If a and b are positive integers, what is the units digit of : GMAT Data Sufficiency (DS)
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# If a and b are positive integers, what is the units digit of

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If a and b are positive integers, what is the units digit of [#permalink]

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17 Jun 2014, 11:28
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If a and b are positive integers, what is the units digit of b ?

(1) b is 25% greater than a.

(2) If b is decreased by 50%, the result is not an integer.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 Jun 2014, 11:32, edited 1 time in total.
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Re: If a and b are positive integers, what is the units digit of [#permalink]

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17 Jun 2014, 11:36
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If a and b are positive integers, what is the units digit of b ?

(1) b is 25% greater than a --> b=1.25a --> b/a = 5/4 --> b is a multiple of 5. So, the units digit of b could be 0 as well as 5. Not sufficient.

(2) If b is decreased by 50%, the result is not an integer --> b/2 is not an integer --> b is not even. Not sufficient.

(1)+(2) Since b is not even, then its units digit cannot be 0, thus from (1) its units digit must be 5. Sufficient.

Hope it's clear.
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Re: If a and b are positive integers, what is the units digit of [#permalink]

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18 Jun 2014, 06:14
dont recollect seeing this question in OG ..
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Re: If a and b are positive integers, what is the units digit of [#permalink]

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28 Jul 2015, 13:01
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Re: If a and b are positive integers, what is the units digit of [#permalink]

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03 Aug 2015, 08:55
Hi Bunuel,

I think it should be A as the question stem states that a & b are positive integers, ruling out the possibility of b being 0.

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If a and b are positive integers, what is the units digit of [#permalink]

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03 Aug 2015, 09:14
kakshay108@gmail.com wrote:
Hi Bunuel,

I think it should be A as the question stem states that a & b are positive integers, ruling out the possibility of b being 0.

Not really. Positive integers can also include numbers such as 10, 20, 35 , 77 or even 1000. Having a ,b POSITIVE INTEGERS only means that the selected integers are >0 NOT that their unit's digit is 0 (this may or may not be true as shown below).

Per statement 1, b = 1.25 a

This statement can not be sufficient as you do not know about a.

Take 2 cases:

a= 4, b = 5, units digit = 5

a =16, b = 20, unit's digit = 0 . Hence you get 2 different answers. Thus this statement is not sufficient.
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Re: If a and b are positive integers, what is the units digit of [#permalink]

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17 Sep 2015, 19:50
kakshay108@gmail.com wrote:
Hi Bunuel,

I think it should be A as the question stem states that a & b are positive integers, ruling out the possibility of b being 0.

Bunuel has mentioned that "the units digit of b could be 0"...he is not saying b is 0..Hope this clears your doubt.
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Re: If a and b are positive integers, what is the units digit of [#permalink]

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14 Apr 2016, 17:24
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honchos wrote:
If a and b are positive integers, what is the units digit of b ?

(1) b is 25% greater than a.

(2) If b is decreased by 50%, the result is not an integer.

1. b=5a/4
so a must be a multiple of 4, and b a multiple of 5.
a=4, b=5. a=8, b=10, 2 options, not sufficient.

2. b/2 = non-integer. so b is odd.

1+2. b is odd, and b is a multiple of 5.
5, 15, 25, 35, 45, etc. so always b has units digit 5.
Re: If a and b are positive integers, what is the units digit of   [#permalink] 14 Apr 2016, 17:24
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