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# How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5,

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5,  [#permalink]

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18 Dec 2018, 02:13
00:00

Difficulty:

35% (medium)

Question Stats:

66% (01:36) correct 34% (01:25) wrong based on 87 sessions

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[Math Revolution GMAT math practice question]

How many $$4$$-digit numbers greater than $$3,000$$ have the digits: $$1, 3, 5,$$ and $$7$$?

$$A. 6$$
$$B. 9$$
$$C. 12$$
$$D. 15$$
$$E. 18$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMAT Club Legend Joined: 18 Aug 2017 Posts: 4476 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5, [#permalink] ### Show Tags 18 Dec 2018, 05:25 2 1 MathRevolution wrote: [Math Revolution GMAT math practice question] How many $$4$$-digit numbers greater than $$3,000$$ have the digits: $$1, 3, 5,$$ and $$7$$? $$A. 6$$ $$B. 9$$ $$C. 12$$ $$D. 15$$ $$E. 18$$ MathRevolution question does not specify whether digits can be repeated or not ; seems answer is co relating to the latter... since we have 4 digits and >3000 so first digit can be either 3,5,7 only '3' possibilities ; second digit : 3 possibliites ; could be any of third digit 2 option and 4th option 1 so 3*3*2*1 = 18 IMO E _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7738 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5, [#permalink] ### Show Tags 20 Dec 2018, 02:00 => We need to count the $$4$$-digit numbers with thousands digits $$3, 5$$ and $$7$$. The number of $$4$$-digit numbers beginning with $$3$$ is $$6$$. The number of $$4$$-digit numbers beginning with $$5$$ is $$6$$. The number of $$4$$-digit numbers beginning with $$7$$ is $$6$$. Thus, the total number of such $$4$$-digit numbers is $$18 = 6 + 6 + 6.$$ Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5,  [#permalink]

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27 Jan 2019, 05:11
chetan2u the question does not specify if the digits are repeating or not

First digit can be taken in 3 ways from 3,5,7
Second digit can be selected in 4 ways from 1,3,5,7
Third digit can be selected in 4 ways from 1,3,5,7
Fourth digit can be selected in 4 ways from 1,3,5,7

If it was mentioned the digits cannot be repeating then,

First digit can be selected in 3 ways from 3,5,7
Second digit can be selected in 3 ways from remaining numbers
Third digit can be selected in 2 ways from remaining numbers
Fourth digit can be selected in 1 way

Which gives 18, but shouldn't it be mentioned in the question?
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Joined: 02 Aug 2009
Posts: 7756
Re: How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5,  [#permalink]

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27 Jan 2019, 06:26
1
Manat wrote:
chetan2u the question does not specify if the digits are repeating or not

First digit can be taken in 3 ways from 3,5,7
Second digit can be selected in 4 ways from 1,3,5,7
Third digit can be selected in 4 ways from 1,3,5,7
Fourth digit can be selected in 4 ways from 1,3,5,7

If it was mentioned the digits cannot be repeating then,

First digit can be selected in 3 ways from 3,5,7
Second digit can be selected in 3 ways from remaining numbers
Third digit can be selected in 2 ways from remaining numbers
Fourth digit can be selected in 1 way

Which gives 18, but shouldn't it be mentioned in the question?

Yes, the language could have been slightly better.
It could be ' How many 4-digit number greater than 3000 can be formed from digits 1, 3, 5 and 7 without repetition.

But, by using AND and the kind of wording, I would take it that the intention is to find the numbers containing all the digits 1, 3, 5 and 7.
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Posts: 44
Re: How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5,  [#permalink]

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27 Jan 2019, 08:59
but its mentioned in question whether repeatation is allowed or not

if repetation is allowed ans would be 192
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Re: How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5,  [#permalink]

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02 Mar 2019, 10:09
MathRevolution wrote:
[Math Revolution GMAT math practice question]

How many $$4$$-digit numbers greater than $$3,000$$ have the digits: $$1, 3, 5,$$ and $$7$$?

$$A. 6$$
$$B. 9$$
$$C. 12$$
$$D. 15$$
$$E. 18$$

We see that we have 3 options for the thousands digit, 3 for the hundreds digit, 2 for the tens digit and 1 for the units digit. Thus, the total number of options is 3 x 3 x 2 x 1= 18.

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Re: How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5,   [#permalink] 02 Mar 2019, 10:09
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