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by sana.noor » Mon Aug 05, 2013 11:53 pm
What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?
(A) 271/900
(B) 27/100
(C) 7/25
(D) 1/9
(E) 1/10

OA is C
Last edited by sana.noor on Wed Aug 07, 2013 9:40 am, edited 1 time in total.
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by lunarpower » Tue Aug 06, 2013 12:37 am
well, the opposite of "one or more 7's" is "no 7"s. do you know how to find the probability of that?
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by macattack » Tue Aug 06, 2013 1:05 am
Experts please what is wrong with this reasonning:
Total number of 3 digit numbers = 999-100+1=900
Desired outcome: 107,117,127,137...
Total number of desired outcome=252
252/900= 7/25

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by sana.noor » Tue Aug 06, 2013 1:42 am
yes Ron i Know
Probability of getting one or more 7 = 1- (probability of No 7's)
Thankyou i got it
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by lunarpower » Tue Aug 06, 2013 1:56 am
[---]
Last edited by lunarpower on Tue Aug 06, 2013 3:34 am, edited 1 time in total.
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by macattack » Tue Aug 06, 2013 3:15 am
100s: 19 desired outcome (107,127,137,147,157,167,170,171,172...)
200s: 19 desired outcome
300s: 19 desired outcome
400s: 19 desired outcome
500s: 19 desired outcome
600s: 19 desired outcome
800s: 19 desired outcome
900s: 19 desired outcome

700s: 100 desired outocme

Total number of desired outcome= 100+19*8=252

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by lunarpower » Tue Aug 06, 2013 3:42 am
macattack -- yeah, you're right here. nice work.

as usual, i misread the problem (yay! dyslexia is fun) as "three-digit code" instead of "three-digit number". so, in other words, i was thinking about 000-999 instead of 100-999.

so, yes, that works.

using the "opposite situation" method:
the chance of getting NO sevens is
(8/9)(9/10)(9/10)
= (8/10)(9/10)
= 72/100
= 18/25

so, the chance of getting at least one seven is 1 - 18/25 = 7/25.

--

you can also do this:
* 90 numbers with "7" in the units place (107, 117, ..., 997); 90 numbers with "7" in the tens place (170, 171, ..., 979), and 100 numbers with "7" in the hundreds place (700-799) ... so, 280.
BUT
* we've counted all the _77 numbers except 777 (eight of them) twice. there are eight of those, so subtract 8.
* we've counted all the 7_7 numbers except 777 (nine of them) twice. there are nine of those, so subtract 9.
* we've counted all the 77_ numbers except 777 (nine of them) twice. there are nine of those, so subtract 9.
so, right now, 254.
FINALLY
* we've counted 777 three times. so, subtract two of them (so that one still counts), leaving 252.

... but your way of counting seems to be more straightforward.
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by macattack » Tue Aug 06, 2013 3:46 am
So the OA is wrong? Hah I am starting to enjoy that whole GMAT ride!

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by lunarpower » Tue Aug 06, 2013 3:47 am
macattack wrote:So the OA is wrong? Hah I am starting to enjoy that whole GMAT ride!
Ya, if the "oa" doesn't say 7/25, then it's wrong.

What does it say?
I'm posting from a tablet, so I can't see behind the cursed blackout thingy.

This is why you should stick with problems from known sources, folks.
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by macattack » Tue Aug 06, 2013 3:55 am
its says 271/900

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by lunarpower » Tue Aug 06, 2013 4:00 am
macattack wrote:its says 271/900
final score...
you: 1
"oa": 0

what's the source?
regard with suspicion from now on...
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by sana.noor » Tue Aug 06, 2013 6:46 am
Ahhh thank you for telling me that the Official answer posted is wrong. i was trying this question since last many hours but couldnt find that how the author reach at 271/900.

Source: initially i took this from BTG Library but later i found that this question was from gmat club tests.
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by [email protected] » Tue Aug 06, 2013 11:09 am
Hi All,

The error in the "correct answer" is that the author of this question considers 3-digit numbers that begin with 0.

For example, this author considers 007 to be one of the 3-digit numbers that has a 7 in it. If you consider those additional terms, you'd find another 19 3-digit numbers with a 7 in them.

eg 007, 072, etc.

Thankfully, the GMAT writers have a rigorous writing, vetting and testing phase, so this type of error rarely ever happens.

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by macattack » Tue Aug 06, 2013 10:05 pm
Hi Rich,
I don't think that is the case!
It is true that if 3digit numbers starting with 0 are to be considered that the total number of desired outcomes would become 271 like stated in the correct answer. However the denominator would change to 1000 instead of the proposed 900. So if what you are saying is true the correct answer should be 271/1000 and not 271/900.
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by [email protected] » Wed Aug 07, 2013 12:23 am
HI macattack,

You are correct; the denominator WOULD change. So there are TWO errors in this question (the one I pointed out and the one you pointed out).

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