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

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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 â‰ˆ 67%.

The correct answer is D.

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

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).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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