\,\left\{ { - 2, - 1} \right\},\left\{ {1,2} \right\}\,\,\,\,\left( {{\rm{product}}\,\,2} \right) \hfill \cr
\,\left\{ { - 2,1} \right\},\left\{ { - 1,2} \right\}\,\,\,\,\left( {{\rm{product}}\,\, - 2} \right)\,\,\,::\,\,\,2\,\,{\rm{favorable}}\,\,{\rm{outcomes}} \hfill \cr
\,\left\{ { - 2,2} \right\}\,\,\,\,\left( {{\rm{product}}\,\, - 4} \right)\,\,\,::\,\,\,1\,\,{\rm{favorable}}\,\,{\rm{outcome}} \hfill \cr
\,\left\{ { - 1,1} \right\}\,\,\,\,\left( {{\rm{product}}\,\, - 1} \right)\,\,\,::\,\,\,1\,\,{\rm{favorable}}\,\,{\rm{outcome}} \hfill \cr} \right.$$
$$?\,\, = \,\,{{2 + 1 + 1} \over 6}\,\, = \,\,{2 \over 3}\,\, \cong \,\,67\% $$

The correct answer is (D).


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