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# M17-17

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:01
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Difficulty:

35% (medium)

Question Stats:

69% (00:56) correct 31% (00:40) wrong based on 258 sessions

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If a bin contains twenty cards numbered 1, 2, ..., 20, what is the probability that the sum of the numbers on two cards extracted from the bin will be even?

A. $$\frac{1}{3}$$
B. $$\frac{7}{18}$$
C. $$\frac{4}{9}$$
D. $$\frac{9}{19}$$
E. $$\frac{1}{2}$$

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16 Sep 2014, 00:01
2
2
Official Solution:

If a bin contains twenty cards numbered 1, 2, ..., 20, what is the probability that the sum of the numbers on two cards extracted from the bin will be even?

A. $$\frac{1}{3}$$
B. $$\frac{7}{18}$$
C. $$\frac{4}{9}$$
D. $$\frac{9}{19}$$
E. $$\frac{1}{2}$$

For the sum of the numbers to be even, either both cards have to bear even numbers or both cards have to bear odd numbers. The probability of the first scenario = $$\frac{10}{20}*\frac{9}{19} = \frac{9}{38}$$. The probability of the second scenario = $$\frac{10}{20}*\frac{9}{19} = \frac{9}{38}$$. The combined probability = $$\frac{9}{38} + \frac{9}{38} = \frac{18}{38} = \frac{9}{19}$$.

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10 Aug 2016, 11:22
1
2 * 10c2 /20c2 =>9/19

2*10c2 => there are 10 even and 10 odd. So you can have either 2 even number cards or 2 odd number cards.
20c2 =>total combinations.
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03 May 2017, 04:57
1
1 to 20

10 even and 10 odd

For a sum of even , we need either two even or two odd

so select 2 from 10 even = 10c2
same for odd = 10c2

So total = 10c2 * 2

for total cases = 20c2

10c2 * 2 / 20 c2 = 10 * 9 / 19 * 10 = 9 /19

D
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03 May 2017, 06:12
Sum of two odd numbers or sum of two even numbers equals an even number. We have 10 odd and 10 even numbers from 1to 20. Hence , 2*(10c2/20c2) = 9/19 or Option D is the answer.
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01 Jul 2017, 02:18
Nice question .

My solution.

Combination to find total= 20C2 = 190

We know, Odd+Odd=Even and Even + Even =Even

Total Odd number = 10 => 10C2=45
Total Even number = 10 => 10C2=45

Now, the numbers can be ODD "OR" EVEN

hence (45+45)/190=90/190

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03 Jun 2018, 08:02
Are these questions named as "M17-17" series from GMAT Club test?

Bunuel wrote:
If a bin contains twenty cards numbered 1, 2, ..., 20, what is the probability that the sum of the numbers on two cards extracted from the bin will be even?

A. $$\frac{1}{3}$$
B. $$\frac{7}{18}$$
C. $$\frac{4}{9}$$
D. $$\frac{9}{19}$$
E. $$\frac{1}{2}$$

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Math Expert
Joined: 02 Sep 2009
Posts: 50585

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03 Jun 2018, 09:22
gmatbusters wrote:
Are these questions named as "M17-17" series from GMAT Club test?

Bunuel wrote:
If a bin contains twenty cards numbered 1, 2, ..., 20, what is the probability that the sum of the numbers on two cards extracted from the bin will be even?

A. $$\frac{1}{3}$$
B. $$\frac{7}{18}$$
C. $$\frac{4}{9}$$
D. $$\frac{9}{19}$$
E. $$\frac{1}{2}$$

Not sure what toy mean. This question is 17th question from set #17. You can check all sets here: https://gmatclub.com/forum/gmat-club-te ... 85003.html
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27 Jun 2018, 16:33
Hi Bunuel

How would we know which case to consider, with replacement or without replacement? I think answer would vary in both cases.
Are we to assume without replacement scenario if the prompt does not mention it specifically?

Thanks.
Math Expert
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27 Jun 2018, 19:11
pantera07 wrote:
Hi Bunuel

How would we know which case to consider, with replacement or without replacement? I think answer would vary in both cases.
Are we to assume without replacement scenario if the prompt does not mention it specifically?

Thanks.

I'd say yes. If nothing is mentioned than the case is without replacement.
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27 Jun 2018, 19:11
pantera07 wrote:
Hi Bunuel

How would we know which case to consider, with replacement or without replacement? I think answer would vary in both cases.
Are we to assume without replacement scenario if the prompt does not mention it specifically?

Thanks.

If it is given you are picking 2 cards, it means you are picking them together so it will be without replacement..
Also if it is with replacement, it will be specifically mentioned or some word to that effect will be used.
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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GMAT 1: 690 Q49 V35
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27 Jun 2018, 19:21
Okay, I get it now.
Thank you Bunuel and chetan2u.
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28 Aug 2018, 22:52
Bunuel chetan2u

I followed the method of taking the total number of o/c as 20C2
and favourable as 10C2 as there are 10 odd numbers.

But I haven't multiplied by 2.

What scenario am I missing out?

Can you pls explain why we are multiplying by 2.
Math Expert
Joined: 02 Sep 2009
Posts: 50585

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28 Aug 2018, 22:56
psych77 wrote:
Bunuel chetan2u

I followed the method of taking the total number of o/c as 20C2
and favourable as 10C2 as there are 10 odd numbers.

But I haven't multiplied by 2.

What scenario am I missing out?

Can you pls explain why we are multiplying by 2.

The sum of two even numbers will also be even, no?
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24 Sep 2018, 13:39
Isn't the question clearly mention. Each card is drawn one after the other without replacement?
Re: M17-17 &nbs [#permalink] 24 Sep 2018, 13:39
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# M17-17

Moderators: chetan2u, Bunuel

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