How many four digit numbers : GMAT Problem Solving (PS)
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# How many four digit numbers

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Manager
Joined: 08 Sep 2010
Posts: 232
Location: India
WE 1: 6 Year, Telecom(GSM)
Followers: 4

Kudos [?]: 251 [0], given: 21

How many four digit numbers [#permalink]

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27 Oct 2010, 02:49
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Question Stats:

25% (00:00) correct 75% (00:59) wrong based on 4 sessions

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How many four digit numbers,that are divisble by 4 can be formed ,using the digits 0 to 7 if no digit is to occur more than once in each number.

A.520
B.370
C.345
D.432
E.353

Consider KUDOS if it is good one.
[Reveal] Spoiler: OA

Last edited by ankitranjan on 27 Oct 2010, 23:20, edited 1 time in total.
Manager
Joined: 08 Sep 2010
Posts: 232
Location: India
WE 1: 6 Year, Telecom(GSM)
Followers: 4

Kudos [?]: 251 [0], given: 21

Re: How many four digit numbers [#permalink]

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27 Oct 2010, 23:36
I have solved it in this way....
A number will be divisible by 4 if the number formed by its last two digit is divisible by 4.
And in this way we have its last two digit as ...
04,12,16,20,24,32,36,40,52,56,60,64,72,76 {Four of these includes 0 and remaining ten are without 0}
( I didnt include 44 as repetition is not allowed and others as digit should be less than 8)

Now consider the case when any of the last two digit is 0. we can get 6*5 = 30 different numbers

so total formed number where any of the last two digit is 0 = 4*30=120

Now consider the case when none of the last two digit is 0 = 5 * 5 =25 (because 1000s place cant be filled by 0 or else it will be a three digit number)

so total formed number when none of the last two digit is 0 = 10 * 25 =250

Hence required answer is 250+120 =170.
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Re: How many four digit numbers   [#permalink] 27 Oct 2010, 23:36
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