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If the positive integer b is 5% greater than the positive in

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If the positive integer b is 5% greater than the positive in  [#permalink]

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New post Updated on: 12 Jan 2014, 19:40
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If the positive integer b is 5% greater than the positive integer a, which of the following expressions must be equal to an integer?

I. b/3
II. b/5
III. b/7

A. None
B. II only
C. I and II only
D. I and III only
E. II and III only

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Originally posted by HarveyS on 12 Jan 2014, 16:53.
Last edited by HarveyS on 12 Jan 2014, 19:40, edited 2 times in total.
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Re: If the positive integer b is 5% greater than the positive in  [#permalink]

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New post 12 Jan 2014, 18:07
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Mountain14 wrote:
If the positive integer b is 5% greater than the positive integer a, which of the following expressions must be equal to an integer?

I. b/3
II. b/5
III. b/7

A.None
B.II only
C.I and II only
D.I and III only
E.II and III only


OA after some discussion


The positive integer b is 5% greater than the positive integer a --> \(b=1.05a\) --> \(b=\frac{21}{20}a\) --> \(\frac{b}{a}=\frac{21}{20}\) --> b is a multiple of 21 (and a is a multiple of 20). Therefore b/3 and b/7 will be equal to an integer.

Answer: D.

P.S. OA must be indicated from the beginning.
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Re: If the positive integer b is 5% greater than the positive in  [#permalink]

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New post 12 Jan 2014, 18:09
I would pick D

b=a(1+(5/100))
b=a+(a/20)

looks like b will be comprised of a positive multiple of 20 + the multiple

b = a + (20a)
b=21a

I believe this makes b positive multiple of 21, so it will have a (7)(3) in its factors.
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Re: If the positive integer b is 5% greater than the positive in  [#permalink]

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New post 14 Mar 2016, 06:07
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Re: If the positive integer b is 5% greater than the positive in  [#permalink]

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New post 03 Apr 2016, 04:15
Chiragjordan wrote:
Here B=21A/20
so B/3 = integer
b/7 too
but not b/5
hence D



To say that B/3 is an integer, what did you do? did you substitute 21a/20 in B/3?

I am close to understand the process but I feel I am missing one step.

Thanks
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Re: If the positive integer b is 5% greater than the positive in  [#permalink]

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New post 25 Jun 2016, 08:23
Bunuel wrote:
Mountain14 wrote:
If the positive integer b is 5% greater than the positive integer a, which of the following expressions must be equal to an integer?

I. b/3
II. b/5
III. b/7

A.None
B.II only
C.I and II only
D.I and III only
E.II and III only


OA after some discussion


The positive integer b is 5% greater than the positive integer a --> \(b=1.05a\) --> \(b=\frac{21}{20}a\) --> \(\frac{b}{a}=\frac{21}{20}\) --> b is a multiple of 21 (and a is a multiple of 20). Therefore b/3 and b/7 will be equal to an integer.

Answer: D.

P.S. OA must be indicated from the beginning.


Hi Bunuel,

I have a doubt, though I understood the process. I prefer working with numbers instead of using equations.

So for this question my approach was to work with distant numbers

i.e a=10 and b=10.5 - 1
and a=100 b =105 - 2

In case 1, b/3 or b/5 or b/7 satisfies.
In case 2, All three do.

As this was an always true question, I went with Choice A i.e None.

Why does working with numbers does not work here, and how to distinguish questions where we should and should not use numbers.

Your guidance will really be appreciated.

TIA :)
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Re: If the positive integer b is 5% greater than the positive in  [#permalink]

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New post 25 Jun 2016, 09:26
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Mountain14 wrote:
If the positive integer b is 5% greater than the positive integer a, which of the following expressions must be equal to an integer?

I. b/3
II. b/5
III. b/7

A. None
B. II only
C. I and II only
D. I and III only
E. II and III only


Plug in some number -

a = 100 , b = 105

Here all the options ( I ) , ( II ) & ( III ) will produce integers

Plug in some diff number -

a = 120, b = 126

Here we can get an integer with options ( I ) & ( III )

Plug in some diff number -

a = 140 , b = 147

Here we can get an integer with options ( I ) & ( III )

So you find options ( I ) & ( III ) common in all the values, so answer must be (D)


believer700 wrote:
Why does working with numbers does not work here, and how to distinguish questions where we should and should not use numbers.


Working with numbers works fine here but you will need to try different values before concluding an answer...

Hope this helps !!

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Re: If the positive integer b is 5% greater than the positive in  [#permalink]

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New post 26 Jun 2016, 00:48
The smallest a has to be 20, in which case b is 21. 20 is the smallest value of a because b-a, or 5% of a, has to be a positive integer, and the smallest value of a positive integer is 1.

B is obviously divisible by 3 and 7 but not 5.

Answer choice D.
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Re: If the positive integer b is 5% greater than the positive in  [#permalink]

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New post 16 Aug 2017, 07:26
I am confused. From where did u get 1. Plz help. Thanks
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Re: If the positive integer b is 5% greater than the positive in  [#permalink]

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New post 16 Aug 2017, 07:27
I am confused. From where did u get 1. Plz help. Thanks
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Re: If the positive integer b is 5% greater than the positive in  [#permalink]

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New post 17 Aug 2017, 07:36
karishmajain06 wrote:
I am confused. From where did u get 1. Plz help. Thanks


Hello,

All he saying is that least possible difference of a and b(20& 21 least possible value for a and b provided both are +ve integer and b is 5% more than a) i.e. b-a = 21-20 = 1.

Hope it helps

Thanks
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Re: If the positive integer b is 5% greater than the positive in  [#permalink]

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New post 17 Aug 2017, 07:59
b = a + 5/100 * a
b= 21a/20
a = b*20/21
b is a multiple of 21, hence also multiple of 3,7 therefore D is correct.
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Re: If the positive integer b is 5% greater than the positive in &nbs [#permalink] 17 Aug 2017, 07:59
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