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# How many four digit numbers are there such that the last two digit gro

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VP
Joined: 07 Dec 2014
Posts: 1192
How many four digit numbers are there such that the last two digit gro  [#permalink]

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12 Nov 2018, 23:00
11
00:00

Difficulty:

65% (hard)

Question Stats:

60% (02:28) correct 40% (02:17) wrong based on 82 sessions

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How many four digit numbers are there such that the last two digit grouping is three times the first two digit grouping?

A. 12
B. 18
C. 24
D. 30
E. 36
Math Expert
Joined: 02 Aug 2009
Posts: 7684
Re: How many four digit numbers are there such that the last two digit gro  [#permalink]

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12 Nov 2018, 23:20
1
3
gracie wrote:
How many four digit numbers are there such that the last two digit grouping is three times the first two digit grouping?

A. 12
B. 18
C. 24
D. 30
E. 36

let number be ABCD
Let us take restrictions on the first digit from left, A - it cannot be greater than 3 as 4_*3 will result in a 3-digit number and it cannot be 0
1) let A be 1, B can be anything from 0 to 9 as even the largest 19*3=57 < 100....so 10 ways
2) let A be 2, B can be anything from 0 to 9 as even the largest 29*3=87 < 100....so 10 ways
3) let A be 3, B can be anything from 0 to 3 as 34*3=102, a 3-digit number and cannot be equal to CD....so 4 ways

total = 10+10+4=24

C
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Intern
Joined: 10 Dec 2017
Posts: 1
Re: How many four digit numbers are there such that the last two digit gro  [#permalink]

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12 Nov 2018, 23:51
chetan2u wrote:
gracie wrote:
How many four digit numbers are there such that the last two digit grouping is three times the first two digit grouping?

A. 12
B. 18
C. 24
D. 30
E. 36

let number be ABCD
Let us take restrictions on the first digit from left, A - it cannot be greater than 3 as 4_*3 will result in a 3-digit number and it cannot be 0
1) let A be 1, B can be anything from 0 to 9 as even the largest 19*3=57 < 100....so 10 ways
2) let A be 2, B can be anything from 0 to 9 as even the largest 29*3=87 < 100....so 10 ways
3) let A be 3, B can be anything from 0 to 3 as 34*3=102, a 3-digit number and cannot be equal to CD....so 4 ways

total = 10+10+4=24

C

According to me correct choice would be D. 30
In addition to the 24 nos which you explained there are 6 more..

4. Let A be 4-9 and B =0; 4012, 5015, 6018, 7021, 8024, 9027.

Total 10+10+4+6 = 30
Intern
Joined: 09 Oct 2018
Posts: 7
Re: How many four digit numbers are there such that the last two digit gro  [#permalink]

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23 Nov 2018, 03:04
rintumitra

I think it's a meaning problem.

AB=40 does not equal "04" but equals "40". Therefore if AB=40, CD=120, which is not possible since we are talking about 4 digit integers.
Manager
Joined: 08 Jan 2013
Posts: 106
Re: How many four digit numbers are there such that the last two digit gro  [#permalink]

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23 Nov 2018, 19:46
3
Choice C is correct.

Range of first 2 digits can be from 10 to 33, inclusive only as 00-09 is not possible since it's a four digit number and anything above 33 will yield last 2 digits as more than 100. So range of numbers = 33-10+1 = 24.
Intern
Joined: 01 Nov 2018
Posts: 37
How many four digit numbers are there such that the last two digit gro  [#permalink]

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02 Mar 2019, 02:32
gracie wrote:
How many four digit numbers are there such that the last two digit grouping is three times the first two digit grouping?

A. 12
B. 18
C. 24
D. 30
E. 36

Ans

Let the no be ABCD, Such that

AB=3CD

the no will start from 1030, 1133, 1236....

so CD will be in AP with difference = 3, the last digit can be 99

so, putting it in the AP equation

99=30+(n-1)3
n= 24

Hence the ans is 24!
How many four digit numbers are there such that the last two digit gro   [#permalink] 02 Mar 2019, 02:32
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