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How many numbers between 1 and 200, inclusive, have a 2 in the units

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How many numbers between 1 and 200, inclusive, have a 2 in the units  [#permalink]

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New post 11 Feb 2019, 01:44
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[GMAT math practice question]

How many numbers between \(1\) and \(200\), inclusive, have a \(2\) in the units place and are divisible by \(4\)?

A. 8
B. 9
C. 10
D. 11
E. 12

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Re: How many numbers between 1 and 200, inclusive, have a 2 in the units  [#permalink]

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New post 11 Feb 2019, 03:21
MathRevolution wrote:
[GMAT math practice question]

How many numbers between \(1\) and \(200\), inclusive, have a \(2\) in the units place and are divisible by \(4\)?

\(A. 8\)
\(B. 9\)
\(C. 10\)
\([m]D. 11\)
E. 12[/m]



Hi...

The property of divisibility by 4 is that the last two digits are divisible by 4..
Now if the number is x2, x has to be an odd number for being divisible by 4, so x can take any of 5 odd numbers.
Alsi the hundreds digit could be 0 or 1 that is 0x2 or 1x2, so 2 ways

Total 2*5=10

C

OA is wrong as A is not the answer
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Re: How many numbers between 1 and 200, inclusive, have a 2 in the units  [#permalink]

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New post 11 Feb 2019, 03:53
MathRevolution wrote:
[GMAT math practice question]

How many numbers between \(1\) and \(200\), inclusive, have a \(2\) in the units place and are divisible by \(4\)?

\(A. 8\)
\(B. 9\)
\(C. 10\)
\([m]D. 11\)
E. 12[/m]


Just see the series
12,32,52...192

There will be 10 numbers

Ans:C
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Re: How many numbers between 1 and 200, inclusive, have a 2 in the units  [#permalink]

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New post 11 Feb 2019, 05:38
How is A the right answer... From 1 to 100 there are 5 multiples of 4 which have 2 in its units place ( 12,32,52,72,92).
The same repeats in 100-200 ( 112,132,152,172,192)

Therefore there are 10 such numbers.... Option c must be the right answer.

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Re: How many numbers between 1 and 200, inclusive, have a 2 in the units  [#permalink]

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New post Updated on: 12 Feb 2019, 04:43
MathRevolution wrote:
[GMAT math practice question]

How many numbers between \(1\) and \(200\), inclusive, have a \(2\) in the units place and are divisible by \(4\)?

\(A. 8\)
\(B. 9\)
\(C. 10\)
\([m]D. 11\)
E. 12[/m]



total integers divisible by 4 from 1 to 200 = 50
and unit digit of 2 would come when 4 is multiplied by 3 or 8
so
we can have two set of digit ranges ( 3,13,23,33,43) and ( 8,18,28,38,48)

total = 10
IMO C
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Originally posted by Archit3110 on 12 Feb 2019, 04:32.
Last edited by Archit3110 on 12 Feb 2019, 04:43, edited 1 time in total.
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Re: How many numbers between 1 and 200, inclusive, have a 2 in the units  [#permalink]

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New post 12 Feb 2019, 04:42
MathRevolution wrote:
[GMAT math practice question]

How many numbers between \(1\) and \(200\), inclusive, have a \(2\) in the units place and are divisible by \(4\)?

\(A. 8\)
\(B. 9\)
\(C. 10\)
\([m]D. 11\)
E. 12[/m]


There will be a difference of 20 among the cases which have a \(2\) in the units place and are divisible by \(4\)

12 ,32,52,72,92,112,132,152,172,192

C
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Re: How many numbers between 1 and 200, inclusive, have a 2 in the units  [#permalink]

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New post 13 Feb 2019, 00:54
=>

In order for a number with 2 in the units place to be divisible by 4, the last two digits must be one of 12, 32, 52, 72 and 92.
Thus, the numbers between 1 and 200, inclusive, satisfying this property are
12, 32, 52, 72, 92, 112, 132, 152 and 172.

There are 8 such numbers. Therefore, A is the answer.
Answer: A
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Re: How many numbers between 1 and 200, inclusive, have a 2 in the units   [#permalink] 13 Feb 2019, 00:54
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