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# M21-36

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Math Expert
Joined: 02 Sep 2009
Posts: 58340

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16 Sep 2014, 01:15
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Difficulty:

5% (low)

Question Stats:

89% (01:05) correct 11% (01:53) wrong based on 113 sessions

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A basket contains cards bearing numbers 10, 11,... , 20. If a card is drawn from the basket and is not returned to it, and then the second card is drawn from the basket, what is the probability that the first card drawn will have a prime number on it while the second will not?

A. $$\frac{14}{55}$$
B. $$\frac{4}{15}$$
C. $$\frac{5}{16}$$
D. $$\frac{27}{80}$$
E. $$\frac{32}{55}$$

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Joined: 02 Sep 2009
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16 Sep 2014, 01:15
Official Solution:

A basket contains cards bearing numbers 10, 11,... , 20. If a card is drawn from the basket and is not returned to it, and then the second card is drawn from the basket, what is the probability that the first card drawn will have a prime number on it while the second will not?

A. $$\frac{14}{55}$$
B. $$\frac{4}{15}$$
C. $$\frac{5}{16}$$
D. $$\frac{27}{80}$$
E. $$\frac{32}{55}$$

There are 4 prime numbers in the range: 11, 13, 17, 19. There are 11 cards in the basket. We have to calculate $$\frac{4}{11} * \frac{11 - 4}{10} = \frac{28}{110}$$.

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Joined: 10 May 2017
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01 Jul 2017, 00:47
Sir,
I am not sure if my thinking is correct, please guide me.

11 numbers and 2 to be selected = 55 combinations. But since the order of selection matters in this question, 55x2=110.

Prime selection=4C1 = 4
Non-prime selection = 7C1 = 7

Since the problem says Prime "AND" non-Prime 4*7=28.

Therefore 28/110.

I know this method is unnecessary, but just want to have an understanding in different ways.

Thank you very much.
Manager
Joined: 12 Jun 2016
Posts: 212
Location: India
WE: Sales (Telecommunications)

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11 Sep 2017, 00:04
Hello Bunuel,

This is similar to a question that I posted few days back.

Do you think the answer choices need to be in their reduced form? Not that its a Big issue, but (atleast for me), I usually reduce the fractions as matter of practice since all the fractions are given in Reduced form in GMAT. Having something in a non reduced form as answer choice sometimes serves as a distraction and eats up more time.

Please correct me if this is too small an issue to even merit giving a thought
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11 Sep 2017, 00:19
susheelh wrote:
Hello Bunuel,

This is similar to a question that I posted few days back.

Do you think the answer choices need to be in their reduced form? Not that its a Big issue, but (atleast for me), I usually reduce the fractions as matter of practice since all the fractions are given in Reduced form in GMAT. Having something in a non reduced form as answer choice sometimes serves as a distraction and eats up more time.

Please correct me if this is too small an issue to even merit giving a thought

_______________
Edited. Thank you.
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GMAT 1: 720 Q47 V41
GPA: 2.98
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17 Aug 2018, 20:02
just as above...i am confused where to use....11C2 and where just 11 x10
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Joined: 08 Jan 2013
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29 Oct 2018, 18:54
Here you cannot use 11C2 as it explicitly states that first card is prime and second is not, so we have to maintain that order and reverse order is not allowed i.e. first drawing a non-prime and then a prime.

Think of 4C1*7C1/11C2 as other way of saying (4/11)*(7/10)*2 when order of drawing prime and non-prime numbers can inter-change.
M21-36   [#permalink] 29 Oct 2018, 18:54
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# M21-36

Moderators: chetan2u, Bunuel