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

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Difficulty:   65% (hard)

Question Stats: 60% (02:01) correct 40% (01:51) wrong based on 442 sessions

### HideShow timer Statistics 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.

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Originally posted by honchos on 17 Jun 2014, 12:28.
Last edited by Bunuel on 17 Jun 2014, 12:32, edited 1 time in total.
Edited the question
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Re: If a and b are positive integers, what is the units digit of  [#permalink]

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10
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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GMAT 1: 650 Q50 V28 Re: If a and b are positive integers, what is the units digit of  [#permalink]

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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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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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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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1
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.
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Re: If a and b are positive integers, what is the units digit of  [#permalink]

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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.

Given : positive integers a and b
DS: units digit of b?

Statement 1 : b = 1.25 a = (5/4)a
So a is multiple of 4 and b is a multiple of 5
a= 4, b =5
a=8, b=10
a=12, b=15
a=16, b= 20

So, unit's digit of b is either 0 or 5
NOT SUFFICIENT

Statement 2 : Lets say the resultant value is c. So c = 0.5b and c is not an integer.
So, c must be an odd integer. Unit's digit can be 1,3,5,7,9
NOT SUFFICIENT

Combined : Unit's digit = 5
SUFFICIENT
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Re: If a and b are positive integers, what is the units digit of  [#permalink]

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shashankism wrote:
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.

Given : positive integers a and b
DS: units digit of b?

Statement 1 : b = 1.25 a = (5/4)a
So a is multiple of 4 and b is a multiple of 5
a= 4, b =5
a=8, b=10
a=12, b=15
a=16, b= 20

So, unit's digit of b is either 0 or 5
NOT SUFFICIENT

Statement 2 : Lets say the resultant value is c. So c = 0.5b and c is not an integer.
So, c must be an odd integer. Unit's digit can be 1,3,5,7,9
NOT SUFFICIENT

Combined : Unit's digit = 5
SUFFICIENT

Do you mean that "b" must be an odd integer? Typo.
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Re: If a and b are positive integers, what is the units digit of  [#permalink]

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_________________ Re: If a and b are positive integers, what is the units digit of   [#permalink] 06 Apr 2019, 13:17
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