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

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New post 18 Dec 2018, 02:13
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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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Re: How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5,  [#permalink]

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New post 18 Dec 2018, 05:25
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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
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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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New post 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
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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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New post 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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Re: How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5,  [#permalink]

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New post 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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Re: How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5,  [#permalink]

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New post 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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New post 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.

Answer: E
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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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